A series of codons in part of a messenger RNA (mRNA) molecule. Each codon consists of three nucleotides, usually corresponding to a single amino acid. The nucleotides are abbreviated with the letters A, U, G and C. This is mRNA, which uses U (uracil). DNA uses T (thymine) instead. This mRNA molecule will instruct a ribosome to synthesize a protein according to this code.
The genetic code is the set of rules used by living cells to translate information encoded within genetic material (DNA or RNA sequences of nucleotide triplets, or codons) into proteins. Translation is accomplished by the ribosome, which links proteinogenic amino acids in an order specified by messenger RNA (mRNA), using transfer RNA (tRNA) molecules to carry amino acids and to read the mRNA three nucleotides at a time. The genetic code is highly similar among all organisms and can be expressed in a simple table with 64 entries.
The codons specify which amino acid will be added next during protein biosynthesis. With some exceptions, a three-nucleotide codon in a nucleic acid sequence specifies a single amino acid. The vast majority of genes are encoded with a single scheme (see the RNA codon table). That scheme is often referred to as the canonical or standard genetic code, or simply the genetic code, though variant codes (such as in mitochondria) exist.
Efforts to understand how proteins are encoded began after DNA's structure was discovered in 1953. The key discoverers, English biophysicist Francis Crick and American biologist James Watson, working together at the Cavendish Laboratory of the University of Cambridge, hypothesied that information flows from DNA and that there is a link between DNA and proteins. Soviet-American physicist George Gamow was the first to give a workable scheme for protein synthesis from DNA.
He postulated that sets of three bases (triplets) must be employed to
encode the 20 standard amino acids used by living cells to build
proteins, which would allow a maximum of 43 = 64 amino acids. He named this DNA–protein interaction (the original genetic code) as the "diamond code".
In 1954, Gamow created an informal scientific organisation the RNA Tie Club, as suggested by Watson, for scientists of different persuasions who were interested in how proteins were synthesised
from genes. However, the club could have only 20 permanent members to
represent each of the 20 amino acids; and four additional honorary
members to represent the four nucleotides of DNA.
The first scientific contribution of the club, later recorded as
"one of the most important unpublished articles in the history of
science" and "the most famous unpublished paper in the annals of molecular biology",
was made by Crick. Crick presented a type-written paper titled "On
Degenerate Templates and the Adaptor Hypothesis: A Note for the RNA Tie
Club"
to the members of the club in January 1955, which "totally changed the
way we thought about protein synthesis", as Watson recalled.
The hypothesis states that the triplet code was not passed on to amino
acids as Gamow thought, but carried by a different molecule, an adaptor,
that interacts with amino acids. The adaptor was later identified as tRNA.
Marshall Nirenberg and Heinrich J. Matthaei were the first to reveal the nature of a codon in 1961. They used a cell-free system to translate a poly-uracil RNA sequence (i.e., UUUUU...) and discovered that the polypeptide that they had synthesized consisted of only the amino acid phenylalanine. They thereby deduced that the codon UUU specified the amino acid phenylalanine.
This was followed by experiments in Severo Ochoa's laboratory that demonstrated that the poly-adenine RNA sequence (AAAAA...) coded for the polypeptide poly-lysine and that the poly-cytosine RNA sequence (CCCCC...) coded for the polypeptide poly-proline. Therefore, the codon AAA specified the amino acid lysine, and the codon CCC specified the amino acid proline. Using various copolymers most of the remaining codons were then determined.
Subsequent work by Har Gobind Khorana identified the rest of the genetic code. Shortly thereafter, Robert W. Holley determined the structure of transfer RNA
(tRNA), the adapter molecule that facilitates the process of
translating RNA into protein. This work was based upon Ochoa's earlier
studies, yielding the latter the Nobel Prize in Physiology or Medicine in 1959 for work on the enzymology of RNA synthesis.
Extending this work, Nirenberg and Philip Leder revealed the code's triplet nature and deciphered its codons. In these experiments, various combinations of mRNA were passed through a filter that contained ribosomes, the components of cells that translate
RNA into protein. Unique triplets promoted the binding of specific
tRNAs to the ribosome. Leder and Nirenberg were able to determine the
sequences of 54 out of 64 codons in their experiments. Khorana, Holley and Nirenberg received the 1968 Nobel for their work.
The three stop codons were named by discoverers Richard Epstein
and Charles Steinberg. "Amber" was named after their friend Harris
Bernstein, whose last name means "amber" in German. The other two stop codons were named "ochre" and "opal" in order to keep the "color names" theme.
In a broad academic audience, the concept of the evolution of the
genetic code from the original and ambiguous genetic code to a
well-defined ("frozen") code with the repertoire of 20 (+2) canonical
amino acids is widely accepted.
However, there are different opinions, concepts, approaches and ideas,
which is the best way to change it experimentally. Even models are
proposed that predict "entry points" for synthetic amino acid invasion
of the genetic code.
Since 2001, 40 non-natural amino acids have been added into
proteins by creating a unique codon (recoding) and a corresponding
transfer-RNA:aminoacyl – tRNA-synthetase pair to encode it with diverse
physicochemical and biological properties in order to be used as a tool
to exploring protein structure and function or to create novel or enhanced proteins.
H. Murakami and M. Sisido extended some codons to have four and five bases. Steven A. Benner constructed a functional 65th (in vivo) codon.
In 2015 N. Budisa, D. Söll and co-workers reported the full substitution of all 20,899 tryptophan residues (UGG codons) with unnatural thienopyrrole-alanine in the genetic code of the bacterium Escherichia coli.
In 2016 the first stable semisynthetic organism was created. It
was a (single cell) bacterium with two synthetic bases (called X and Y).
The bases survived cell division.
In 2017, researchers in South Korea reported that they had
engineered a mouse with an extended genetic code that can produce
proteins with unnatural amino acids.
In May 2019, researchers reported the creation of a new "Syn61" strain of the bacteriumEscherichia coli. This strain has a fully synthetic
genome that is refactored (all overlaps expanded), recoded (removing
the use of three out of 64 codons completely), and further modified to
remove the now unnecessary tRNAs and release factors. It is fully viable
and grows 1.6× slower than its wild-type counterpart "MDS42".
Features
Reading frames in the DNA sequence of a region of the human mitochondrial genome coding for the genes MT-ATP8 and MT-ATP6 (in black: positions 8,525 to 8,580 in the sequence accession NC_012920).
There are three possible reading frames in the 5' → 3' forward
direction, starting on the first (+1), second (+2) and third position
(+3). For each codon (square brackets), the amino acid is given by the vertebrate mitochondrial code, either in the +1 frame for MT-ATP8 (in red) or in the +3 frame for MT-ATP6 (in blue). The MT-ATP8 genes terminates with the TAG stop codon (red dot) in the +1 frame. The MT-ATP6 gene starts with the ATG codon (blue circle for the M amino acid) in the +3 frame.
Reading frame
A
reading frame is defined by the initial triplet of nucleotides from
which translation starts. It sets the frame for a run of successive,
non-overlapping codons, which is known as an "open reading frame"
(ORF). For example, the string 5'-AAATGAACG-3' (see figure), if read
from the first position, contains the codons AAA, TGA, and ACG ; if read
from the second position, it contains the codons AAT and GAA ; and if
read from the third position, it contains the codons ATG and AAC. Every
sequence can, thus, be read in its 5' → 3' direction in three reading frames,
each producing a possibly distinct amino acid sequence: in the given
example, Lys (K)-Trp (W)-Thr (T), Asn (N)-Glu (E), or Met (M)-Asn (N),
respectively (when translating with the vertebrate mitochondrial code).
When DNA is double-stranded, six possible reading frames are defined, three in the forward orientation on one strand and three reverse on the opposite strand. Protein-coding frames are defined by a start codon, usually the first AUG (ATG) codon in the RNA (DNA) sequence.
Translation starts with a chain-initiation codon or start codon. The start codon alone is not sufficient to begin the process. Nearby sequences such as the Shine-Dalgarno sequence in E. coli and initiation factors are also required to start translation. The most common start codon is AUG, which is read as methionine or as formylmethionine
(in bacteria, mitochondria, and plastids). Alternative start codons
depending on the organism include "GUG" or "UUG"; these codons normally
represent valine and leucine, respectively, but as start codons they are translated as methionine or formylmethionine.
The three stop codons have names: UAG is amber, UGA is opal (sometimes also called umber), and UAA is ochre.
Stop codons are also called "termination" or "nonsense" codons. They
signal release of the nascent polypeptide from the ribosome because no
cognate tRNA has anticodons complementary to these stop signals,
allowing a release factor to bind to the ribosome instead.
Effect of mutations
Examples of notable mutations that can occur in humans
During the process of DNA replication, errors occasionally occur in the polymerization of the second strand. These errors, mutations, can affect an organism's phenotype,
especially if they occur within the protein coding sequence of a gene.
Error rates are typically 1 error in every 10–100 million bases—due to
the "proofreading" ability of DNA polymerases.
Missense mutations and nonsense mutations are examples of point mutations that can cause genetic diseases such as sickle-cell disease and thalassemia respectively.
Clinically important missense mutations generally change the properties
of the coded amino acid residue among basic, acidic, polar or non-polar
states, whereas nonsense mutations result in a stop codon.
Mutations that disrupt the reading frame sequence by indels (insertions or deletions) of a non-multiple of 3 nucleotide bases are known as frameshift mutations. These mutations usually result in a completely different translation from the original, and likely cause a stop codon to be read, which truncates the protein. These mutations may impair the protein's function and are thus rare in in vivo
protein-coding sequences. One reason inheritance of frameshift
mutations is rare is that, if the protein being translated is essential
for growth under the selective pressures the organism faces, absence of a
functional protein may cause death before the organism becomes viable. Frameshift mutations may result in severe genetic diseases such as Tay–Sachs disease.
Although most mutations that change protein sequences are harmful or neutral, some mutations have benefits. These mutations may enable the mutant organism to withstand particular environmental stresses better than wild type organisms, or reproduce more quickly. In these cases a mutation will tend to become more common in a population through natural selection. Viruses that use RNA as their genetic material have rapid mutation rates, which can be an advantage, since these viruses thereby evolve rapidly, and thus evade the immune system defensive responses. In large populations of asexually reproducing organisms, for example, E. coli, multiple beneficial mutations may co-occur. This phenomenon is called clonal interference and causes competition among the mutations.
Grouping of codons by amino acid residue molar volume and hydropathicity. A more detailed version is available.Axes 1, 2, 3 are the first, second, and third positions in the codon. The 20 amino acids and stop codons (X) are shown in single letter code.
Degeneracy is the redundancy of the genetic code. This term was given
by Bernfield and Nirenberg. The genetic code has redundancy but no
ambiguity (see the codon tables below for the full correlation). For example, although codons GAA and GAG both specify glutamic acid
(redundancy), neither specifies another amino acid (no ambiguity). The
codons encoding one amino acid may differ in any of their three
positions. For example, the amino acid leucine is specified by YUR or CUN (UUA, UUG, CUU, CUC, CUA, or CUG) codons (difference in the first or third position indicated using IUPAC notation), while the amino acid serine is specified by UCN or AGY (UCA, UCG, UCC, UCU, AGU, or AGC) codons (difference in the first, second, or third position).
A practical consequence of redundancy is that errors in the third
position of the triplet codon cause only a silent mutation or an error
that would not affect the protein because the hydrophilicity or hydrophobicity
is maintained by equivalent substitution of amino acids; for example, a
codon of NUN (where N = any nucleotide) tends to code for hydrophobic
amino acids. NCN yields amino acid residues that are small in size and
moderate in hydropathicity;
NAN encodes average size hydrophilic residues. The genetic code is so
well-structured for hydropathicity that a mathematical analysis (Singular Value Decomposition)
of 12 variables (4 nucleotides x 3 positions) yields a remarkable
correlation (C = 0.95) for predicting the hydropathicity of the encoded
amino acid directly from the triplet nucleotide sequence, without translation.
Note in the table, below, eight amino acids are not affected at all by
mutations at the third position of the codon, whereas in the figure
above, a mutation at the second position is likely to cause a radical
change in the physicochemical properties of the encoded amino acid.
Nevertheless, changes in the first position of the codons are more
important than changes in the second position on a global scale.
The reason may be that charge reversal (from a positive to a negative
charge or vice versa) can only occur upon mutations in the first
position of certain codons, but not upon changes in the second position
of any codon. Such charge reversal may have dramatic consequences for
the structure or function of a protein. This aspect may have been
largely underestimated by previous studies.
Codon usage bias
The frequency of codons, also known as codon usage bias, can vary from species to species with functional implications for the control of translation.
The codon varies by organism; for example, most common proline codon in
E. coli is CCG, whereas in humans this is the least used proline codon.
In
some proteins, non-standard amino acids are substituted for standard
stop codons, depending on associated signal sequences in the messenger
RNA. For example, UGA can code for selenocysteine and UAG can code for pyrrolysine. Selenocysteine came to be seen as the 21st amino acid, and pyrrolysine as the 22nd. Unlike selenocysteine, pyrrolysine-encoded UAG is translated with the participation of a dedicated aminoacyl-tRNA synthetase. Both selenocysteine and pyrrolysine may be present in the same organism. Although the genetic code is normally fixed in an organism, the achaeal prokaryote Acetohalobium arabaticum can expand its genetic code from 20 to 21 amino acids (by including pyrrolysine) under different conditions of growth.
Genetic code logo of the Globobulimina pseudospinescens mitochondrial genome by FACIL.
The logo shows the 64 codons from left to right, predicted alternatives
in red (relative to the standard genetic code). Red line: stop codons.
The height of each amino acid in the stack shows how often it is aligned
to the codon in homologous protein domains. The stack height indicates
the support for the prediction.
There was originally a simple and widely accepted argument that the
genetic code should be universal: namely, that any variation in the
genetic code would be lethal to the organism (although Crick had stated
that viruses were an exception). This is known as the "frozen accident"
argument for the universality of the genetic code. However, in his
seminal paper on the origins of the genetic code in 1968, Francis Crick
still stated that the universality of the genetic code in all organisms
was an unproven assumption, and was probably not true in some instances.
He predicted that "The code is universal (the same in all organisms) or
nearly so". The first variation was discovered in 1979, by researchers studying human mitochondrial genes. Many slight variants were discovered thereafter, including various alternative mitochondrial codes. These minor variants for example involve translation of the codon UGA as tryptophan in Mycoplasma species, and translation of CUG as a serine rather than leucine in yeasts of the "CTG clade" (such as Candida albicans).
Because viruses must use the same genetic code as their hosts,
modifications to the standard genetic code could interfere with viral
protein synthesis or functioning. However, viruses such as totiviruses have adapted to the host's genetic code modification. In bacteria and archaea, GUG and UUG are common start codons. In rare cases, certain proteins may use alternative start codons.
Surprisingly, variations in the interpretation of the genetic code exist
also in human nuclear-encoded genes: In 2016, researchers studying the
translation of malate dehydrogenase found that in about 4% of the mRNAs
encoding this enzyme the stop codon is naturally used to encode the
amino acids tryptophan and arginine. This type of recoding is induced by a high-readthrough stop codon context and it is referred to as functional translational readthrough.
Despite these differences, all known naturally occurring codes
are very similar. The coding mechanism is the same for all organisms:
three-base codons, tRNA, ribosomes, single direction reading and translating single codons into single amino acids.
The most extreme variations occur in certain ciliates where the meaning
of stop codons depends on their position within mRNA. When close to the
3' end they act as terminators while in internal positions they either
code for amino acids as in Condylostoma magnum or trigger ribosomal frameshifting as in Euplotes.
The origins and variation of the genetic code, including the
mechanisms behind the evolvability of the genetic code, have been widely
studied, and some studies have been done experimentally evolving the genetic code of some organisms.
Inference
Variant
genetic codes used by an organism can be inferred by identifying highly
conserved genes encoded in that genome, and comparing its codon usage
to the amino acids in homologous proteins of other organisms. For
example, the program FACIL infers a genetic code by searching which
amino acids in homologous protein domains are most often aligned to
every codon. The resulting amino acid (or stop codon) probabilities for
each codon are displayed in a genetic code logo.
As of January 2022, the most complete survey of genetic codes is
done by Shulgina and Eddy, who screened 250,000 prokaryotic genomes
using their Codetta tool. This tool uses a similar approach to FACIL
with a larger Pfam
database. Despite the NCBI already providing 33 translation tables, the
authors were able to find new 5 genetic code variations (corroborated
by tRNA mutations) and correct several misattributions.
Origin
The genetic code is a key part of the history of life, according to one version of which self-replicating RNA molecules preceded life as we know it. This is the RNA world hypothesis. Under this hypothesis, any model for the emergence of the genetic code is intimately related to a model of the transfer from ribozymes
(RNA enzymes) to proteins as the principal enzymes in cells. In line
with the RNA world hypothesis, transfer RNA molecules appear to have
evolved before modern aminoacyl-tRNA synthetases, so the latter cannot be part of the explanation of its patterns.
A hypothetical randomly evolved genetic code further motivates a
biochemical or evolutionary model for its origin. If amino acids were
randomly assigned to triplet codons, there would be 1.5 × 1084 possible genetic codes.
This number is found by calculating the number of ways that 21 items
(20 amino acids plus one stop) can be placed in 64 bins, wherein each
item is used at least once. However, the distribution of codon assignments in the genetic code is nonrandom. In particular, the genetic code clusters certain amino acid assignments.
Amino acids that share the same biosynthetic pathway tend to have
the same first base in their codons. This could be an evolutionary
relic of an early, simpler genetic code with fewer amino acids that
later evolved to code a larger set of amino acids.
It could also reflect steric and chemical properties that had another
effect on the codon during its evolution. Amino acids with similar
physical properties also tend to have similar codons, reducing the problems caused by point mutations and mistranslations.
Given the non-random genetic triplet coding scheme, a tenable
hypothesis for the origin of genetic code could address multiple aspects
of the codon table, such as absence of codons for D-amino acids,
secondary codon patterns for some amino acids, confinement of synonymous
positions to third position, the small set of only 20 amino acids
(instead of a number approaching 64), and the relation of stop codon
patterns to amino acid coding patterns.
Three main hypotheses address the origin of the genetic code. Many models belong to one of them or to a hybrid:
Random freeze: the genetic code was randomly created. For example, early tRNA-like
ribozymes may have had different affinities for amino acids, with
codons emerging from another part of the ribozyme that exhibited random
variability. Once enough peptides were coded for, any major random change in the genetic code would have been lethal; hence it became "frozen".
Stereochemical affinity: the genetic code is a result of a high
affinity between each amino acid and its codon or anti-codon; the latter
option implies that pre-tRNA molecules matched their corresponding
amino acids by this affinity. Later during evolution, this matching was
gradually replaced with matching by aminoacyl-tRNA synthetases.
Optimality: the genetic code continued to evolve after its initial creation, so that the current code maximizes some fitness function, usually some kind of error minimization.
Hypotheses have addressed a variety of scenarios:
Chemical principles govern specific RNA interaction with amino acids. Experiments with aptamers showed that some amino acids have a selective chemical affinity for their codons. Experiments showed that of 8 amino acids tested, 6 show some RNA triplet-amino acid association.
Biosynthetic expansion. The genetic code grew from a simpler earlier
code through a process of "biosynthetic expansion". Primordial life
"discovered" new amino acids (for example, as by-products of metabolism) and later incorporated some of these into the machinery of genetic coding. Although much circumstantial evidence has been found to suggest that fewer amino acid types were used in the past, precise and detailed hypotheses about which amino acids entered the code in what order are controversial.
However, several studies have suggested that Gly, Ala, Asp, Val, Ser,
Pro, Glu, Leu, Thr may belong to a group of early-addition amino acids,
whereas Cys, Met, Tyr, Trp, His, Phe may belong to a group of
later-addition amino acids.
Natural selection has led to codon assignments of the genetic code that minimize the effects of mutations. A recent hypothesis
suggests that the triplet code was derived from codes that used longer
than triplet codons (such as quadruplet codons). Longer than triplet
decoding would increase codon redundancy and would be more error
resistant. This feature could allow accurate decoding absent complex
translational machinery such as the ribosome, such as before cells began making ribosomes.
Information channels: Information-theoretic
approaches model the process of translating the genetic code into
corresponding amino acids as an error-prone information channel.
The inherent noise (that is, the error) in the channel poses the
organism with a fundamental question: how can a genetic code be
constructed to withstand noise while accurately and efficiently translating information? These "rate-distortion" models
suggest that the genetic code originated as a result of the interplay
of the three conflicting evolutionary forces: the needs for diverse
amino acids, for error-tolerance
and for minimal resource cost. The code emerges at a transition when
the mapping of codons to amino acids becomes nonrandom. The code's
emergence is governed by the topology defined by the probable errors and is related to the map coloring problem.
Game theory: Models based on signaling games
combine elements of game theory, natural selection and information
channels. Such models have been used to suggest that the first
polypeptides were likely short and had non-enzymatic function. Game
theoretic models suggested that the organization of RNA strings into
cells may have been necessary to prevent "deceptive" use of the genetic
code, i.e. preventing the ancient equivalent of viruses from
overwhelming the RNA world.
Stop codons: Codons for translational stops are also an interesting
aspect to the problem of the origin of the genetic code. As an example
for addressing stop codon evolution, it has been suggested that the stop
codons are such that they are most likely to terminate translation
early in the case of a frame shift error. In contrast, some stereochemical molecular models explain the origin of stop codons as "unassignable".
Interactions involving electrons with other subatomic particles are of interest in fields such as chemistry and nuclear physics. The Coulomb force interaction between the positive protons within atomic nuclei and the negative electrons without allows the composition of the two known as atoms. Ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the main cause of chemical bonding.
The ancient Greeks noticed that amber attracted small objects when rubbed with fur. Along with lightning, this phenomenon is one of humanity's earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the Neo-Latin term electrica, to refer to those substances with property similar to that of amber which attract small objects after being rubbed. Both electric and electricity are derived from the Latin ēlectrum (also the root of the alloy of the same name), which came from the Greek word for amber, ἤλεκτρον (ēlektron).
Discovery of two kinds of charges
In the early 1700s, French chemist Charles François du Fay
found that if a charged gold-leaf is repulsed by glass rubbed with
silk, then the same charged gold-leaf is attracted by amber rubbed with
wool. From this and other results of similar types of experiments, du
Fay concluded that electricity consists of two electrical fluids, vitreous fluid from glass rubbed with silk and resinous fluid from amber rubbed with wool. These two fluids can neutralize each other when combined. American scientist Ebenezer Kinnersley later also independently reached the same conclusion. A decade later Benjamin Franklin
proposed that electricity was not from different types of electrical
fluid, but a single electrical fluid showing an excess (+) or deficit
(−). He gave them the modern charge nomenclature of positive and negative respectively.
Franklin thought of the charge carrier as being positive, but he did
not correctly identify which situation was a surplus of the charge
carrier, and which situation was a deficit.
Between 1838 and 1851, British natural philosopher Richard Laming developed the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unit electric charges. Beginning in 1846, German physicist Wilhelm Eduard Weber theorized that electricity was composed of positively and negatively charged fluids, and their interaction was governed by the inverse square law. After studying the phenomenon of electrolysis in 1874, Irish physicist George Johnstone Stoney suggested that there existed a "single definite quantity of electricity", the charge of a monovalention. He was able to estimate the value of this elementary charge e by means of Faraday's laws of electrolysis. However, Stoney believed these charges were permanently attached to atoms and could not be removed. In 1881, German physicist Hermann von Helmholtz
argued that both positive and negative charges were divided into
elementary parts, each of which "behaves like atoms of electricity".
Stoney initially coined the term electrolion in 1881. Ten years later, he switched to electron
to describe these elementary charges, writing in 1894: "... an estimate
was made of the actual amount of this most remarkable fundamental unit
of electricity, for which I have since ventured to suggest the name electron". A 1906 proposal to change to electrion failed because Hendrik Lorentz preferred to keep electron. The word electron is a combination of the words electric and ion. The suffix -on which is now used to designate other subatomic particles, such as a proton or neutron, is in turn derived from electron.
Discovery of free electrons outside matter
A beam of electrons deflected by a magnetic field into a circle
While studying electrical conductivity in rarefied gases in 1859, the German physicist Julius Plücker
observed the radiation emitted from the cathode caused phosphorescent
light to appear on the tube wall near the cathode; and the region of the
phosphorescent light could be moved by application of a magnetic field. In 1869, Plücker's student Johann Wilhelm Hittorf
found that a solid body placed in between the cathode and the
phosphorescence would cast a shadow upon the phosphorescent region of
the tube. Hittorf inferred that there are straight rays emitted from
the cathode and that the phosphorescence was caused by the rays striking
the tube walls. In 1876, the German physicist Eugen Goldstein
showed that the rays were emitted perpendicular to the cathode surface,
which distinguished between the rays that were emitted from the cathode
and the incandescent light. Goldstein dubbed the rays cathode rays. Decades of experimental and theoretical research involving cathode rays were important in J. J. Thomson's eventual discovery of electrons.
During the 1870s, the English chemist and physicist Sir William Crookes developed the first cathode-ray tube to have a high vacuum inside.
He then showed in 1874 that the cathode rays can turn a small paddle
wheel when placed in their path. Therefore, he concluded that the rays
carried momentum. Furthermore, by applying a magnetic field, he was able
to deflect the rays, thereby demonstrating that the beam behaved as
though it were negatively charged.
In 1879, he proposed that these properties could be explained by
regarding cathode rays as composed of negatively charged gaseous molecules in a fourth state of matter in which the mean free path of the particles is so long that collisions may be ignored.
The German-born British physicist Arthur Schuster expanded upon Crookes's experiments by placing metal plates parallel to the cathode rays and applying an electric potential between the plates.
The field deflected the rays toward the positively charged plate,
providing further evidence that the rays carried negative charge. By
measuring the amount of deflection for a given electric and magnetic field, in 1890 Schuster was able to estimate the charge-to-mass ratio
of the ray components. However, this produced a value that was more
than a thousand times greater than what was expected, so little credence
was given to his calculations at the time. This is because it was assumed that the charge carriers were much heavier hydrogen or nitrogen atoms. Schuster's estimates would subsequently turn out to be largely correct.
In 1892 Hendrik Lorentz suggested that the mass of these particles (electrons) could be a consequence of their electric charge.
While studying naturally fluorescing minerals in 1896, the French physicist Henri Becquerel discovered that they emitted radiation without any exposure to an external energy source. These radioactive materials became the subject of much interest by scientists, including the New Zealand physicist Ernest Rutherford who discovered they emitted particles. He designated these particles alpha and beta, on the basis of their ability to penetrate matter. In 1900, Becquerel showed that the beta rays emitted by radium could be deflected by an electric field, and that their mass-to-charge ratio was the same as for cathode rays. This evidence strengthened the view that electrons existed as components of atoms.
In 1897, the British physicist J. J. Thomson, with his colleagues John S. Townsend and H. A. Wilson,
performed experiments indicating that cathode rays really were unique
particles, rather than waves, atoms or molecules as was believed
earlier. Thomson made good estimates of both the charge e and the mass m,
finding that cathode ray particles, which he called "corpuscles", had
perhaps one thousandth of the mass of the least massive ion known:
hydrogen. He showed that their charge-to-mass ratio, e/m,
was independent of cathode material. He further showed that the
negatively charged particles produced by radioactive materials, by
heated materials and by illuminated materials were universal. The name electron was adopted for these particles by the scientific community, mainly due to the advocation by G. F. FitzGerald, J. Larmor, and H. A. Lorentz. In the same year Emil Wiechert and Walter Kaufmann
also calculated the e/m ratio but they failed short of interpreting
their results while J. J. Thomson would subsequently in 1899 give
estimates for the electron charge and mass as well: e~6.8×10−10esu and m~3×10−26 g
The electron's charge was more carefully measured by the American physicists Robert Millikan and Harvey Fletcher in their oil-drop experiment
of 1909, the results of which were published in 1911. This experiment
used an electric field to prevent a charged droplet of oil from falling
as a result of gravity. This device could measure the electric charge
from as few as 1–150 ions with an error margin of less than 0.3%.
Comparable experiments had been done earlier by Thomson's team, using clouds of charged water droplets generated by electrolysis, and in 1911 by Abram Ioffe,
who independently obtained the same result as Millikan using charged
microparticles of metals, then published his results in 1913.
However, oil drops were more stable than water drops because of their
slower evaporation rate, and thus more suited to precise experimentation
over longer periods of time.
Around the beginning of the twentieth century, it was found that
under certain conditions a fast-moving charged particle caused a
condensation of supersaturated water vapor along its path. In 1911, Charles Wilson used this principle to devise his cloud chamber so he could photograph the tracks of charged particles, such as fast-moving electrons.
Atomic theory
The Bohr model of the atom, showing states of an electron with energy quantized by the number n. An electron dropping to a lower orbit emits a photon equal to the energy difference between the orbits.
By 1914, experiments by physicists Ernest Rutherford, Henry Moseley, James Franck and Gustav Hertz had largely established the structure of an atom as a dense nucleus of positive charge surrounded by lower-mass electrons. In 1913, Danish physicist Niels Bohr
postulated that electrons resided in quantized energy states, with
their energies determined by the angular momentum of the electron's
orbit about the nucleus. The electrons could move between those states,
or orbits, by the emission or absorption of photons of specific
frequencies. By means of these quantized orbits, he accurately explained
the spectral lines of the hydrogen atom.
However, Bohr's model failed to account for the relative intensities of
the spectral lines and it was unsuccessful in explaining the spectra of
more complex atoms.
Chemical bonds between atoms were explained by Gilbert Newton Lewis, who in 1916 proposed that a covalent bond between two atoms is maintained by a pair of electrons shared between them. Later, in 1927, Walter Heitler and Fritz London gave the full explanation of the electron-pair formation and chemical bonding in terms of quantum mechanics. In 1919, the American chemist Irving Langmuir
elaborated on the Lewis's static model of the atom and suggested that
all electrons were distributed in successive "concentric (nearly)
spherical shells, all of equal thickness".
In turn, he divided the shells into a number of cells each of which
contained one pair of electrons. With this model Langmuir was able to
qualitatively explain the chemical properties of all elements in the periodic table, which were known to largely repeat themselves according to the periodic law.
In 1924, Austrian physicist Wolfgang Pauli
observed that the shell-like structure of the atom could be explained
by a set of four parameters that defined every quantum energy state, as
long as each state was occupied by no more than a single electron. This
prohibition against more than one electron occupying the same quantum
energy state became known as the Pauli exclusion principle.
The physical mechanism to explain the fourth parameter, which had two
distinct possible values, was provided by the Dutch physicists Samuel Goudsmit and George Uhlenbeck.
In 1925, they suggested that an electron, in addition to the angular
momentum of its orbit, possesses an intrinsic angular momentum and magnetic dipole moment.
This is analogous to the rotation of the Earth on its axis as it orbits
the Sun. The intrinsic angular momentum became known as spin, and explained the previously mysterious splitting of spectral lines observed with a high-resolution spectrograph; this phenomenon is known as fine structure splitting.
In his 1924 dissertation Recherches sur la théorie des quanta (Research on Quantum Theory), French physicist Louis de Broglie hypothesized that all matter can be represented as a de Broglie wave in the manner of light. That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment.
The wave-like nature of light is displayed, for example, when a beam of
light is passed through parallel slits thereby creating interference patterns. In 1927, George Paget Thomson
and Alexander Reid discovered the interference effect was produced when
a beam of electrons was passed through thin celluloid foils and later
metal films, and by American physicists Clinton Davisson and Lester Germer by the reflection of electrons from a crystal of nickel.
Alexander Reid, who was Thomson's graduate student, performed the first
experiments but he died soon after in a motorcycle accident and is rarely mentioned.
In quantum mechanics, the behavior of an electron in an atom is described by an orbital,
which is a probability distribution rather than an orbit. In the
figure, the shading indicates the relative probability to "find" the
electron, having the energy corresponding to the given quantum numbers, at that point.
De Broglie's prediction of a wave nature for electrons led Erwin Schrödinger to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, the Schrödinger equation, successfully described how electron waves propagated.
Rather than yielding a solution that determined the location of an
electron over time, this wave equation also could be used to predict the
probability of finding an electron near a position, especially a
position near where the electron was bound in space, for which the
electron wave equations did not change in time. This approach led to a
second formulation of quantum mechanics
(the first by Heisenberg in 1925), and solutions of Schrödinger's
equation, like Heisenberg's, provided derivations of the energy states
of an electron in a hydrogen atom that were equivalent to those that had
been derived first by Bohr in 1913, and that were known to reproduce
the hydrogen spectrum.
Once spin and the interaction between multiple electrons were
describable, quantum mechanics made it possible to predict the
configuration of electrons in atoms with atomic numbers greater than
hydrogen.
In 1928, building on Wolfgang Pauli's work, Paul Dirac produced a model of the electron – the Dirac equation, consistent with relativity theory, by applying relativistic and symmetry considerations to the hamiltonian formulation of the quantum mechanics of the electro-magnetic field.
In order to resolve some problems within his relativistic equation,
Dirac developed in 1930 a model of the vacuum as an infinite sea of
particles with negative energy, later dubbed the Dirac sea. This led him to predict the existence of a positron, the antimatter counterpart of the electron. This particle was discovered in 1932 by Carl Anderson, who proposed calling standard electrons negatrons and using electron as a generic term to describe both the positively and negatively charged variants.
In 1947, Willis Lamb, working in collaboration with graduate student Robert Retherford,
found that certain quantum states of the hydrogen atom, which should
have the same energy, were shifted in relation to each other; the
difference came to be called the Lamb shift. About the same time, Polykarp Kusch, working with Henry M. Foley,
discovered the magnetic moment of the electron is slightly larger than
predicted by Dirac's theory. This small difference was later called anomalous magnetic dipole moment of the electron. This difference was later explained by the theory of quantum electrodynamics, developed by Sin-Itiro Tomonaga, Julian Schwinger and
Richard Feynman in the late 1940s.
Particle accelerators
With the development of the particle accelerator during the first half of the twentieth century, physicists began to delve deeper into the properties of subatomic particles. The first successful attempt to accelerate electrons using electromagnetic induction was made in 1942 by Donald Kerst. His initial betatron reached energies of 2.3 MeV, while subsequent betatrons achieved 300 MeV. In 1947, synchrotron radiation was discovered with a 70 MeV electron synchrotron at General Electric. This radiation was caused by the acceleration of electrons through a magnetic field as they moved near the speed of light.
With a beam energy of 1.5 GeV, the first high-energy
particle collider was ADONE, which began operations in 1968.
This device accelerated electrons and positrons in opposite directions,
effectively doubling the energy of their collision when compared to
striking a static target with an electron. The Large Electron–Positron Collider (LEP) at CERN, which was operational from 1989 to 2000, achieved collision energies of 209 GeV and made important measurements for the Standard Model of particle physics.
Confinement of individual electrons
Individual electrons can now be easily confined in ultra small (L = 20 nm, W = 20 nm) CMOS transistors operated at cryogenic temperature over a range of −269 °C (4 K) to about −258 °C (15 K).
The electron wavefunction spreads in a semiconductor lattice and
negligibly interacts with the valence band electrons, so it can be
treated in the single particle formalism, by replacing its mass with the
effective mass tensor.
Characteristics
Classification
Standard Model of elementary particles. The electron (symbol e) is on the left.
In the Standard Model of particle physics, electrons belong to the group of subatomic particles called leptons, which are believed to be fundamental or elementary particles. Electrons have the lowest mass of any charged lepton (or electrically charged particle of any type) and belong to the first-generation of fundamental particles. The second and third generation contain charged leptons, the muon and the tau, which are identical to the electron in charge, spin and interactions, but are more massive. Leptons differ from the other basic constituent of matter, the quarks, by their lack of strong interaction. All members of the lepton group are fermions because they all have half-odd integer spin; the electron has spin 1/2.
Electrons have an electric charge of −1.602176634×10−19coulombs, which is used as a standard unit of charge for subatomic particles, and is also called the elementary charge.
Within the limits of experimental accuracy, the electron charge is
identical to the charge of a proton, but with the opposite sign. The electron is commonly symbolized by e− , and the positron is symbolized by e+ .
The electron has an intrinsic angular momentum or spin of ħ/2. This property is usually stated by referring to the electron as a spin-1/2 particle. For such particles the spin magnitude is ħ/2, while the result of the measurement of a projection of the spin on any axis can only be ±ħ/2. In addition to spin, the electron has an intrinsic magnetic moment along its spin axis. It is approximately equal to one Bohr magneton, which is a physical constant equal to 9.27400915(23)×10−24joules per tesla. The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known as helicity.
The electron has no known substructure. Nevertheless, in condensed matter physics, spin–charge separation can occur in some materials. In such cases, electrons 'split' into three independent particles, the spinon, the orbiton and the holon
(or chargon). The electron can always be theoretically considered as a
bound state of the three, with the spinon carrying the spin of the
electron, the orbiton carrying the orbital degree of freedom and the
chargon carrying the charge, but in certain conditions they can behave
as independent quasiparticles.
The issue of the radius of the electron is a challenging problem
of modern theoretical physics. The admission of the hypothesis of a
finite radius of the electron is incompatible to the premises of the
theory of relativity. On the other hand, a point-like electron (zero
radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity. Observation of a single electron in a Penning trap suggests the upper limit of the particle's radius to be 10−22 meters.
The upper bound of the electron radius of 10−18 meters can be derived using the uncertainty relation in energy. There is also a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m,
greater than the radius of the proton. However, the terminology comes
from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.
There are elementary particles that spontaneously decay into less massive particles. An example is the muon, with a mean lifetime of 2.2×10−6 seconds, which decays into an electron, a muon neutrino and an electron antineutrino.
The electron, on the other hand, is thought to be stable on theoretical
grounds: the electron is the least massive particle with non-zero
electric charge, so its decay would violate charge conservation. The experimental lower bound for the electron's mean lifetime is 6.6×1028 years, at a 90% confidence level.
The wave-like nature of the electron allows it to pass through
two parallel slits simultaneously, rather than just one slit as would be
the case for a classical particle. In quantum mechanics, the wave-like
property of one particle can be described mathematically as a complex-valued function, the wave function, commonly denoted by the Greek letterpsi (ψ). When the absolute value of this function is squared, it gives the probability that a particle will be observed near a location—a probability density.
Example of an antisymmetric wave function for a quantum state of two identical fermions in a one-dimensional box,
with each horizontal axis corresponding to the position of one
particle. If the particles swap position, the wave function inverts its
sign.
Electrons are identical particles
because they cannot be distinguished from each other by their intrinsic
physical properties. In quantum mechanics, this means that a pair of
interacting electrons must be able to swap positions without an
observable change to the state of the system. The wave function of
fermions, including electrons, is antisymmetric, meaning that it changes
sign when two electrons are swapped; that is, ψ(r1, r2) = −ψ(r2, r1), where the variables r1 and r2
correspond to the first and second electrons, respectively. Since the
absolute value is not changed by a sign swap, this corresponds to equal
probabilities. Bosons, such as the photon, have symmetric wave functions instead.
In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle,
which precludes any two electrons from occupying the same quantum
state. This principle explains many of the properties of electrons. For
example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit.
In a simplified picture, which often tends to give the wrong idea but
may serve to illustrate some aspects, every photon spends some time as a
combination of a virtual electron plus its antiparticle, the virtual
positron, which rapidly annihilate each other shortly thereafter.
The combination of the energy variation needed to create these
particles, and the time during which they exist, fall under the
threshold of detectability expressed by the Heisenberg uncertainty relation, ΔE · Δt ≥ ħ. In effect, the energy needed to create these virtual particles, ΔE, can be "borrowed" from the vacuum for a period of time, Δt, so that their product is no more than the reduced Planck constant, ħ ≈ 6.6×10−16 eV·s. Thus, for a virtual electron, Δt is at most 1.3×10−21 s.
A schematic depiction of virtual electron–positron pairs appearing at random near an electron (at lower left)
While an electron–positron virtual pair is in existence, the Coulomb force from the ambient electric field
surrounding an electron causes a created positron to be attracted to
the original electron, while a created electron experiences a repulsion.
This causes what is called vacuum polarization. In effect, the vacuum behaves like a medium having a dielectric permittivity more than unity.
Thus the effective charge of an electron is actually smaller than its
true value, and the charge decreases with increasing distance from the
electron. This polarization was confirmed experimentally in 1997 using the Japanese TRISTAN particle accelerator. Virtual particles cause a comparable shielding effect for the mass of the electron.
The interaction with virtual particles also explains the small
(about 0.1%) deviation of the intrinsic magnetic moment of the electron
from the Bohr magneton (the anomalous magnetic moment).
The extraordinarily precise agreement of this predicted difference with
the experimentally determined value is viewed as one of the great
achievements of quantum electrodynamics.
The apparent paradox in classical physics of a point particle electron having intrinsic angular momentum and magnetic moment can be explained by the formation of virtual photons
in the electric field generated by the electron. These photons can
heuristically be thought of as causing the electron to shift about in a
jittery fashion (known as zitterbewegung), which results in a net circular motion with precession. This motion produces both the spin and the magnetic moment of the electron. In atoms, this creation of virtual photons explains the Lamb shift observed in spectral lines.
The Compton Wavelength shows that near elementary particles such as the
electron, the uncertainty of the energy allows for the creation of
virtual particles near the electron. This wavelength explains the
"static" of virtual particles around elementary particles at a close
distance.
Interaction
An
electron generates an electric field that exerts an attractive force on
a particle with a positive charge, such as the proton, and a repulsive
force on a particle with a negative charge. The strength of this force
in nonrelativistic approximation is determined by Coulomb's inverse square law. When an electron is in motion, it generates a magnetic field. The Ampère–Maxwell law relates the magnetic field to the mass motion of electrons (the current) with respect to an observer. This property of induction supplies the magnetic field that drives an electric motor. The electromagnetic field of an arbitrary moving charged particle is expressed by the Liénard–Wiechert potentials, which are valid even when the particle's speed is close to that of light (relativistic).
A particle with charge q (at left) is moving with velocity v through a magnetic field B that is oriented toward the viewer. For an electron, q is negative so it follows a curved trajectory toward the top.
When an electron is moving through a magnetic field, it is subject to the Lorentz force that acts perpendicularly to the plane defined by the magnetic field and the electron velocity. This centripetal force causes the electron to follow a helical trajectory through the field at a radius called the gyroradius. The acceleration from this curving motion induces the electron to radiate energy in the form of synchrotron radiation. The energy emission in turn causes a recoil of the electron, known as the Abraham–Lorentz–Dirac Force, which creates a friction that slows the electron. This force is caused by a back-reaction of the electron's own field upon itself.
Here, Bremsstrahlung is produced by an electron e deflected by the electric field of an atomic nucleus. The energy change E2 − E1 determines the frequency f of the emitted photon.
Photons mediate electromagnetic interactions between particles in quantum electrodynamics. An isolated electron at a constant velocity cannot emit or absorb a real photon; doing so would violate conservation of energy and momentum.
Instead, virtual photons can transfer momentum between two charged
particles. This exchange of virtual photons, for example, generates the
Coulomb force.
Energy emission can occur when a moving electron is deflected by a
charged particle, such as a proton. The deceleration of the electron
results in the emission of Bremsstrahlung radiation.
An inelastic collision between a photon (light) and a solitary (free) electron is called Compton scattering.
This collision results in a transfer of momentum and energy between the
particles, which modifies the wavelength of the photon by an amount
called the Compton shift. The maximum magnitude of this wavelength shift is h/mec, which is known as the Compton wavelength. For an electron, it has a value of 2.43×10−12 m. When the wavelength of the light is long (for instance, the wavelength of the visible light is 0.4–0.7 μm) the wavelength shift becomes negligible. Such interaction between the light and free electrons is called Thomson scattering or linear Thomson scattering.
The relative strength of the electromagnetic interaction between
two charged particles, such as an electron and a proton, is given by the
fine-structure constant.
This value is a dimensionless quantity formed by the ratio of two
energies: the electrostatic energy of attraction (or repulsion) at a
separation of one Compton wavelength, and the rest energy of the charge.
It is given by α ≈ 7.297353×10−3, which is approximately equal to 1/137.
When electrons and positrons collide, they annihilate each other, giving rise to two or more gamma ray photons. If the electron and positron have negligible momentum, a positronium atom can form before annihilation results in two or three gamma ray photons totalling 1.022 MeV. On the other hand, a high-energy photon can transform into an electron and a positron by a process called pair production, but only in the presence of a nearby charged particle, such as a nucleus.
In the theory of electroweak interaction, the left-handed component of electron's wavefunction forms a weak isospin doublet with the electron neutrino. This means that during weak interactions, electron neutrinos behave like electrons. Either member of this doublet can undergo a charged current interaction by emitting or absorbing a W
and be converted into the other member. Charge is conserved during this
reaction because the W boson also carries a charge, canceling out any
net change during the transmutation. Charged current interactions are
responsible for the phenomenon of beta decay in a radioactive atom. Both the electron and electron neutrino can undergo a neutral current interaction via a Z0 exchange, and this is responsible for neutrino-electron elastic scattering.
Probability
densities for the first few hydrogen atom orbitals, seen in
cross-section. The energy level of a bound electron determines the
orbital it occupies, and the color reflects the probability of finding
the electron at a given position.
An electron can be bound to the nucleus of an atom by the
attractive Coulomb force. A system of one or more electrons bound to a
nucleus is called an atom. If the number of electrons is different from
the nucleus's electrical charge, such an atom is called an ion. The wave-like behavior of a bound electron is described by a function called an atomic orbital.
Each orbital has its own set of quantum numbers such as energy, angular
momentum and projection of angular momentum, and only a discrete set of
these orbitals exist around the nucleus. According to the Pauli
exclusion principle each orbital can be occupied by up to two electrons,
which must differ in their spin quantum number.
Electrons can transfer between different orbitals by the emission
or absorption of photons with an energy that matches the difference in
potential. Other methods of orbital transfer include collisions with particles, such as electrons, and the Auger effect. To escape the atom, the energy of the electron must be increased above its binding energy to the atom. This occurs, for example, with the photoelectric effect, where an incident photon exceeding the atom's ionization energy is absorbed by the electron.
The orbital angular momentum of electrons is quantized.
Because the electron is charged, it produces an orbital magnetic moment
that is proportional to the angular momentum. The net magnetic moment
of an atom is equal to the vector sum of orbital and spin magnetic
moments of all electrons and the nucleus. The magnetic moment of the
nucleus is negligible compared with that of the electrons. The magnetic
moments of the electrons that occupy the same orbital (so called, paired
electrons) cancel each other out.
The chemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum mechanics. The strongest bonds are formed by the sharing or transfer of electrons between atoms, allowing the formation of molecules. Within a molecule, electrons move under the influence of several nuclei, and occupy molecular orbitals; much as they can occupy atomic orbitals in isolated atoms. A fundamental factor in these molecular structures is the existence of electron pairs.
These are electrons with opposed spins, allowing them to occupy the
same molecular orbital without violating the Pauli exclusion principle
(much like in atoms). Different molecular orbitals have different
spatial distribution of the electron density. For instance, in bonded
pairs (i.e. in the pairs that actually bind atoms together) electrons
can be found with the maximal probability in a relatively small volume
between the nuclei. By contrast, in non-bonded pairs electrons are
distributed in a large volume around nuclei.
Conductivity
A lightning discharge consists primarily of a flow of electrons. The electric potential needed for lightning can be generated by a triboelectric effect.
If a body has more or fewer electrons than are required to balance
the positive charge of the nuclei, then that object has a net electric
charge. When there is an excess of electrons, the object is said to be
negatively charged. When there are fewer electrons than the number of
protons in nuclei, the object is said to be positively charged. When the
number of electrons and the number of protons are equal, their charges
cancel each other and the object is said to be electrically neutral. A
macroscopic body can develop an electric charge through rubbing, by the triboelectric effect.
Independent electrons moving in vacuum are termed free
electrons. Electrons in metals also behave as if they were free. In
reality the particles that are commonly termed electrons in metals and
other solids are quasi-electrons—quasiparticles, which have the same electrical charge, spin, and magnetic moment as real electrons but might have a different mass. When free electrons—both in vacuum and metals—move, they produce a net flow of charge called an electric current,
which generates a magnetic field. Likewise a current can be created by a
changing magnetic field. These interactions are described
mathematically by Maxwell's equations.
At a given temperature, each material has an electrical conductivity that determines the value of electric current when an electric potential is applied. Examples of good conductors include metals such as copper and gold, whereas glass and Teflon are poor conductors. In any dielectric material, the electrons remain bound to their respective atoms and the material behaves as an insulator. Most semiconductors have a variable level of conductivity that lies between the extremes of conduction and insulation. On the other hand, metals have an electronic band structure
containing partially filled electronic bands. The presence of such
bands allows electrons in metals to behave as if they were free or delocalized electrons.
These electrons are not associated with specific atoms, so when an
electric field is applied, they are free to move like a gas (called Fermi gas) through the material much like free electrons.
Because of collisions between electrons and atoms, the drift velocity
of electrons in a conductor is on the order of millimeters per second.
However, the speed at which a change of current at one point in the
material causes changes in currents in other parts of the material, the velocity of propagation, is typically about 75% of light speed. This occurs because electrical signals propagate as a wave, with the velocity dependent on the dielectric constant of the material.
Metals make relatively good conductors of heat, primarily because
the delocalized electrons are free to transport thermal energy between
atoms. However, unlike electrical conductivity, the thermal conductivity
of a metal is nearly independent of temperature. This is expressed
mathematically by the Wiedemann–Franz law, which states that the ratio of thermal conductivity
to the electrical conductivity is proportional to the temperature. The
thermal disorder in the metallic lattice increases the electrical resistivity of the material, producing a temperature dependence for electric current.
When cooled below a point called the critical temperature, materials can undergo a phase transition in which they lose all resistivity to electric current, in a process known as superconductivity. In BCS theory, pairs of electrons called Cooper pairs have their motion coupled to nearby matter via lattice vibrations called phonons, thereby avoiding the collisions with atoms that normally create electrical resistance. (Cooper pairs have a radius of roughly 100 nm, so they can overlap each other.) However, the mechanism by which higher temperature superconductors operate remains uncertain.
Electrons inside conducting solids, which are quasi-particles themselves, when tightly confined at temperatures close to absolute zero, behave as though they had split into three other quasiparticles: spinons, orbitons and holons. The former carries spin and magnetic moment, the next carries its orbital location while the latter electrical charge.
Motion and energy
According to Einstein's theory of special relativity, as an electron's speed approaches the speed of light, from an observer's point of view its relativistic mass
increases, thereby making it more and more difficult to accelerate it
from within the observer's frame of reference. The speed of an electron
can approach, but never reach, the speed of light in vacuum, c. However, when relativistic electrons—that is, electrons moving at a speed close to c—are injected into a dielectric medium such as water, where the local speed of light is significantly less than c,
the electrons temporarily travel faster than light in the medium. As
they interact with the medium, they generate a faint light called Cherenkov radiation.
Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity as v approaches c.
The effects of special relativity are based on a quantity known as the Lorentz factor, defined as where v is the speed of the particle. The kinetic energy Ke of an electron moving with velocity v is:
where me is the mass of electron. For example, the Stanford linear accelerator can accelerate an electron to roughly 51 GeV.
Since an electron behaves as a wave, at a given velocity it has a characteristic de Broglie wavelength. This is given by λe = h/p where h is the Planck constant and p is the momentum. For the 51 GeV electron above, the wavelength is about 2.4×10−17 m, small enough to explore structures well below the size of an atomic nucleus.
Formation
Pair production
of an electron and positron, caused by the close approach of a photon
with an atomic nucleus. The lightning symbol represents an exchange of a
virtual photon, thus an electric force acts. The angle between the
particles is very small.
The Big Bang theory is the most widely accepted scientific theory to explain the early stages in the evolution of the Universe. For the first millisecond of the Big Bang, the temperatures were over 10 billion kelvins and photons had mean energies over a million electronvolts.
These photons were sufficiently energetic that they could react with
each other to form pairs of electrons and positrons. Likewise,
positron-electron pairs annihilated each other and emitted energetic
photons:
An equilibrium between electrons, positrons and photons was
maintained during this phase of the evolution of the Universe. After 15
seconds had passed, however, the temperature of the universe dropped
below the threshold where electron-positron formation could occur. Most
of the surviving electrons and positrons annihilated each other,
releasing gamma radiation that briefly reheated the universe.
For reasons that remain uncertain, during the annihilation
process there was an excess in the number of particles over
antiparticles. Hence, about one electron for every billion
electron-positron pairs survived. This excess matched the excess of
protons over antiprotons, in a condition known as baryon asymmetry, resulting in a net charge of zero for the universe. The surviving protons and neutrons began to participate in reactions with each other—in the process known as nucleosynthesis, forming isotopes of hydrogen and helium, with trace amounts of lithium. This process peaked after about five minutes. Any leftover neutrons underwent negative beta decay with a half-life of about a thousand seconds, releasing a proton and electron in the process,
For about the next 300000–400000 years, the excess electrons remained too energetic to bind with atomic nuclei. What followed is a period known as recombination, when neutral atoms were formed and the expanding universe became transparent to radiation.
Roughly one million years after the big bang, the first generation of stars began to form. Within a star, stellar nucleosynthesis
results in the production of positrons from the fusion of atomic
nuclei. These antimatter particles immediately annihilate with
electrons, releasing gamma rays. The net result is a steady reduction in
the number of electrons, and a matching increase in the number of
neutrons. However, the process of stellar evolution
can result in the synthesis of radioactive isotopes. Selected isotopes
can subsequently undergo negative beta decay, emitting an electron and
antineutrino from the nucleus. An example is the cobalt-60 (60Co) isotope, which decays to form nickel-60 (60 Ni ).
An extended air shower generated by an energetic cosmic ray striking the Earth's atmosphere
When a pair of virtual particles (such as an electron and
positron) is created in the vicinity of the event horizon, random
spatial positioning might result in one of them to appear on the
exterior; this process is called quantum tunnelling. The gravitational potential
of the black hole can then supply the energy that transforms this
virtual particle into a real particle, allowing it to radiate away into
space.
In exchange, the other member of the pair is given negative energy,
which results in a net loss of mass-energy by the black hole. The rate
of Hawking radiation increases with decreasing mass, eventually causing
the black hole to evaporate away until, finally, it explodes.
Cosmic rays are particles traveling through space with high energies. Energy events as high as 3.0×1020 eV have been recorded. When these particles collide with nucleons in the Earth's atmosphere, a shower of particles is generated, including pions. More than half of the cosmic radiation observed from the Earth's surface consists of muons. The particle called a muon is a lepton produced in the upper atmosphere by the decay of a pion.
Aurorae are mostly caused by energetic electrons precipitating into the atmosphere.
Remote observation of electrons requires detection of their radiated
energy. For example, in high-energy environments such as the corona of a star, free electrons form a plasma that radiates energy due to Bremsstrahlung radiation. Electron gas can undergo plasma oscillation,
which is waves caused by synchronized variations in electron density,
and these produce energy emissions that can be detected by using radio telescopes.
The frequency of a photon
is proportional to its energy. As a bound electron transitions between
different energy levels of an atom, it absorbs or emits photons at
characteristic frequencies. For instance, when atoms are irradiated by a
source with a broad spectrum, distinct dark lines
appear in the spectrum of transmitted radiation in places where the
corresponding frequency is absorbed by the atom's electrons. Each
element or molecule displays a characteristic set of spectral lines,
such as the hydrogen spectral series. When detected, spectroscopic
measurements of the strength and width of these lines allow the
composition and physical properties of a substance to be determined.
In laboratory conditions, the interactions of individual electrons can be observed by means of particle detectors, which allow measurement of specific properties such as energy, spin and charge. The development of the Paul trap and Penning trap
allows charged particles to be contained within a small region for long
durations. This enables precise measurements of the particle
properties. For example, in one instance a Penning trap was used to
contain a single electron for a period of 10 months.
The magnetic moment of the electron was measured to a precision of
eleven digits, which, in 1980, was a greater accuracy than for any other
physical constant.
The first video images of an electron's energy distribution were captured by a team at Lund University in Sweden, February 2008. The scientists used extremely short flashes of light, called attosecond pulses, which allowed an electron's motion to be observed for the first time.
The distribution of the electrons in solid materials can be visualized by angle-resolved photoemission spectroscopy (ARPES). This technique employs the photoelectric effect to measure the reciprocal space—a
mathematical representation of periodic structures that is used to
infer the original structure. ARPES can be used to determine the
direction, speed and scattering of electrons within the material.
Electron beams are used in welding. They allow energy densities up to 107 W·cm−2 across a narrow focus diameter of 0.1–1.3 mm
and usually require no filler material. This welding technique must be
performed in a vacuum to prevent the electrons from interacting with the
gas before reaching their target, and it can be used to join conductive
materials that would otherwise be considered unsuitable for welding.
Electron-beam lithography (EBL) is a method of etching semiconductors at resolutions smaller than a micrometer.
This technique is limited by high costs, slow performance, the need to
operate the beam in the vacuum and the tendency of the electrons to
scatter in solids. The last problem limits the resolution to about
10 nm. For this reason, EBL is primarily used for the production of
small numbers of specialized integrated circuits.
Electron beam processing is used to irradiate materials in order to change their physical properties or sterilize medical and food products.
Electron beams fluidise or quasi-melt glasses without significant
increase of temperature on intensive irradiation: e.g. intensive
electron radiation causes a many orders of magnitude decrease of
viscosity and stepwise decrease of its activation energy.
Linear particle accelerators generate electron beams for treatment of superficial tumors in radiation therapy. Electron therapy can treat such skin lesions as basal-cell carcinomas
because an electron beam only penetrates to a limited depth before
being absorbed, typically up to 5 cm for electron energies in the range
5–20 MeV. An electron beam can be used to supplement the treatment of
areas that have been irradiated by X-rays.
Particle accelerators
use electric fields to propel electrons and their antiparticles to high
energies. These particles emit synchrotron radiation as they pass
through magnetic fields. The dependency of the intensity of this
radiation upon spin polarizes the electron beam—a process known as the Sokolov–Ternov effect. Polarized electron beams can be useful for various experiments. Synchrotron radiation can also cool
the electron beams to reduce the momentum spread of the particles.
Electron and positron beams are collided upon the particles'
accelerating to the required energies; particle detectors observe the resulting energy emissions, which particle physics studies .
Imaging
Low-energy electron diffraction (LEED) is a method of bombarding a crystalline material with a collimated beam
of electrons and then observing the resulting diffraction patterns to
determine the structure of the material. The required energy of the
electrons is typically in the range 20–200 eV. The reflection high-energy electron diffraction
(RHEED) technique uses the reflection of a beam of electrons fired at
various low angles to characterize the surface of crystalline materials.
The beam energy is typically in the range 8–20 keV and the angle of
incidence is 1–4°.
The electron microscope
directs a focused beam of electrons at a specimen. Some electrons
change their properties, such as movement direction, angle, and relative
phase and energy as the beam interacts with the material. Microscopists
can record these changes in the electron beam to produce atomically
resolved images of the material. In blue light, conventional optical microscopes have a diffraction-limited resolution of about 200 nm. By comparison, electron microscopes are limited by the de Broglie wavelength of the electron. This wavelength, for example, is equal to 0.0037 nm for electrons accelerated across a 100,000-volt potential. The Transmission Electron Aberration-Corrected Microscope is capable of sub-0.05 nm resolution, which is more than enough to resolve individual atoms.
This capability makes the electron microscope a useful laboratory
instrument for high resolution imaging. However, electron microscopes
are expensive instruments that are costly to maintain.
Two main types of electron microscopes exist: transmission and scanning. Transmission electron microscopes function like overhead projectors, with a beam of electrons passing through a slice of material then being projected by lenses on a photographic slide or a charge-coupled device. Scanning electron microscopes rasteri
a finely focused electron beam, as in a TV set, across the studied
sample to produce the image. Magnifications range from 100× to
1,000,000× or higher for both microscope types. The scanning tunneling microscope
uses quantum tunneling of electrons from a sharp metal tip into the
studied material and can produce atomically resolved images of its
surface.
Other applications
In the free-electron laser (FEL), a relativistic electron beam passes through a pair of undulators that contain arrays of dipole magnets whose fields point in alternating directions. The electrons emit synchrotron radiation that coherently interacts with the same electrons to strongly amplify the radiation field at the resonance frequency. FEL can emit a coherent high-brilliance electromagnetic radiation with a wide range of frequencies, from microwaves
to soft X-rays. These devices are used in manufacturing, communication,
and in medical applications, such as soft tissue surgery.
Electrons are important in cathode-ray tubes, which have been extensively used as display devices in laboratory instruments, computer monitors and television sets. In a photomultiplier tube, every photon striking the photocathode initiates an avalanche of electrons that produces a detectable current pulse. Vacuum tubes
use the flow of electrons to manipulate electrical signals, and they
played a critical role in the development of electronics technology.
However, they have been largely supplanted by solid-state devices such as the transistor.
