Einsteinium

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Einsteinium,  ₉₉Es

Einsteinium
Pronunciation	/aɪnˈstaɪniəm/ ​(eyen-STY-nee-əm)
Appearance	silvery; glows blue in the dark
Mass number	252 (most stable isotope)
Einsteinium in the periodic table
Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorus Sulfur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury (element) Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Darmstadtium Roentgenium Copernicium Nihonium Flerovium Moscovium Livermorium Tennessine Oganesson Ho ↑ Es ↓ (Upt) californium ← einsteinium → fermium
Atomic number (Z)	99
Group	group n/a
Period	period 7
Block	f-block
Element category	actinide
Electron configuration	[Rn] 5f11 7s2
Electrons per shell	2, 8, 18, 32, 29, 8, 2
Physical properties
Phase at STP	solid
Melting point	1133 K ​(860 °C, ​1580 °F)
Boiling point	1269 K ​(996 °C, ​1825 °F) (estimated)
Density (near r.t.)	8.84 g/cm3
Atomic properties
Oxidation states	+2, +3, +4
Electronegativity	Pauling scale: 1.3
Ionization energies	1st: 619 kJ/mol
Spectral lines of einsteinium
Other properties
Natural occurrence	synthetic
Crystal structure	​face-centered cubic (fcc)
Magnetic ordering	paramagnetic
CAS Number	7429-92-7
History
Naming	after Albert Einstein
Discovery	Lawrence Berkeley National Laboratory (1952)
Main isotopes of einsteinium
Iso­tope Abun­dance Half-life (t1/2) Decay mode Pro­duct 252Es syn 471.7 d α 248Bk ε 252Cf β− 252Fm 253Es syn 20.47 d SF – α 249Bk 254Es syn 275.7 d ε 254Cf β− 254Fm α 250Bk 255Es syn 39.8 d β− 255Fm α 251Bk SF –

Einsteinium is a synthetic element with symbol Es and atomic number 99. A member of the actinide series, it is the seventh transuranic element.

Einsteinium was discovered as a component of the debris of the first hydrogen bomb explosion in 1952, and named after Albert Einstein. Its most common isotope einsteinium-253 (half-life 20.47 days) is produced artificially from decay of californium-253 in a few dedicated high-power nuclear reactors with a total yield on the order of one milligram per year. The reactor synthesis is followed by a complex process of separating einsteinium-253 from other actinides and products of their decay. Other isotopes are synthesized in various laboratories, but at much smaller amounts, by bombarding heavy actinide elements with light ions. Owing to the small amounts of produced einsteinium and the short half-life of its most easily produced isotope, there are currently almost no practical applications for it outside basic scientific research. In particular, einsteinium was used to synthesize, for the first time, 17 atoms of the new element mendelevium in 1955.

Einsteinium is a soft, silvery, paramagnetic metal. Its chemistry is typical of the late actinides, with a preponderance of the +3 oxidation state; the +2 oxidation state is also accessible, especially in solids. The high radioactivity of einsteinium-253 produces a visible glow and rapidly damages its crystalline metal lattice, with released heat of about 1000 watts per gram. Difficulty in studying its properties is due to einsteinium-253's decay to berkelium-249 and then californium-249 at a rate of about 3% per day. The isotope of einsteinium with the longest half-life, einsteinium-252 (half-life 471.7 days) would be more suitable for investigation of physical properties, but it has proven far more difficult to produce and is available only in minute quantities, and not in bulk. Einsteinium is the element with the highest atomic number which has been observed in macroscopic quantities in its pure form, and this was the common short-lived isotope einsteinium-253.

Like all synthetic transuranic elements, isotopes of einsteinium are very radioactive and are considered highly dangerous to health on ingestion.

History

Einsteinium was first observed in the fallout from the Ivy Mike nuclear test.

 

Einsteinium was first identified in December 1952 by Albert Ghiorso and co-workers at the University of California, Berkeley in collaboration with the Argonne and Los Alamos National Laboratories, in the fallout from the Ivy Mike nuclear test. The test was carried out on November 1, 1952 at Enewetak Atoll in the Pacific Ocean and was the first successful test of a hydrogen bomb. Initial examination of the debris from the explosion had shown the production of a new isotope of plutonium, ²⁴⁴
₉₄Pu
, which could only have formed by the absorption of six neutrons by a uranium-238 nucleus followed by two beta decays. 

${\displaystyle {\ce {^{238}_{92}U->[{\ce {+6(n,\gamma )}}][-2\ \beta ^{-}]{}_{94}^{244}Pu}}}$

At the time, the multiple neutron absorption was thought to be an extremely rare process, but the identification of ²⁴⁴
₉₄Pu
indicated that still more neutrons could have been captured by the uranium nuclei, thereby producing new elements heavier than californium.

The element was discovered by a team headed by Albert Ghiorso.

 

Ghiorso and co-workers analyzed filter papers which had been flown through the explosion cloud on airplanes (the same sampling technique that had been used to discover ²⁴⁴
₉₄Pu
). Larger amounts of radioactive material were later isolated from coral debris of the atoll, which were delivered to the U.S. The separation of suspected new elements was carried out in the presence of a citric acid/ammonium buffer solution in a weakly acidic medium (pH ≈ 3.5), using ion exchange at elevated temperatures; fewer than 200 atoms of einsteinium were recovered in the end. Nevertheless, element 99 (einsteinium), namely its ²⁵³Es isotope, could be detected via its characteristic high-energy alpha decay at 6.6 MeV. It was produced by the capture of 15 neutrons by uranium-238 nuclei followed by seven beta-decays, and had a half-life of 20.5 days. Such multiple neutron absorption was made possible by the high neutron flux density during the detonation, so that newly generated heavy isotopes had plenty of available neutrons to absorb before they could disintegrate into lighter elements. Neutron capture initially raised the mass number without changing the atomic number of the nuclide, and the concomitant beta-decays resulted in a gradual increase in the atomic number:

${\displaystyle {\ce {^{238}_{92}U ->[{\ce {+15n}}][6 \beta^-] ^{253}_{98}Cf ->[\beta^-] ^{253}_{99}Es}}}$

Some ²³⁸U atoms, however, could absorb two additional neutrons (for a total of 17), resulting in ²⁵⁵Es, as well as in the ²⁵⁵Fm isotope of another new element, fermium. The discovery of the new elements and the associated new data on multiple neutron capture were initially kept secret on the orders of the U.S. military until 1955 due to Cold War tensions and competition with Soviet Union in nuclear technologies. However, the rapid capture of so many neutrons would provide needed direct experimental confirmation of the so-called r-process multiple neutron absorption needed to explain the cosmic nucleosynthesis (production) of certain heavy chemical elements (heavier than nickel) in supernova explosions, before beta decay. Such a process is needed to explain the existence of many stable elements in the universe.

Meanwhile, isotopes of element 99 (as well as of new element 100, fermium) were produced in the Berkeley and Argonne laboratories, in a nuclear reaction between nitrogen-14 and uranium-238, and later by intense neutron irradiation of plutonium or californium:

${\displaystyle {\ce {^{252}_{98}Cf ->[{\ce {(n,\gamma)}}] ^{253}_{98}Cf ->[\beta^-][17.81 {\ce {d}}] ^{253}_{99}Es ->[{\ce {(n,\gamma)}}] ^{254}_{99}Es ->[\beta^-] ^{254}_{100}Fm}}}$

These results were published in several articles in 1954 with the disclaimer that these were not the first studies that had been carried out on the elements. The Berkeley team also reported some results on the chemical properties of einsteinium and fermium. The Ivy Mike results were declassified and published in 1955.

The element was named after Albert Einstein.

In their discovery of the elements 99 and 100, the American teams had competed with a group at the Nobel Institute for Physics, Stockholm, Sweden. In late 1953 – early 1954, the Swedish group succeeded in the synthesis of light isotopes of element 100, in particular ²⁵⁰Fm, by bombarding uranium with oxygen nuclei. These results were also published in 1954. Nevertheless, the priority of the Berkeley team was generally recognized, as its publications preceded the Swedish article, and they were based on the previously undisclosed results of the 1952 thermonuclear explosion; thus the Berkeley team was given the privilege to name the new elements. As the effort which had led to the design of Ivy Mike was code named Project PANDA, element 99 had been jokingly nicknamed "Pandamonium" but the official names suggested by the Berkeley group derived from two prominent scientists, Albert Einstein and Enrico Fermi: "We suggest for the name for the element with the atomic number 99, einsteinium (symbol E) after Albert Einstein and for the name for the element with atomic number 100, fermium (symbol Fm), after Enrico Fermi." Both Einstein and Fermi died between the time the names were originally proposed and when they were announced. The discovery of these new elements was announced by Albert Ghiorso at the first Geneva Atomic Conference held on 8–20 August 1955. The symbol for einsteinium was first given as "E" and later changed to "Es" by IUPAC.

Characteristics

Physical

Glow due to the intense radiation from ~300 µg of ²⁵³Es.

 

Einsteinium is a synthetic, silvery-white, radioactive metal. In the periodic table, it is located to the right of the actinide californium, to the left of the actinide fermium and below the lanthanide holmium with which it shares many similarities in physical and chemical properties. Its density of 8.84 g/cm³ is lower than that of californium (15.1 g/cm³) and is nearly the same as that of holmium (8.79 g/cm³), despite atomic einsteinium being much heavier than holmium. The melting point of einsteinium (860 °C) is also relatively low – below californium (900 °C), fermium (1527 °C) and holmium (1461 °C). Einsteinium is a soft metal, with the bulk modulus of only 15 GPa, which value is one of the lowest among non-alkali metals.

Contrary to the lighter actinides californium, berkelium, curium and americium which crystallize in a double hexagonal structure at ambient conditions, einsteinium is believed to have a face-centered cubic (fcc) symmetry with the space group Fm3m and the lattice constant a = 575 pm. However, there is a report of room-temperature hexagonal einsteinium metal with a = 398 pm and c = 650 pm, which converted to the fcc phase upon heating to 300 °C.

The self-damage induced by the radioactivity of einsteinium is so strong that it rapidly destroys the crystal lattice, and the energy release during this process, 1000 watts per gram of ²⁵³Es, induces a visible glow. These processes may contribute to the relatively low density and melting point of einsteinium. Further, owing to the small size of the available samples, the melting point of einsteinium was often deduced by observing the sample being heated inside an electron microscope. Thus the surface effects in small samples could reduce the melting point value. 

The metal is divalent and has a noticeably high volatility. In order to reduce the self-radiation damage, most measurements of solid einsteinium and its compounds are performed right after thermal annealing. Also, some compounds are studied under the atmosphere of the reductant gas, for example H₂O+HCl for EsOCl so that the sample is partly regrown during its decomposition.

Apart from the self-destruction of solid einsteinium and its compounds, other intrinsic difficulties in studying this element include scarcity – the most common ²⁵³Es isotope is available only once or twice a year in sub-milligram amounts – and self-contamination due to rapid conversion of einsteinium to berkelium and then to californium at a rate of about 3.3% per day:

${\displaystyle {\ce {^{253}_{99}Es ->[\alpha][20 {\ce {d}}] ^{249}_{97}Bk ->[\beta^-][314 {\ce {d}}] ^{249}_{98}Cf}}}$

Thus, most einsteinium samples are contaminated, and their intrinsic properties are often deduced by extrapolating back experimental data accumulated over time. Other experimental techniques to circumvent the contamination problem include selective optical excitation of einsteinium ions by a tunable laser, such as in studying its luminescence properties.

Magnetic properties have been studied for einsteinium metal, its oxide and fluoride. All three materials showed Curie–Weiss paramagnetic behavior from liquid helium to room temperature. The effective magnetic moments were deduced as 10.4±0.3 µ_B for Es₂O₃ and 11.4±0.3 µ_B for the EsF₃, which are the highest values among actinides, and the corresponding Curie temperatures are 53 and 37 K.

Chemical

Like all actinides, einsteinium is rather reactive. Its trivalent oxidation state is most stable in solids and aqueous solution where it induces a pale pink color. The existence of divalent einsteinium is firmly established, especially in the solid phase; such +2 state is not observed in many other actinides, including protactinium, uranium, neptunium, plutonium, curium and berkelium. Einsteinium(II) compounds can be obtained, for example, by reducing einsteinium(III) with samarium(II) chloride. The oxidation state +4 was postulated from vapor studies and is yet uncertain.

Isotopes

Nineteen nuclides and three nuclear isomers are known for einsteinium with atomic weights ranging from 240 to 258. All are radioactive and the most stable nuclide, ²⁵²Es, has a half-life of 471.7 days. Next most stable isotopes are ²⁵⁴Es (half-life 275.7 days), ²⁵⁵Es (39.8 days) and ²⁵³Es (20.47 days). All of the remaining isotopes have half-lives shorter than 40 hours, and most of them decay within less than 30 minutes. Of the three nuclear isomers, the most stable is ^254mEs with half-life of 39.3 hours.

Nuclear fission

Einsteinium has a high rate of nuclear fission that results in a low critical mass for a sustained nuclear chain reaction. This mass is 9.89 kilograms for a bare sphere of ²⁵⁴Es isotope, and can be lowered to 2.9 by adding a 30-centimeter-thick steel neutron reflector, or even to 2.26 kilograms with a 20-cm-thick reflector made of water. However, even this small critical mass greatly exceeds the total amount of einsteinium isolated thus far, especially of the rare ²⁵⁴Es isotope.

Natural occurrence

Because of the short half-life of all isotopes of einsteinium, any primordial einsteinium — that is, einsteinium that could possibly have been present on the Earth during its formation — has long since decayed. Synthesis of einsteinium from naturally-occurring actinides uranium and thorium in the Earth's crust requires multiple neutron capture, which is an extremely unlikely event. Therefore, all terrestrial einsteinium is produced in scientific laboratories, high-power nuclear reactors, or in nuclear weapons tests, and is present only within a few years from the time of the synthesis. The transuranic elements from americium to fermium, including einsteinium, occurred naturally in the natural nuclear fission reactor at Oklo, but no longer do so. Einsteinium was observed in Przybylski's Star in 2008.

Synthesis and extraction

Early evolution of einsteinium production in the U.S.

 

Einsteinium is produced in minute quantities by bombarding lighter actinides with neutrons in dedicated high-flux nuclear reactors. The world's major irradiation sources are the 85-megawatt High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory in Tennessee, U.S., and the SM-2 loop reactor at the Research Institute of Atomic Reactors (NIIAR) in Dimitrovgrad, Russia, which are both dedicated to the production of transcurium (Z > 96) elements. These facilities have similar power and flux levels, and are expected to have comparable production capacities for transcurium elements, although the quantities produced at NIIAR are not widely reported. In a "typical processing campaign" at Oak Ridge, tens of grams of curium are irradiated to produce decigram quantities of californium, milligram quantities of berkelium (²⁴⁹Bk) and einsteinium and picogram quantities of fermium.

The first microscopic sample of ²⁵³Es sample weighing about 10 nanograms was prepared in 1961 at HFIR. A special magnetic balance was designed to estimate its weight. Larger batches were produced later starting from several kilograms of plutonium with the einsteinium yields (mostly ²⁵³Es) of 0.48 milligrams in 1967–1970, 3.2 milligrams in 1971–1973, followed by steady production of about 3 milligrams per year between 1974 and 1978. These quantities however refer to the integral amount in the target right after irradiation. Subsequent separation procedures reduced the amount of isotopically pure einsteinium roughly tenfold.

Laboratory synthesis

Heavy neutron irradiation of plutonium results in four major isotopes of einsteinium: ²⁵³Es (α-emitter with half-life of 20.47 days and with a spontaneous fission half-life of 7×10⁵ years); ^254mEs (β-emitter with half-life of 39.3 hours), ²⁵⁴Es (α-emitter with half-life of about 276 days) and ²⁵⁵Es (β-emitter with half-life of 39.8 days). An alternative route involves bombardment of uranium-238 with high-intensity nitrogen or oxygen ion beams.

Einsteinium-247 (half-life 4.55 minutes) was produced by irradiating americium-241 with carbon or uranium-238 with nitrogen ions. The latter reaction was first realized in 1967 in Dubna, Russia, and the involved scientists were awarded the Lenin Komsomol Prize.

The isotope ²⁴⁸Es was produced by irradiating ²⁴⁹Cf with deuterium ions. It mainly decays by emission of electrons to ²⁴⁸Cf with a half-life of 25±5 minutes, but also releases α-particles of 6.87 MeV energy, with the ratio of electrons to α-particles of about 400.

${\displaystyle {\ce {^{249}_{98}Cf + ^{2}_{1}D -> ^{248}_{99}Es + 3^{1}_{0}n}}\quad \left({\ce {^{248}_{99}Es ->[\epsilon][27 {\ce {min}}] ^{248}_{98}Cf}}\right)}$

The heavier isotopes ²⁴⁹Es, ²⁵⁰Es, ²⁵¹Es and ²⁵²Es were obtained by bombarding ²⁴⁹Bk with α-particles. One to four neutrons are liberated in this process making possible the formation of four different isotopes in one reaction.

${\displaystyle {\ce {^{249}_{97}Bk ->[+\alpha] ^{249,250,251,252}_{99}Es}}}$

Einsteinium-253 was produced by irradiating a 0.1–0.2 milligram ²⁵²Cf target with a thermal neutron flux of (2–5)×10¹⁴ neutrons·cm⁻²·s⁻¹ for 500–900 hours:

${\displaystyle {\ce {^{252}_{98}Cf ->[{\ce {(n,\gamma)}}] ^{253}_{98}Cf ->[\beta^-][17.81 {\ce {d}}] ^{253}_{99}Es}}}$

Synthesis in nuclear explosions

Estimated yield of transuranium elements in the U.S. nuclear tests Hutch and Cyclamen.

 

The analysis of the debris at the 10-megaton Ivy Mike nuclear test was a part of long-term project. One of the goals of which was studying the efficiency of production of transuranium elements in high-power nuclear explosions. The motivation for these experiments was that synthesis of such elements from uranium requires multiple neutron capture. The probability of such events increases with the neutron flux, and nuclear explosions are the most powerful man-made neutron sources, providing densities of the order 10²³ neutrons/cm² within a microsecond, or about 10²⁹ neutrons/(cm²·s). In comparison, the flux of the HFIR reactor is 5×10¹⁵ neutrons/(cm²·s). A dedicated laboratory was set up right at Enewetak Atoll for preliminary analysis of debris, as some isotopes could have decayed by the time the debris samples reached the mainland U.S. The laboratory was receiving samples for analysis as soon as possible, from airplanes equipped with paper filters which flew over the atoll after the tests. Whereas it was hoped to discover new chemical elements heavier than fermium, none of these were found even after a series of megaton explosions conducted between 1954 and 1956 at the atoll.

The atmospheric results were supplemented by the underground test data accumulated in the 1960s at the Nevada Test Site, as it was hoped that powerful explosions conducted in confined space might result in improved yields and heavier isotopes. Apart from traditional uranium charges, combinations of uranium with americium and thorium have been tried, as well as a mixed plutonium-neptunium charge, but they were less successful in terms of yield and was attributed to stronger losses of heavy isotopes due to enhanced fission rates in heavy-element charges. Product isolation was problematic as the explosions were spreading debris through melting and vaporizing the surrounding rocks at depths of 300–600 meters. Drilling to such depths to extract the products was both slow and inefficient in terms of collected volumes.

Among the nine underground tests that were carried between 1962 and 1969, the last one was the most powerful and had the highest yield of transuranium elements. Milligrams of einsteinium that would normally take a year of irradiation in a high-power reactor, were produced within a microsecond. However, the major practical problem of the entire proposal was collecting the radioactive debris dispersed by the powerful blast. Aircraft filters adsorbed only about 4×10⁻¹⁴ of the total amount, and collection of tons of corals at Enewetak Atoll increased this fraction by only two orders of magnitude. Extraction of about 500 kilograms of underground rocks 60 days after the Hutch explosion recovered only about 1×10⁻⁷ of the total charge. The amount of transuranium elements in this 500-kg batch was only 30 times higher than in a 0.4 kg rock picked up 7 days after the test which demonstrated the highly non-linear dependence of the transuranium elements yield on the amount of retrieved radioactive rock. Shafts were drilled at the site before the test in order to accelerate sample collection after explosion, so that explosion would expel radioactive material from the epicenter through the shafts and to collecting volumes near the surface. This method was tried in two tests and instantly provided hundreds kilograms of material, but with actinide concentration 3 times lower than in samples obtained after drilling. Whereas such method could have been efficient in scientific studies of short-lived isotopes, it could not improve the overall collection efficiency of the produced actinides.

Although no new elements (apart from einsteinium and fermium) could be detected in the nuclear test debris, and the total yields of transuranium elements were disappointingly low, these tests did provide significantly higher amounts of rare heavy isotopes than previously available in laboratories.

Separation

Elution curves: chromatographic separation of Fm(100), Es(99), Cf, Bk, Cm and Am

 

Separation procedure of einsteinium depends on the synthesis method. In the case of light-ion bombardment inside a cyclotron, the heavy ion target is attached to a thin foil, and the generated einsteinium is simply washed off the foil after the irradiation. However, the produced amounts in such experiments are relatively low. The yields are much higher for reactor irradiation, but there, the product is a mixture of various actinide isotopes, as well as lanthanides produced in the nuclear fission decays. In this case, isolation of einsteinium is a tedious procedure which involves several repeating steps of cation exchange, at elevated temperature and pressure, and chromatography. Separation from berkelium is important, because the most common einsteinium isotope produced in nuclear reactors, ²⁵³Es, decays with a half-life of only 20 days to ²⁴⁹Bk, which is fast on the timescale of most experiments. Such separation relies on the fact that berkelium easily oxidizes to the solid +4 state and precipitates, whereas other actinides, including einsteinium, remain in their +3 state in solutions.

Separation of trivalent actinides from lanthanide fission products can be done by a cation-exchange resin column using a 90% water/10% ethanol solution saturated with hydrochloric acid (HCl) as eluant. It is usually followed by anion-exchange chromatography using 6 molar HCl as eluant. A cation-exchange resin column (Dowex-50 exchange column) treated with ammonium salts is then used to separate fractions containing elements 99, 100 and 101. These elements can be then identified simply based on their elution position/time, using α-hydroxyisobutyrate solution (α-HIB), for example, as eluant.

Separation of the 3+ actinides can also be achieved by solvent extraction chromatography, using bis-(2-ethylhexyl) phosphoric acid (abbreviated as HDEHP) as the stationary organic phase, and nitric acid as the mobile aqueous phase. The actinide elution sequence is reversed from that of the cation-exchange resin column. The einsteinium separated by this method has the advantage to be free of organic complexing agent, as compared to the separation using a resin column.

Preparation of the metal

Einsteinium is highly reactive and therefore strong reducing agents are required to obtain the pure metal from its compounds. This can be achieved by reduction of einsteinium(III) fluoride with metallic lithium:

EsF₃ + 3 Li → Es + 3 LiF

However, owing to its low melting point and high rate of self-radiation damage, einsteinium has high vapor pressure, which is higher than that of lithium fluoride. This makes this reduction reaction rather inefficient. It was tried in the early preparation attempts and quickly abandoned in favor of reduction of einsteinium(III) oxide with lanthanum metal:

Es₂O₃ + 2 La → 2 Es + La₂O₃

Chemical compounds

Oxides

Einsteinium(III) oxide (Es₂O₃) was obtained by burning einsteinium(III) nitrate. It forms colorless cubic crystals, which were first characterized from microgram samples sized about 30 nanometers. Two other phases, monoclinic and hexagonal, are known for this oxide. The formation of a certain Es₂O₃ phase depends on the preparation technique and sample history, and there is no clear phase diagram. Interconversions between the three phases can occur spontaneously, as a result of self-irradiation or self-heating. The hexagonal phase is isotypic with lanthanum(III) oxide where the Es³⁺ ion is surrounded by a 6-coordinated group of O²⁻ ions.

Halides

Einsteinium(III) iodide glowing in the dark

 

Einsteinium halides are known for the oxidation states +2 and +3. The most stable state is +3 for all halides from fluoride to iodide. 

Einsteinium(III) fluoride (EsF₃) can be precipitated from einsteinium(III) chloride solutions upon reaction with fluoride ions. An alternative preparation procedure is to exposure einsteinium(III) oxide to chlorine trifluoride (ClF₃) or F₂ gas at a pressure of 1–2 atmospheres and a temperature between 300 and 400 °C. The EsF₃ crystal structure is hexagonal, as in californium(III) fluoride (CfF₃) where the Es³⁺ ions are 8-fold coordinated by fluorine ions in a bicapped trigonal prism arrangement.

Einsteinium(III) chloride (EsCl₃) can be prepared by annealing einsteinium(III) oxide in the atmosphere of dry hydrogen chloride vapors at about 500 °C for some 20 minutes. It crystallizes upon cooling at about 425 °C into an orange solid with a hexagonal structure of UCl₃ type, where einsteinium atoms are 9-fold coordinated by chlorine atoms in a tricapped trigonal prism geometry. Einsteinium(III) bromide (EsBr₃) is a pale-yellow solid with a monoclinic structure of AlCl₃ type, where the einsteinium atoms are octahedrally coordinated by bromine (coordination number 6).

The divalent compounds of einsteinium are obtained by reducing the trivalent halides with hydrogen:

2 EsX₃ + H₂ → 2 EsX₂ + 2 HX,    X = F, Cl, Br, I

Einsteinium(II) chloride (EsCl₂), einsteinium(II) bromide (EsBr₂), and einsteinium(II) iodide (EsI₂) have been produced and characterized by optical absorption, with no structural information available yet.

Known oxyhalides of einsteinium include EsOCl, EsOBr and EsOI. They are synthesized by treating a trihalide with a vapor mixture of water and the corresponding hydrogen halide: for example, EsCl₃ + H₂O/HCl to obtain EsOCl.

Organoeinsteinium compounds

The high radioactivity of einsteinium has a potential use in radiation therapy, and organometallic complexes have been synthesized in order to deliver einsteinium atoms to an appropriate organ in the body. Experiments have been performed on injecting einsteinium citrate (as well as fermium compounds) to dogs. Einsteinium(III) was also incorporated into beta-diketone chelate complexes, since analogous complexes with lanthanides previously showed strongest UV-excited luminescence among metallorganic compounds. When preparing einsteinium complexes, the Es³⁺ ions were 1000 times diluted with Gd³⁺ ions. This allowed reducing the radiation damage so that the compounds did not disintegrate during the period of 20 minutes required for the measurements. The resulting luminescence from Es³⁺ was much too weak to be detected. This was explained by the unfavorable relative energies of the individual constituents of the compound that hindered efficient energy transfer from the chelate matrix to Es³⁺ ions. Similar conclusion was drawn for other actinides americium, berkelium and fermium.

Luminescence of Es³⁺ ions was however observed in inorganic hydrochloric acid solutions as well as in organic solution with di(2-ethylhexyl)orthophosphoric acid. It shows a broad peak at about 1064 nanometers (half-width about 100 nm) which can be resonantly excited by green light (ca. 495 nm wavelength). The luminescence has a lifetime of several microseconds and the quantum yield below 0.1%. The relatively high, compared to lanthanides, non-radiative decay rates in Es³⁺ were associated with the stronger interaction of f-electrons with the inner Es³⁺ electrons.

Applications

There is almost no use for any isotope of einsteinium outside basic scientific research aiming at production of higher transuranic elements and transactinides.

In 1955, mendelevium was synthesized by irradiating a target consisting of about 10⁹ atoms of ²⁵³Es in the 60-inch cyclotron at Berkeley Laboratory. The resulting ²⁵³Es(α,n)²⁵⁶Md reaction yielded 17 atoms of the new element with the atomic number of 101.

The rare isotope einsteinium-254 is favored for production of ultraheavy elements because of its large mass, relatively long half-life of 270 days, and availability in significant amounts of several micrograms. Hence einsteinium-254 was used as a target in the attempted synthesis of ununennium (element 119) in 1985 by bombarding it with calcium-48 ions at the superHILAC linear accelerator at Berkeley, California. No atoms were identified, setting an upper limit for the cross section of this reaction at 300 nanobarns.

${\displaystyle {\ce {{^{254}_{99}Es}+{^{48}_{20}Ca}->{^{302}_{119}Uue^{\ast }}->no\ atoms}}}$

Einsteinium-254 was used as the calibration marker in the chemical analysis spectrometer ("alpha-scattering surface analyzer") of the Surveyor 5 lunar probe. The large mass of this isotope reduced the spectral overlap between signals from the marker and the studied lighter elements of the lunar surface.

Safety

Most of the available einsteinium toxicity data originate from research on animals. Upon ingestion by rats, only about 0.01% einsteinium ends in the blood stream. From there, about 65% goes to the bones, where it remains for about 50 years, 25% to the lungs (biological half-life about 20 years, although this is rendered irrelevant by the short half-lives of einsteinium isotopes), 0.035% to the testicles or 0.01% to the ovaries – where einsteinium stays indefinitely. About 10% of the ingested amount is excreted. The distribution of einsteinium over the bone surfaces is uniform and is similar to that of plutonium.

Bohr–Einstein debates

From Wikipedia, the free encyclopedia

Niels Bohr with Albert Einstein at Paul Ehrenfest's home in Leiden (December 1925)

The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr. Their debates are remembered because of their importance to the philosophy of science. An account of the debates was written by Bohr in an article titled "Discussions with Einstein on Epistemological Problems in Atomic Physics". Despite their differences of opinion regarding quantum mechanics, Bohr and Einstein had a mutual admiration that was to last the rest of their lives.

The debates represent one of the highest points of scientific research in the first half of the twentieth century because it called attention to an element of quantum theory, quantum non-locality, which is central to our modern understanding of the physical world. The consensus view of professional physicists has been that Bohr proved victorious in his defense of quantum theory, and definitively established the fundamental probabilistic character of quantum measurement.

Pre-revolutionary debates

Einstein was the first physicist to say that Planck's discovery of the quantum (h) would require a rewriting of the laws of physics. To support his point, in 1905 he proposed that light sometimes acts as a particle which he called a light quantum. Bohr was one of the most vocal opponents of the photon idea and did not openly embrace it until 1925. The photon appealed to Einstein because he saw it as a physical reality (although a confusing one) behind the numbers. Bohr disliked it because it made the choice of mathematical solution arbitrary. He did not like a scientist having to choose between equations.

1913 brought the Bohr model of the hydrogen atom, which made use of the quantum to explain the atomic spectrum. Einstein was at first skeptical, but quickly changed his mind and admitted his shift in mindset.

The quantum revolution

The quantum revolution of the mid-1920s occurred under the direction of both Einstein and Bohr, and their post-revolutionary debates were about making sense of the change. The shocks for Einstein began in 1925 when Werner Heisenberg introduced matrix equations that removed the Newtonian elements of space and time from any underlying reality. The next shock came in 1926 when Max Born proposed that mechanics were to be understood as a probability without any causal explanation.

Einstein rejected this interpretation. In a 1926 letter to Max Born, Einstein wrote: "I, at any rate, am convinced that He [God] does not throw dice."

At the Fifth Solvay Conference held in October 1927 Heisenberg and Born concluded that the revolution was over and nothing further was needed. It was at that last stage that Einstein's skepticism turned to dismay. He believed that much had been accomplished, but the reasons for the mechanics still needed to be understood.

Einstein's refusal to accept the revolution as complete reflected his desire to see developed a model for the underlying causes from which these apparent random statistical methods resulted. He did not reject the idea that positions in space-time could never be completely known but did not want to allow the uncertainty principle to necessitate a seemingly random, non-deterministic mechanism by which the laws of physics operated. Einstein himself was a statistical thinker but disagreed that no more needed to be discovered and clarified. Bohr, meanwhile, was dismayed by none of the elements that troubled Einstein. He made his own peace with the contradictions by proposing a principle of complementarity that emphasized the role of the observer over the observed.

Post-revolution: First stage

As mentioned above, Einstein's position underwent significant modifications over the course of the years. In the first stage, Einstein refused to accept quantum indeterminism and sought to demonstrate that the principle of indeterminacy could be violated, suggesting ingenious thought experiments which should permit the accurate determination of incompatible variables, such as position and velocity, or to explicitly reveal simultaneously the wave and the particle aspects of the same process.

Einstein's argument

The first serious attack by Einstein on the "orthodox" conception took place during the Fifth Solvay International Conference on Electrons and Photons in 1927. Einstein pointed out how it was possible to take advantage of the (universally accepted) laws of conservation of energy and of impulse (momentum) in order to obtain information on the state of a particle in a process of interference which, according to the principle of indeterminacy or that of complementarity, should not be accessible. 

Figure A. A monochromatic beam (one for which all the particles have the same impulse) encounters a first screen, diffracts, and the diffracted wave encounters a second screen with two slits, resulting in the formation of an interference figure on the background F. As always, it is assumed that only one particle at a time is able to pass the entire mechanism. From the measure of the recoil of the screen S₁, according to Einstein, one can deduce from which slit the particle has passed without destroying the wave aspects of the process.

 

Figure B. Einstein's slit.

 

In order to follow his argumentation and to evaluate Bohr's response, it is convenient to refer to the experimental apparatus illustrated in figure A. A beam of light perpendicular to the X axis propagates in the direction z and encounters a screen S₁ with a narrow (relative to the wavelength of the ray) slit. After having passed through the slit, the wave function diffracts with an angular opening that causes it to encounter a second screen S₂ with two slits. The successive propagation of the wave results in the formation of the interference figure on the final screen F. 

At the passage through the two slits of the second screen S₂, the wave aspects of the process become essential. In fact, it is precisely the interference between the two terms of the quantum superposition corresponding to states in which the particle is localized in one of the two slits which implies that the particle is "guided" preferably into the zones of constructive interference and cannot end up in a point in the zones of destructive interference (in which the wave function is nullified). It is also important to note that any experiment designed to evidence the "corpuscular" aspects of the process at the passage of the screen S₂ (which, in this case, reduces to the determination of which slit the particle has passed through) inevitably destroys the wave aspects, implies the disappearance of the interference figure and the emergence of two concentrated spots of diffraction which confirm our knowledge of the trajectory followed by the particle.

At this point Einstein brings into play the first screen as well and argues as follows: since the incident particles have velocities (practically) perpendicular to the screen S₁, and since it is only the interaction with this screen that can cause a deflection from the original direction of propagation, by the law of conservation of impulse which implies that the sum of the impulses of two systems which interact is conserved, if the incident particle is deviated toward the top, the screen will recoil toward the bottom and vice versa. In realistic conditions the mass of the screen is so large that it will remain stationary, but, in principle, it is possible to measure even an infinitesimal recoil. If we imagine taking the measurement of the impulse of the screen in the direction X after every single particle has passed, we can know, from the fact that the screen will be found recoiled toward the top (bottom), whether the particle in question has been deviated toward the bottom or top, and therefore through which slit in S₂ the particle has passed. But since the determination of the direction of the recoil of the screen after the particle has passed cannot influence the successive development of the process, we will still have an interference figure on the screen F. The interference takes place precisely because the state of the system is the superposition of two states whose wave functions are non-zero only near one of the two slits. On the other hand, if every particle passes through only the slit b or the slit c, then the set of systems is the statistical mixture of the two states, which means that interference is not possible. If Einstein is correct, then there is a violation of the principle of indeterminacy.

Bohr's response

Bohr's response was to illustrate Einstein's idea more clearly using the diagram in Figure C. (Figure C shows a fixed screen S₁ that is bolted down. Then try to imagine one that can slide up or down along a rod instead of a fixed bolt.) Bohr observes that extremely precise knowledge of any (potential) vertical motion of the screen is an essential presupposition in Einstein's argument. In fact, if its velocity in the direction X before the passage of the particle is not known with a precision substantially greater than that induced by the recoil (that is, if it were already moving vertically with an unknown and greater velocity than that which it derives as a consequence of the contact with the particle), then the determination of its motion after the passage of the particle would not give the information we seek. However, Bohr continues, an extremely precise determination of the velocity of the screen, when one applies the principle of indeterminacy, implies an inevitable imprecision of its position in the direction X. Before the process even begins, the screen would therefore occupy an indeterminate position at least to a certain extent (defined by the formalism). Now consider, for example, the point d in figure A, where the interference is destructive. Any displacement of the first screen would make the lengths of the two paths, a–b–d and a–c–d, different from those indicated in the figure. If the difference between the two paths varies by half a wavelength, at point d there will be constructive rather than destructive interference. The ideal experiment must average over all the possible positions of the screen S₁, and, for every position, there corresponds, for a certain fixed point F, a different type of interference, from the perfectly destructive to the perfectly constructive. The effect of this averaging is that the pattern of interference on the screen F will be uniformly grey. Once more, our attempt to evidence the corpuscular aspects in S₂ has destroyed the possibility of interference in F, which depends crucially on the wave aspects. 

Figure C. In order to realize Einstein's proposal, it is necessary to replace the first screen in Figure A (S₁) with a diaphragm that can move vertically, such as this proposed by Bohr.

 

It should be noted that, as Bohr recognized, for the understanding of this phenomenon "it is decisive that, contrary to genuine instruments of measurement, these bodies along with the particles would constitute, in the case under examination, the system to which the quantum-mechanical formalism must apply. With respect to the precision of the conditions under which one can correctly apply the formalism, it is essential to include the entire experimental apparatus. In fact, the introduction of any new apparatus, such as a mirror, in the path of a particle could introduce new effects of interference which influence essentially the predictions about the results which will be registered at the end." Further along, Bohr attempts to resolve this ambiguity concerning which parts of the system should be considered macroscopic and which not:

In particular, it must be very clear that...the unambiguous use of spatiotemporal concepts in the description of atomic phenomena must be limited to the registration of observations which refer to images on a photographic lens or to analogous practically irreversible effects of amplification such as the formation of a drop of water around an ion in a dark room.

Bohr's argument about the impossibility of using the apparatus proposed by Einstein to violate the principle of indeterminacy depends crucially on the fact that a macroscopic system (the screen S₁) obeys quantum laws. On the other hand, Bohr consistently held that, in order to illustrate the microscopic aspects of reality, it is necessary to set off a process of amplification, which involves macroscopic apparatuses, whose fundamental characteristic is that of obeying classical laws and which can be described in classical terms. This ambiguity would later come back in the form of what is still called today the measurement problem.

The principle of indeterminacy applied to time and energy

Figure D. A wave extended longitudinally passes through a slit which remains open only for a brief interval of time. Beyond the slit, there is a spatially limited wave in the direction of propagation.

 

In many textbook examples and popular discussions of quantum mechanics, the principle of indeterminacy is explained by reference to the pair of variables position and velocity (or momentum). It is important to note that the wave nature of physical processes implies that there must exist another relation of indeterminacy: that between time and energy. In order to comprehend this relation, it is convenient to refer to the experiment illustrated in Figure D, which results in the propagation of a wave which is limited in spatial extension. Assume that, as illustrated in the figure, a ray which is extremely extended longitudinally is propagated toward a screen with a slit furnished with a shutter which remains open only for a very brief interval of time ${\displaystyle \Delta t}$. Beyond the slit, there will be a wave of limited spatial extension which continues to propagate toward the right. 

A perfectly monochromatic wave (such as a musical note which cannot be divided into harmonics) has infinite spatial extent. In order to have a wave which is limited in spatial extension (which is technically called a wave packet), several waves of different frequencies must be superimposed and distributed continuously within a certain interval of frequencies around an average value, such as ${\displaystyle \nu _{0}}$. It then happens that at a certain instant, there exists a spatial region (which moves over time) in which the contributions of the various fields of the superposition add up constructively. Nonetheless, according to a precise mathematical theorem, as we move far away from this region, the phases of the various fields, at any specified point, are distributed causally and destructive interference is produced. The region in which the wave has non-zero amplitude is therefore spatially limited. It is easy to demonstrate that, if the wave has a spatial extension equal to ${\displaystyle \Delta x}$ (which means, in our example, that the shutter has remained open for a time ${\displaystyle \Delta t=\Delta x/v}$ where v is the velocity of the wave), then the wave contains (or is a superposition of) various monochromatic waves whose frequencies cover an interval ${\displaystyle \Delta \nu }$ which satisfies the relation:

${\displaystyle \Delta \nu \geq {\frac {1}{\Delta t}}.}$

Remembering that in the universal relation of Planck, frequency and energy are proportional:

${\displaystyle E=h\nu \,}$

it follows immediately from the preceding inequality that the particle associated with the wave should possess an energy which is not perfectly defined (since different frequencies are involved in the superposition) and consequently there is indeterminacy in energy:

${\displaystyle \Delta E=h\,\Delta \nu \geq {\frac {h}{\Delta t}}.}$

From this it follows immediately that:

${\displaystyle \Delta E\,\Delta t\geq h}$

which is the relation of indeterminacy between time and energy.

Einstein's second criticism

Einstein's thought experiment of 1930 as designed by Bohr. Einstein's box was supposed to prove the violation of the indeterminacy relation between time and energy.

 

At the sixth Congress of Solvay in 1930, the indeterminacy relation just discussed was Einstein's target of criticism. His idea contemplates the existence of an experimental apparatus which was subsequently designed by Bohr in such a way as to emphasize the essential elements and the key points which he would use in his response. 

Einstein considers a box (called Einstein's box; see figure) containing electromagnetic radiation and a clock which controls the opening of a shutter which covers a hole made in one of the walls of the box. The shutter uncovers the hole for a time ${\displaystyle \Delta t}$ which can be chosen arbitrarily. During the opening, we are to suppose that a photon, from among those inside the box, escapes through the hole. In this way a wave of limited spatial extension has been created, following the explanation given above. In order to challenge the indeterminacy relation between time and energy, it is necessary to find a way to determine with adequate precision the energy that the photon has brought with it. At this point, Einstein turns to his celebrated relation between mass and energy of special relativity: ${\displaystyle E=mc^{2}}$. From this it follows that knowledge of the mass of an object provides a precise indication about its energy. The argument is therefore very simple: if one weighs the box before and after the opening of the shutter and if a certain amount of energy has escaped from the box, the box will be lighter. The variation in mass multiplied by ${\displaystyle c^{2}}$ will provide precise knowledge of the energy emitted. Moreover, the clock will indicate the precise time at which the event of the particle's emission took place. Since, in principle, the mass of the box can be determined to an arbitrary degree of accuracy, the energy emitted can be determined with a precision ${\displaystyle \Delta E}$ as accurate as one desires. Therefore, the product ${\displaystyle \Delta E\Delta t}$ can be rendered less than what is implied by the principle of indeterminacy. 

George Gamow's make-believe experimental apparatus for validating the thought experiment at the Niels Bohr Institute in Copenhagen.

 

The idea is particularly acute and the argument seemed unassailable. It's important to consider the impact of all of these exchanges on the people involved at the time. Leon Rosenfeld, a scientist who had participated in the Congress, described the event several years later:

It was a real shock for Bohr...who, at first, could not think of a solution. For the entire evening he was extremely agitated, and he continued passing from one scientist to another, seeking to persuade them that it could not be the case, that it would have been the end of physics if Einstein were right; but he couldn't come up with any way to resolve the paradox. I will never forget the image of the two antagonists as they left the club: Einstein, with his tall and commanding figure, who walked tranquilly, with a mildly ironic smile, and Bohr who trotted along beside him, full of excitement...The morning after saw the triumph of Bohr.

Bohr's Triumph

The "Triumph of Bohr" consisted in his demonstrating, once again, that Einstein's subtle argument was not conclusive, but even more so in the way that he arrived at this conclusion by appealing precisely to one of the great ideas of Einstein: the principle of equivalence between gravitational mass and inertial mass, together with the time dilation of special relativity, and a consequence of these—the Gravitational redshift. Bohr showed that, in order for Einstein's experiment to function, the box would have to be suspended on a spring in the middle of a gravitational field. In order to obtain a measurement of the weight of the box, a pointer would have to be attached to the box which corresponded with the index on a scale. After the release of a photon, a mass ${\displaystyle m}$ could be added to the box to restore it to its original position and this would allow us to determine the energy ${\displaystyle E=mc^{2}}$ that was lost when the photon left. The box is immersed in a gravitational field of strength ${\displaystyle g}$, and the gravitational redshift affects the speed of the clock, yielding uncertainty ${\displaystyle \Delta t}$ in the time ${\displaystyle t}$ required for the pointer to return to its original position. Bohr gave the following calculation establishing the uncertainty relation ${\displaystyle \Delta E\Delta t\geq h}$. 

Let the uncertainty in the mass ${\displaystyle m}$ be denoted by ${\displaystyle \Delta m}$. Let the error in the position of the pointer be ${\displaystyle \Delta q}$. Adding the load ${\displaystyle m}$ to the box imparts a momentum ${\displaystyle p}$ that we can measure with an accuracy ${\displaystyle \Delta p}$, where ${\displaystyle \Delta p\Delta q}$ ≈ ${\displaystyle h}$. Clearly ${\displaystyle \Delta p\leq tg\Delta m}$, and therefore ${\displaystyle tg\Delta m\Delta q\geq h}$. By the redshift formula (which follows from the principle of equivalence and the time dilation), the uncertainty in the time ${\displaystyle t}$ is ${\displaystyle \Delta t=c^{-2}gt\Delta q}$, and ${\displaystyle \Delta E=c^{2}\Delta m}$, and so ${\displaystyle \Delta E\Delta t=c^{2}\Delta m\Delta t\geq h}$. We have therefore proven the claimed ${\displaystyle \Delta E\Delta t\geq h}$.

Post-revolution: Second stage

The second phase of Einstein's "debate" with Bohr and the orthodox interpretation is characterized by an acceptance of the fact that it is, as a practical matter, impossible to simultaneously determine the values of certain incompatible quantities, but the rejection that this implies that these quantities do not actually have precise values. Einstein rejects the probabilistic interpretation of Born and insists that quantum probabilities are epistemic and not ontological in nature. As a consequence, the theory must be incomplete in some way. He recognizes the great value of the theory, but suggests that it "does not tell the whole story", and, while providing an appropriate description at a certain level, it gives no information on the more fundamental underlying level:

I have the greatest consideration for the goals which are pursued by the physicists of the latest generation which go under the name of quantum mechanics, and I believe that this theory represents a profound level of truth, but I also believe that the restriction to laws of a statistical nature will turn out to be transitory....Without doubt quantum mechanics has grasped an important fragment of the truth and will be a paragon for all future fundamental theories, for the fact that it must be deducible as a limiting case from such foundations, just as electrostatics is deducible from Maxwell's equations of the electromagnetic field or as thermodynamics is deducible from statistical mechanics.

These thoughts of Einstein would set off a line of research into hidden variable theories, such as the Bohm interpretation, in an attempt to complete the edifice of quantum theory. If quantum mechanics can be made complete in Einstein's sense, it cannot be done locally; this fact was demonstrated by John Stewart Bell with the formulation of Bell's inequality in 1964.

Post-revolution: Third stage

The argument of EPR

Title sections of historical papers on EPR.

In 1935 Einstein, Boris Podolsky and Nathan Rosen developed an argument, published in the magazine Physical Review with the title Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, based on an entangled state of two systems. Before coming to this argument, it is necessary to formulate another hypothesis that comes out of Einstein's work in relativity: the principle of locality. The elements of physical reality which are objectively possessed cannot be influenced instantaneously at a distance.

 

The argument of EPR was in 1957 picked up by David Bohm and Yakir Aharonov in a paper published in Physical Review with the title Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky. The authors reformulated the argument in terms of an entangled state of two particles, which can be summarized as follows: 

1) Consider a system of two photons which at time t are located, respectively, in the spatially distant regions A and B and which are also in the entangled state of polarization ${\displaystyle \left|\Psi \right\rangle }$ described below:

${\displaystyle \left|\Psi ,t\right\rangle ={\frac {1}{\sqrt {2}}}\left|1,V\right\rangle \left|2,V\right\rangle +{\frac {1}{\sqrt {2}}}\left|1,H\right\rangle \left|2,H\right\rangle .}$

2) At time t the photon in region A is tested for vertical polarization. Suppose that the result of the measurement is that the photon passes through the filter. According to the reduction of the wave packet, the result is that, at time t + dt, the system becomes

${\displaystyle \left|\Psi ,t+dt\right\rangle =\left|1,V\right\rangle \left|2,V\right\rangle .}$

3) At this point, the observer in A who carried out the first measurement on photon 1, without doing anything else that could disturb the system or the other photon ("assumption (R)", below), can predict with certainty that photon 2 will pass a test of vertical polarization. It follows that photon 2 possesses an element of physical reality: that of having a vertical polarization. 

4) According to the assumption of locality, it cannot have been the action carried out in A which created this element of reality for photon 2. Therefore, we must conclude that the photon possessed the property of being able to pass the vertical polarization test before and independently of the measurement of photon 1. 

5) At time t, the observer in A could have decided to carry out a test of polarization at 45°, obtaining a certain result, for example, that the photon passes the test. In that case, he could have concluded that photon 2 turned out to be polarized at 45°. Alternatively, if the photon did not pass the test, he could have concluded that photon 2 turned out to be polarized at 135°. Combining one of these alternatives with the conclusion reached in 4, it seems that photon 2, before the measurement took place, possessed both the property of being able to pass with certainty a test of vertical polarization and the property of being able to pass with certainty a test of polarization at either 45° or 135°. These properties are incompatible according to the formalism. 

6) Since natural and obvious requirements have forced the conclusion that photon 2 simultaneously possesses incompatible properties, this means that, even if it is not possible to determine these properties simultaneously and with arbitrary precision, they are nevertheless possessed objectively by the system. But quantum mechanics denies this possibility and it is therefore an incomplete theory.

Bohr's response

Bohr's response to this argument was published, five months later than the original publication of EPR, in the same magazine Physical Review and with exactly the same title as the original. The crucial point of Bohr's answer is distilled in a passage which he later had republished in Paul Arthur Schilpp's book Albert Einstein, scientist-philosopher in honor of the seventieth birthday of Einstein. Bohr attacks assumption (R) of EPR by stating:

The statement of the criterion in question is ambiguous with regard to the expression "without disturbing the system in any way". Naturally, in this case no mechanical disturbance of the system under examination can take place in the crucial stage of the process of measurement. But even in this stage there arises the essential problem of an influence on the precise conditions which define the possible types of prediction which regard the subsequent behaviour of the system...their arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete...This description can be characterized as a rational use of the possibilities of an unambiguous interpretation of the process of measurement compatible with the finite and uncontrollable interaction between the object and the instrument of measurement in the context of quantum theory.

Post-revolution: Fourth stage

In his last writing on the topic, Einstein further refined his position, making it completely clear that what really disturbed him about the quantum theory was the problem of the total renunciation of all minimal standards of realism, even at the microscopic level, that the acceptance of the completeness of the theory implied. Although the majority of experts in the field agree that Einstein was wrong, the current understanding is still not complete. There is no scientific consensus that determinism would have been refuted.