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Friday, December 8, 2023

Moral responsibility

From Wikipedia, the free encyclopedia

In philosophy, moral responsibility is the status of morally deserving praise, blame, reward, or punishment for an act or omission in accordance with one's moral obligations. Deciding what (if anything) counts as "morally obligatory" is a principal concern of ethics.

Philosophers refer to people who have moral responsibility for an action as "moral agents". Agents have the capability to reflect upon their situation, to form intentions about how they will act, and then to carry out that action. The notion of free will has become an important issue in the debate on whether individuals are ever morally responsible for their actions and, if so, in what sense. Incompatibilists regard determinism as at odds with free will, whereas compatibilists think the two can coexist.

Moral responsibility does not necessarily equate to legal responsibility. A person is legally responsible for an event when a legal system is liable to penalise that person for that event. Although it may often be the case that when a person is morally responsible for an act, they are also legally responsible for it, the two states do not always coincide.

Preferential promoters of the concept of personal responsibility (or some popularization thereof) may include (for example) parents, managers, politicians, technocrats, large-group awareness trainings (LGATs), and religious groups.

Some see individual responsibility as an important component of neoliberalism.

Philosophical stance

Various philosophical positions exist, disagreeing over determinism and free will.

Depending on how a philosopher conceives of free will, they will have different views on moral responsibility.

Metaphysical libertarianism

Metaphysical libertarians think actions are not always causally determined, allowing for the possibility of free will and thus moral responsibility. All libertarians are also incompatibilists; for think that if causal determinism were true of human action, people would not have free will. Accordingly, some libertarians subscribe to the principle of alternate possibilities, which posits that moral responsibility requires that people could have acted differently.

Phenomenological considerations are sometimes invoked by incompatibilists to defend a libertarian position. In daily life, we feel as though choosing otherwise is a viable option. Although this feeling doesn't firmly establish the existence of free will, some incompatibilists claim the phenomenological feeling of alternate possibilities is a prerequisite for free will.

Jean-Paul Sartre suggested that people sometimes avoid incrimination and responsibility by hiding behind determinism: "we are always ready to take refuge in a belief in determinism if this freedom weighs upon us or if we need an excuse".

A similar view is that individual moral culpability lies in individual character. That is, a person with the character of a murderer has no choice other than to murder, but can still be punished because it is right to punish those of bad character. How one's character was determined is irrelevant from this perspective. Robert Cummins, for example, argues that people should not be judged for their individual actions, but rather for how those actions "reflect on their character". If character (however defined) is the dominant causal factor in determining one's choices, and one's choices are morally wrong, then one should be held accountable for those choices, regardless of genes and other such factors.

In law, there is a known exception to the assumption that moral culpability lies in either individual character or freely willed acts. The insanity defense—or its corollary, diminished responsibility (a sort of appeal to the fallacy of the single cause)—can be used to argue that the guilty deed was not the product of a guilty mind. In such cases, the legal systems of most Western societies assume that the person is in some way not at fault, because his actions were a consequence of abnormal brain function (implying brain function is a deterministic causal agent of mind and motive).

The argument from luck

The argument from luck is a criticism against the libertarian conception of moral responsibility. It suggests that any given action, and even a person's character, is the result of various forces outside a person's control. It may not be appropriate, then, to hold that person solely morally responsible. Thomas Nagel suggests that four different types of luck (including genetic influences and other external factors) end up influencing the way that a person's actions are evaluated morally. For instance, a person driving drunk may make it home without incident, and yet this action of drunk driving might seem more morally objectionable if someone happens to jaywalk along his path (getting hit by the car).

This argument can be traced back to David Hume. If physical indeterminism is true, then those events that are not determined are scientifically described as probabilistic or random. It is therefore argued that it is doubtful that one can praise or blame someone for performing an action generated randomly by his nervous system (without there being any non-physical agency responsible for the observed probabilistic outcome).

Hard determinism

Hard determinists (not to be confused with fatalists) often use liberty in practical moral considerations, rather than a notion of a free will. Indeed, faced with the possibility that determinism requires a completely different moral system, some proponents say "So much the worse for free will!". Clarence Darrow, the famous defense attorney, pleaded the innocence of his clients, Leopold and Loeb, by invoking such a notion of hard determinism. During his summation, he declared:

What has this boy to do with it? He was not his own father; he was not his own mother; he was not his own grandparents. All of this was handed to him. He did not surround himself with governesses and wealth. He did not make himself. And yet he is to be compelled to pay.

Paul the Apostle, in his Epistle to the Romans addresses the question of moral responsibility as follows: "Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?" In this view, individuals can still be dishonoured for their acts even though those acts were ultimately completely determined by God.

Joshua Greene and Jonathan Cohen, researchers in the emerging field of neuroethics, argue, on the basis of such cases, that our current notion of moral responsibility is founded on libertarian (and dualist) intuitions. They argue that cognitive neuroscience research (e.g. neuroscience of free will) is undermining these intuitions by showing that the brain is responsible for our actions, not only in cases of florid psychosis, but also in less obvious situations. For example, damage to the frontal lobe reduces the ability to weigh uncertain risks and make prudent decisions, and therefore leads to an increased likelihood that someone will commit a violent crime. This is true not only of patients with damage to the frontal lobe due to accident or stroke, but also of adolescents, who show reduced frontal lobe activity compared to adults, and even of children who are chronically neglected or mistreated. In each case, the guilty party can, they argue, be said to have less responsibility for his actions. Greene and Cohen predict that, as such examples become more common and well known, jurors’ interpretations of free will and moral responsibility will move away from the intuitive libertarian notion that currently underpins them. They also argue that the legal system does not require this libertarian interpretation. Rather, they suggest that only retributive notions of justice, in which the goal of the legal system is to punish people for misdeeds, require the libertarian intuition. Many forms of ethically realistic and consequentialist approaches to justice, which are aimed at promoting future welfare rather than retribution, can survive even a hard determinist interpretation of free will. Accordingly, the legal system and notions of justice can thus be maintained even in the face of emerging neuroscientific evidence undermining libertarian intuitions of free will.

David Eagleman explains that nature and nurture cause all criminal behavior. He likewise believes that science demands that change and improvement, rather than guilt, must become the focus of the legal justice system.

Neuroscientist David Eagleman maintains similar ideas. Eagleman says that the legal justice system ought to become more forward looking. He says it is wrong to ask questions of narrow culpability, rather than focusing on what is important: what needs to change in a criminal's behavior and brain. Eagleman is not saying that no one is responsible for their crimes, but rather that the "sentencing phase" should correspond with modern neuroscientific evidence. To Eagleman, it is damaging to entertain the illusion that a person can make a single decision that is somehow, suddenly, independent of their physiology and history. He describes what scientists have learned from brain damaged patients, and offers the case of a school teacher who exhibited escalating pedophilic tendencies on two occasions—each time as results of growing tumors. Eagleman also warns that less attractive people and minorities tend to get longer sentencing—all of which he sees as symptoms that more science is needed in the legal system.

Hard incompatibilism

Derk Pereboom defends a skeptical position about free will he calls hard incompatibilism. In his view, we cannot have free will if our actions are causally determined by factors beyond our control, or if our actions are indeterministic events—if they happen by chance. Pereboom conceives of free will as the control in action required for moral responsibility in the sense involving deserved blame and praise, punishment and reward. While he acknowledges that libertarian agent causation, the capacity of agents as substances to cause actions without being causally determined by factors beyond their control, is still a possibility, he regards it as unlikely against the backdrop of the most defensible physical theories. Without libertarian agent causation, Pereboom thinks the free will required for moral responsibility in the desert-involving sense is not in the offing. However, he also contends that by contrast with the backward-looking, desert-involving sense of moral responsibility, forward-looking senses are compatible with causal determination. For instance, causally determined agents who act badly might justifiably be blamed with the aim of forming faulty character, reconciling impaired relationships, and protecting others from harm they are apt to cause.

Pereboom proposes that a viable criminal jurisprudence is compatible with the denial of deserved blame and punishment. His view rules out retributivist justifications for punishment, but it allows for incapacitation of dangerous criminals on the analogy with quarantine of carriers of dangerous diseases. Isolation of carriers of the Ebola virus can be justified on the ground of the right to defend against threat, a justification that does not reference desert. Pereboom contends that the analogy holds for incapacitation of dangerous criminals. He also argues that the less serious the threat, the more moderate the justifiable method of incapacitation; for certain crimes only monitoring may be needed. In addition, just as we should do what we can, within reasonable bounds, to cure the carriers of the Ebola virus we quarantine, so we should aim to rehabilitate and reintegrate the criminals we incapacitate. Pereboom also proposes that given hard incompatibilism, punishment justified as general deterrence may be legitimate when the penalties don't involve undermining an agent's capacity to live a meaningful, flourishing life, since justifying such moderate penalties need not invoke desert.

Compatibilism

Some forms of compatibilism suggest the term free will should only be used to mean something more like liberty.

Compatibilists contend that even if determinism were true, it would still be possible for us to have free will. The Hindu text The Bhagavad Gita offers one very early compatibilist account. Facing the prospect of going to battle against kinsmen to whom he has bonds, Arjuna despairs. Krishna attempts to assuage Arjuna's anxieties. He argues that forces of nature come together to produce actions, and it is only vanity that causes us to regard ourselves as the agent in charge of these actions. However, Krishna adds this caveat: "... [But] the Man who knows the relation between the forces of Nature and actions, witnesses how some forces of Nature work upon other forces of Nature, and becomes [not] their slave..." When we are ignorant of the relationship between forces of Nature, we become passive victims of nomological facts. Krishna's admonition is intended to get Arjuna to perform his duty (i.e., fight in the battle), but he is also claiming that being a successful moral agent requires being mindful of the wider circumstances in which one finds oneself. Paramahansa Yogananda also said, "Freedom means the power to act by soul guidance, not by the compulsions of desires and habits. Obeying the ego leads to bondage; obeying the soul brings liberation."

In the Western tradition, Baruch Spinoza echoes the Bhagavad Gita's point about agents and natural forces, writing "men think themselves free because they are conscious of their volitions and their appetite, and do not think, even in their dreams, of the causes by which they are disposed to wanting and willing, because they are ignorant [of those causes]." Krishna is hostile to the influence of passions on our rational faculties, speaking up instead for the value of heeding the dictates of one's own nature: "Even a wise man acts under the impulse of his nature. Of what use is restraint?" Spinoza similarly identifies the taming of one's passions as a way to extricate oneself from merely being passive in the face of external forces and a way toward following our own natures.

Jesus asserted that "There is a path that SEEMS right to a man which leads to Destruction". The contrapositive (equivalent) is the origin of this position of Spinoza. "If a man is Not on the road to destruction, then he has not taken the path that ONLY SEEMS right to him."

P.F. Strawson is a major example of a contemporary compatibilist. His paper "Freedom and Resentment," which adduces reactive attitudes, has been widely cited as an important response to incompatibilist accounts of free will. Other compatibilists, who have been inspired by Strawson's paper, are as follows: Gary Watson, Susan Wolf, R. Jay Wallace, Paul Russell, and David Shoemaker.

Other views

Daniel Dennett asks why anyone would care about whether someone had the property of responsibility and speculates that the idea of moral responsibility may be "a purely metaphysical hankering". In this view, the denial of moral responsibility is the moral hankering to be able to assert that one has some fictitious right such as asserting PARENTAL rights instead of parent responsibility.

Bruce Waller has argued, in Against Moral Responsibility (MIT Press), that moral responsibility "belongs with the ghosts and gods and that it cannot survive in a naturalistic environment devoid of miracles". We cannot punish another for wrong acts committed, contends Waller, because the causal forces which precede and have brought about the acts may ultimately be reduced to luck, namely, factors over which the individual has no control. One may not be blamed even for one’s character traits, he maintains, since they too are heavily influenced by evolutionary, environmental, and genetic factors (inter alia). Although his view would fall in the same category as the views of philosophers like Dennett who argue against moral responsibility, Waller's view differs in an important manner: He tries to, as he puts it, "rescue" free will from moral responsibility (See Chapter 3). This move goes against the commonly held assumption that how one feels about free will is ipso facto a claim about moral responsibility.

Epistemic condition for moral responsibility

In philosophical discussions of moral responsibility, two necessary conditions are usually cited: the control (or freedom) condition (which answers the question 'did the individual doing the action in question have free will?') and the epistemic condition, the former of which is explored in the above discussion. The epistemic condition, in contrast to the control condition, focuses on the question 'was the individual aware of, for instance, the moral implications of what she did?' Not all philosophers think this condition to be a distinct condition, separate from the control condition: For instance, Alfred Mele thinks that the epistemic condition is a component of the control condition. Nonetheless, there seems to be philosophical consensus of sorts that it is both distinct and explanatorily relevant. One major concept associated with the condition is "awareness". According to those philosophers who affirm this condition, one needs to be "aware" of four things to be morally responsible: the action (which one is doing), its moral significance, consequences, and alternatives.

Experimental research

Mauro suggests that a sense of personal responsibility does not operate or evolve universally among humankind. He argues that it was absent in the successful civilization of the Iroquois.

In recent years, research in experimental philosophy has explored whether people's untutored intuitions about determinism and moral responsibility are compatibilist or incompatibilist. Some experimental work has included cross-cultural studies. However, the debate about whether people naturally have compatibilist or incompatibilist intuitions has not come out overwhelmingly in favor of one view or the other, finding evidence for both views. For instance, when people are presented with abstract cases that ask if a person could be morally responsible for an immoral act when they could not have done otherwise, people tend to say no, or give incompatibilist answers. When presented with a specific immoral act that a specific person committed, people tend to say that that person is morally responsible for their actions, even if they were determined (that is, people also give compatibilist answers).

The neuroscience of free will investigates various experiments that might shed light on free will.

Collective

When people attribute moral responsibility, they usually attribute it to individual moral agents. However, Joel Feinberg, among others, has argued that corporations and other groups of people can have what is called ‘collective moral responsibility’ for a state of affairs. For example, when South Africa had an apartheid regime, the country's government might have been said to have had collective moral responsibility for the violation of the rights of non-European South Africans.

Psychopathy's lack of sense of responsibility

One of the attributes defined for psychopathy is "failure to accept responsibility for own actions".

Artificial systems

The emergence of automation, robotics and related technologies prompted the question, 'Can an artificial system be morally responsible?' The question has a closely related variant, 'When (if ever) does moral responsibility transfer from its human creator(s) to the system?'.

The questions arguably adjoin with but are distinct from machine ethics, which is concerned with the moral behavior of artificial systems. Whether an artificial system's behavior qualifies it to be morally responsible has been a key focus of debate.

Arguments that artificial systems cannot be morally responsible

Batya Friedman and Peter Kahn Jr. posited that intentionality is a necessary condition for moral responsibility, and that computer systems as conceivable in 1992 in material and structure could not have intentionality.

Arthur Kuflik asserted that humans must bear the ultimate moral responsibility for a computer's decisions, as it is humans who design the computers and write their programs. He further proposed that humans can never relinquish oversight of computers.

Frances Grodzinsky et al. considered artificial systems that could be modelled as finite state machines. They posited that if the machine had a fixed state transition table, then it could not be morally responsible. If the machine could modify its table, then the machine's designer still retained some moral responsibility.

Patrick Hew argued that for an artificial system to be morally responsible, its rules for behaviour and the mechanisms for supplying those rules must not be supplied entirely by external humans. He further argued that such systems are a substantial departure from technologies and theory as extant in 2014. An artificial system based on those technologies will carry zero responsibility for its behaviour. Moral responsibility is apportioned to the humans that created and programmed the system.

(A more extensive review of arguments may be found in.)

Arguments that artificial systems can be morally responsible

Colin Allen et al. proposed that an artificial system may be morally responsible if its behaviours are functionally indistinguishable from a moral person, coining the idea of a 'Moral Turing Test'. They subsequently disavowed the Moral Turing Test in recognition of controversies surrounding the Turing Test.

Andreas Matthias described a 'responsibility gap' where to hold humans responsible for a machine would be an injustice, but to hold the machine responsible would challenge 'traditional' ways of ascription. He proposed three cases where the machine's behaviour ought to be attributed to the machine and not its designers or operators. First, he argued that modern machines are inherently unpredictable (to some degree), but perform tasks that need to be performed yet cannot be handled by simpler means. Second, that there are increasing 'layers of obscurity' between manufacturers and system, as hand coded programs are replaced with more sophisticated means. Third, in systems that have rules of operation that can be changed during the operation of the machine.

Trade-off

From Wikipedia, the free encyclopedia

A trade-off (or tradeoff) is a situational decision that involves diminishing or losing on quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and another must decrease. Tradeoffs stem from limitations of many origins, including simple physics – for instance, only a certain volume of objects can fit into a given space, so a full container must remove some items in order to accept any more, and vessels can carry a few large items or multiple small items. Tradeoffs also commonly refer to different configurations of a single item, such as the tuning of strings on a guitar to enable different notes to be played, as well as an allocation of time and attention towards different tasks.

The concept of a tradeoff suggests a tactical or strategic choice made with full comprehension of the advantages and disadvantages of each setup. An economic example is the decision to invest in stocks, which are risky but carry great potential return, versus bonds, which are generally safer but with lower potential returns.

Theoretical description

The theoretical description of trade-offs involves the pareto front.

Examples

The concept of a trade-off is often used to describe situations in everyday life.

Economics

In economics a trade-off is expressed in terms of the opportunity cost of a particular choice, which is the loss of the most preferred alternative given up. A tradeoff, then, involves a sacrifice that must be made to obtain a certain product, service, or experience, rather than others that could be made or obtained using the same required resources. For example, for a person going to a basketball game, their opportunity cost is the loss of the alternative of watching a particular television program at home. If the basketball game occurs during her or his working hours, then the opportunity cost would be several hours of lost work, as they would need to take time off work.

Many factors affect the tradeoff environment within a particular country, including the availability of raw materials, a skilled labor force, machinery for producing a product, technology and capital, market rate to produce that product on a reasonable time scale, and so forth.

A trade-off in economics is often illustrated graphically by a Pareto frontier (named after the economist Vilfredo Pareto), which shows the greatest (or least) amount of one thing that can be attained for each of various given amounts of the other. As an example, in production theory, the trade-off between the output of one good and the output of another is illustrated graphically by the production possibilities frontier. The Pareto frontier is also used in multi-objective optimization. In finance, the capital asset pricing model includes an efficient frontier that shows the highest level of expected return that any portfolio could have given any particular level of risk, as measured by the variance of portfolio return.

Opportunity cost

An opportunity cost example of trade-offs for an individual would be the decision by a full-time worker to take time off work with a salary of $50,000 to attend medical school with an annual tuition of $30,000 and earning $150,000 as a doctor after 7 years of study. If we assume for the sake of simplicity that the medical school only allows full-time study, then the individual considering stopping work would face a trade-off between not going to medical school and earning $50,000 at work, or going to medical school and losing $50,000 in salary and having to pay $30,000 in tuition but earning $150,000 or more per year after 7 years of study.

Trash cans

Trash cans that are used inside and then taken out to the street and emptied into a dumpster can be small or large. A large trash can does not need to be taken out to the dumpster so often, but it may become very heavy and difficult to move when full. The choice of big versus small trash can is a trade-off between the frequency of needing to take out the trash and ease of use.

In the case of food waste, a second trade-off presents itself. Large trash cans are more likely to sit for a long time in the kitchen, leading to the food decomposing and a nasty odor. A small trash can will likely need to be taken out to the dumpster more often, thus greatly reducing or eliminating the odor. Of course, a user of a large trash can could simply carry the can outside frequently, but the larger can would be more cumbersome to take out often, and the user would have to think more about when to take the can out.

Mittens

In cold climates, mittens in which all the fingers are in the same compartment work well to keep the hands warm, but this arrangement also confines finger movement and prevents the full range of hand function. Gloves, with their separate fingers, do not have this drawback, but they do not keep the fingers as warm as mittens do. As such, with mittens and gloves, the trade-off is warmth versus dexterity. Similarly, warm coats are often bulky and impede the wearer's freedom of movement. Thin coats give the wearer more freedom of movement, but they are not as warm as a thicker coat would be.

Music

When copying music from compact discs to a computer, lossy compression formats, such as MP3, are used routinely to save hard disk space, but some information is lost resulting in lower sound quality. Lossless compression schemes, such as FLAC or ALAC take much more disk space, but do not affect sound quality.

Cars

Large cars can carry many people, and since they have larger crumple zones, they may be safer in an accident. However, they also tend to be heavy (and often not very aerodynamic) and thus usually have relatively poor fuel economy. Small cars like the Smart Car can only carry two people, and being lightweight, they are more fuel-efficient. At the same time, the smaller size and weight of small cars mean that they have smaller crumple zones, which means occupants are less protected in case of an accident. In addition, if a small car has an accident with a larger, heavier car, the occupants of the smaller car will fare more poorly. Thus car size (large versus small) involves multiple tradeoffs regarding passenger capacity, accident safety, and fuel economy.

Athletics

In athletics, sprint running demands different physical attributes from running a marathon. Accordingly, the two contests have distinct events in such competitions as the Olympics, and each pursuit features distinct teams of athletes. Whether a professional runner is better suited to marathon running versus sprinting is a trade-off based on the runner's morphology and physiology (e.g., variation in muscle fiber type), as well as the runner's individual interest, preference, and other motivational factors. Sports recruiters are mindful of these tradeoffs as they decide what role a prospective athlete would best suit on a team.

Biology

In biology, several types of tradeoffs have been recognized. Most simply, a tradeoff occurs when a beneficial change in one trait is linked to a detrimental change in another trait. In environmental resource management, trade-offs occur among different targets. For example, these occur among biodiversity conservation, carbon sequestration and distributive equity in the distribution of funds of the program for Reducing Emissions from Deforestation and forest Degradation (REDD+), as maximizing one of these targets implies reducing the outcomes in the other two targets.

The term is also used widely in an evolutionary context, in which case the processes of natural selection and sexual selection are in reference as the ultimate decisive factors. In biology, the concepts of tradeoffs and constraints are often closely related.

Demography

In demography, tradeoff examples may include maturity, fecundity, parental care, parity, senescence, and mate choice. For example, the higher the fecundity (number of offspring), the lower the parental care that each offspring will receive. Parental care as a function of fecundity would show a negative sloped linear graph. A related phenomenon, known as demographic compensation, arises when the different components of species life cycles (survival, growth, fecundity, etc.) show negative correlations across the distribution ranges. For example, survival may be higher towards the northern edge of the distribution, while fecundity or growth increases towards the south, leading to a compensation that allows the species to persist along an environmental gradient. Contrasting trends in life cycle components may arise through tradeoffs in resource allocation, but also through independent but opposite responses to environmental conditions.

Engineering

Tradeoffs are important in engineering. For example, in electrical engineering, negative feedback is used in amplifiers to trade gain for other desirable properties, such as improved bandwidth, stability of the gain and/or bias point, noise immunity, and reduction of nonlinear distortion. Similarly, tradeoffs are used to maximize power efficiency in medical devices whilst guaranteeing the required measurement quality.

Computer science

In computer science, tradeoffs are viewed as a tool of the trade. A program can often run faster if it uses more memory (a space–time tradeoff). Consider the following examples:

  • By compressing an image, you can reduce transmission time/costs at the expense of CPU time to perform the compression and decompression. Depending on the compression method, this may also involve the tradeoff of a loss in image quality.
  • By using a lookup table, you may be able to reduce CPU time at the expense of space to hold the table, e.g. to determine the parity of a byte you can either look at each bit individually (using shifts and masks), or use a 256-entry table giving the parity for each possible bit-pattern, or combine the upper and lower nibbles and use a 16-entry table.
  • For some situations (e.g. string manipulation), a compiler may be able to use inline code for greater speed, or call run-time routines for reduced memory; the user of the compiler should be able to indicate whether speed or space is more important.

The Software Engineering Institute has a specific method for analyzing tradeoffs, called the Architecture Tradeoff Analysis Method (ATAM).

Board games

Strategy board games often involve tradeoffs: for example, in chess you might trade a pawn for an improved position. In a worst-case scenario, a chess player might even tradeoff the loss of a valuable piece (even the Queen) to protect the King. In Go, you might trade thickness for influence.

Ethics

Ethics often involves competing for interests that must be traded off against each other, such as the interests of different people, or different principles (e.g. is it ethical to use information resulting from inhumane or illegal experiments to treat disease today?)

Medicine

In medicine, patients and physicians are often faced with difficult decisions involving tradeoffs. One example is localized prostate cancer where patients need to weigh the possibility of a prolonged life expectancy against possible stressful or unpleasant treatment side-effects (patient trade-off).

Government

Governmental tradeoffs are among the most controversial political and social difficulties of any time. All of politics can be viewed as a series of tradeoffs based upon which core values are most core to most people or politicians. Political campaigns also involve tradeoffs, as when attack ads may energize the political base but alienate undecided voters.

Work schedules

With work schedules, employees will often use a tradeoff of "9/80" where an 80-hour work period is compressed into a narrow group of 9 nearly-9 hour working days over the traditional 10 8-hour working days, allowing the employee to take every second Friday off.

Atomic radius

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Atomic_radius
Diagram of a helium atom, showing the electron probability density as shades of gray.

The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Four widely used definitions of atomic radius are: Van der Waals radius, ionic radius, metallic radius and covalent radius. Typically, because of the difficulty to isolate atoms in order to measure their radii separately, atomic radius is measured in a chemically bonded state; however theoretical calculations are simpler when considering atoms in isolation. The dependencies on environment, probe, and state lead to a multiplicity of definitions.

Depending on the definition, the term may apply to atoms in condensed matter, covalently bonding in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. The value of the radius may depend on the atom's state and context.

Electrons do not have definite orbits nor sharply defined ranges. Rather, their positions must be described as probability distributions that taper off gradually as one moves away from the nucleus, without a sharp cutoff; these are referred to as atomic orbitals or electron clouds. Moreover, in condensed matter and molecules, the electron clouds of the atoms usually overlap to some extent, and some of the electrons may roam over a large region encompassing two or more atoms.

Under most definitions the radii of isolated neutral atoms range between 30 and 300 pm (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm), and less than 1/1000 of the wavelength of visible light (400–700 nm).

The approximate shape of a molecule of ethanol, CH3CH2OH. Each atom is modeled by a sphere with the element's Van der Waals radius.

For many purposes, atoms can be modeled as spheres. This is only a crude approximation, but it can provide quantitative explanations and predictions for many phenomena, such as the density of liquids and solids, the diffusion of fluids through molecular sieves, the arrangement of atoms and ions in crystals, and the size and shape of molecules.

History

In 1920, shortly after it had become possible to determine the sizes of atoms using X-ray crystallography, it was suggested that all atoms of the same element have the same radii. However, in 1923, when more crystal data had become available, it was found that the approximation of an atom as a sphere does not necessarily hold when comparing the same atom in different crystal structures.

Definitions

Widely used definitions of atomic radius include:

  • Van der Waals radius: In the simplest definition, half the minimum distance between the nuclei of two atoms of the element that are not otherwise bound by covalent or metallic interactions. The Van der Waals radius may be defined even for elements (such as metals) in which Van der Waals forces are dominated by other interactions. Because Van der Waals interactions arise through quantum fluctuations of the atomic polarisation, the polarisability (which can usually be measured or calculated more easily) may be used to define the Van der Waals radius indirectly.
  • Ionic radius: the nominal radius of the ions of an element in a specific ionization state, deduced from the spacing of atomic nuclei in crystalline salts that include that ion. In principle, the spacing between two adjacent oppositely charged ions (the length of the ionic bond between them) should equal the sum of their ionic radii.
  • Covalent radius: the nominal radius of the atoms of an element when covalently bound to other atoms, as deduced from the separation between the atomic nuclei in molecules. In principle, the distance between two atoms that are bound to each other in a molecule (the length of that covalent bond) should equal the sum of their covalent radii.
  • Metallic radius: the nominal radius of atoms of an element when joined to other atoms by metallic bonds.
  • Bohr radius: the radius of the lowest-energy electron orbit predicted by Bohr model of the atom (1913). It is only applicable to atoms and ions with a single electron, such as hydrogen, singly ionized helium, and positronium. Although the model itself is now obsolete, the Bohr radius for the hydrogen atom is still regarded as an important physical constant, because it is equivalent to the quantum-mechanical most probable distance of the electron from the nucleus.

Empirically measured atomic radius

The following table shows empirically measured covalent radii for the elements, as published by J. C. Slater in 1964. The values are in picometers (pm or 1×10−12 m), with an accuracy of about 5 pm. The shade of the box ranges from red to yellow as the radius increases; gray indicates lack of data.

Group
(column)
1 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period
(row)

1 H
25

He
 
2 Li
145
Be
105

B
85
C
70
N
65
O
60
F
50
Ne
 
3 Na
180
Mg
150

Al
125
Si
110
P
100
S
100
Cl
100
Ar
 
4 K
220
Ca
180

Sc
160
Ti
140
V
135
Cr
140
Mn
140
Fe
140
Co
135
Ni
135
Cu
135
Zn
135
Ga
130
Ge
125
As
115
Se
115
Br
115
Kr
 
5 Rb
235
Sr
200

Y
180
Zr
155
Nb
145
Mo
145
Tc
135
Ru
130
Rh
135
Pd
140
Ag
160
Cd
155
In
155
Sn
145
Sb
145
Te
140
I
140
Xe
 
6 Cs
260
Ba
215
*
 
Lu
175
Hf
155
Ta
145
W
135
Re
135
Os
130
Ir
135
Pt
135
Au
135
Hg
150
Tl
190
Pb
180
Bi
160
Po
190
At
 
Rn
 
7 Fr
 
Ra
215
**
 
Lr
 
Rf
 
Db
 
Sg
 
Bh
 
Hs
 
Mt
 
Ds
 
Rg
 
Cn
 
Nh
 
Fl
 
Mc
 
Lv
 
Ts
 
Og
 




*
 
La
195
Ce
185
Pr
185
Nd
185
Pm
185
Sm
185
Eu
185
Gd
180
Tb
175
Dy
175
Ho
175
Er
175
Tm
175
Yb
175



**
 
Ac
195
Th
180
Pa
180
U
175
Np
175
Pu
175
Am
175
Cm
 
Bk
 
Cf
 
Es
 
Fm
 
Md
 
No
 

Explanation of the general trends

A graph comparing the atomic radius of elements with atomic numbers 1–100. Accuracy of ±5 pm.

The way the atomic radius varies with increasing atomic number can be explained by the arrangement of electrons in shells of fixed capacity. The shells are generally filled in order of increasing radius, since the negatively charged electrons are attracted by the positively charged protons in the nucleus. As the atomic number increases along each row of the periodic table, the additional electrons go into the same outermost shell; whose radius gradually contracts, due to the increasing nuclear charge. In a noble gas, the outermost shell is completely filled; therefore, the additional electron of next alkali metal will go into the next outer shell, accounting for the sudden increase in the atomic radius.

The increasing nuclear charge is partly counterbalanced by the increasing number of electrons, a phenomenon that is known as shielding; which explains why the size of atoms usually increases down each column. However, there is one notable exception, known as the lanthanide contraction: the 5d block of elements are much smaller than one would expect, due to the weak shielding of the 4f electrons.

Essentially, the atomic radius decreases across the periods due to an increasing number of protons. Therefore, there is a greater attraction between the protons and electrons because opposite charges attract, and more protons create a stronger charge. The greater attraction draws the electrons closer to the protons, decreasing the size of the particle. Therefore, the atomic radius decreases. Down the groups, atomic radius increases. This is because there are more energy levels and therefore a greater distance between protons and electrons. In addition, electron shielding causes attraction to decrease, so remaining electrons can go farther away from the positively charged nucleus. Therefore, the size, or atomic radius, increases.

The following table summarizes the main phenomena that influence the atomic radius of an element:

factor principle increase with... tend to effect on radius
electron shells quantum mechanics principal and azimuthal quantum numbers increase down each column increases the atomic radius
nuclear charge attractive force acting on electrons by protons in nucleus atomic number increase along each period (left to right) decreases the atomic radius
shielding repulsive force acting on outermost shell electrons by inner electrons number of electrons in inner shells reduce the effect of nuclear charge increases the atomic radius

Lanthanide contraction

The electrons in the 4f-subshell, which is progressively filled from lanthanum (Z = 57) to ytterbium (Z = 70), are not particularly effective at shielding the increasing nuclear charge from the sub-shells further out. The elements immediately following the lanthanides have atomic radii which are smaller than would be expected and which are almost identical to the atomic radii of the elements immediately above them. Hence lutetium is in fact slightly smaller than yttrium, hafnium has virtually the same atomic radius (and chemistry) as zirconium, and tantalum has an atomic radius similar to niobium, and so forth. The effect of the lanthanide contraction is noticeable up to platinum (Z = 78), after which it is masked by a relativistic effect known as the inert-pair effect.

Due to lanthanide contraction, the 5 following observations can be drawn:

  1. The size of Ln3+ ions regularly decreases with atomic number. According to Fajans' rules, decrease in size of Ln3+ ions increases the covalent character and decreases the basic character between Ln3+ and OH ions in Ln(OH)3, to the point that Yb(OH)3 and Lu(OH)3 can dissolve with difficulty in hot concentrated NaOH. Hence the order of size of Ln3+ is given:
    La3+ > Ce3+ > ..., ... > Lu3+.
  2. There is a regular decrease in their ionic radii.
  3. There is a regular decrease in their tendency to act as a reducing agent, with an increase in atomic number.
  4. The second and third rows of d-block transition elements are quite close in properties.
  5. Consequently, these elements occur together in natural minerals and are difficult to separate.

d-block contraction

The d-block contraction is less pronounced than the lanthanide contraction but arises from a similar cause. In this case, it is the poor shielding capacity of the 3d-electrons which affects the atomic radii and chemistries of the elements immediately following the first row of the transition metals, from gallium (Z = 31) to bromine (Z = 35).

Calculated atomic radius

The following table shows atomic radii computed from theoretical models, as published by Enrico Clementi and others in 1967. The values are in picometres (pm).

Group
(column)
1 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period
(row)

1 H
53

He
31
2 Li
167
Be
112

B
87
C
67
N
56
O
48
F
42
Ne
38
3 Na
190
Mg
145

Al
118
Si
111
P
98
S
88
Cl
79
Ar
71
4 K
243
Ca
194

Sc
184
Ti
176
V
171
Cr
166
Mn
161
Fe
156
Co
152
Ni
149
Cu
145
Zn
142
Ga
136
Ge
125
As
114
Se
103
Br
94
Kr
88
5 Rb
265
Sr
219

Y
212
Zr
206
Nb
198
Mo
190
Tc
183
Ru
178
Rh
173
Pd
169
Ag
165
Cd
161
In
156
Sn
145
Sb
133
Te
123
I
115
Xe
108
6 Cs
298
Ba
253
*
 
Lu
217
Hf
208
Ta
200
W
193
Re
188
Os
185
Ir
180
Pt
177
Au
174
Hg
171
Tl
156
Pb
154
Bi
143
Po
135
At
127
Rn
120
7 Fr
 
Ra
 
**
 
Lr
 
Rf
 
Db
 
Sg
 
Bh
 
Hs
 
Mt
 
Ds
 
Rg
 
Cn
 
Nh
 
Fl
 
Mc
 
Lv
 
Ts
 
Og
 




*
 
La
226
Ce
210
Pr
247
Nd
206
Pm
205
Sm
238
Eu
231
Gd
233
Tb
225
Dy
228
Ho
226
Er
226
Tm
222
Yb
222



**
 
Ac
 
Th
 
Pa
 
U
 
Np
 
Pu
 
Am
 
Cm
 
Bk
 
Cf
 
Es
 
Fm
 
Md
 
No

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