Beta Minus Mechanic

 



Angle beta is found by cos to the minus 1 h over CB, giving b equals 33.1 degrees. Now you have found the angles, you can find the resultant of the two forces from the force transducers. You can vector add using the cosine and sine rules, but the scheme that follows is probably easier.

The processes separately introduced at the beginning of this section as beta-minus decay, beta-plus decay, and orbital electron capture can be appropriately treated together. They all are processes whereby neutrons and protons may transform to one another by weak interaction. In striking contrast to alpha decay, the electrons (minus or plus charged) emitted in beta-minus and beta-plus decay do not exhibit sharp, discrete energy spectra but have distributions of electron energies ranging from zero up to the maximum energy release, Qβ . Furthermore, measurements of heat released by beta emitters (most radiation stopped in surrounding material is converted into heat energy) show a substantial fraction of the energy, Qβ , is missing. These observations, along with other considerations involving the spins or angular momenta of nuclei and electrons, led Wolfgang Pauli to postulate the simultaneous emission of the neutrino (1931). The neutrino, as a light and uncharged particle with nearly no interaction with matter, was supposed to carry off the missing heat energy. Today, neutrino theory is well accepted with the elaboration that there are six kinds of neutrinos, the electron neutrino, mu neutrino, and tau neutrino and corresponding antineutrinos of each. The electron neutrinos are involved in nuclear beta-decay transformations, the mu neutrinos are encountered in decay of muons to electrons, and the tau neutrinos are produced when a massive lepton called a tau breaks down.

Although in general the more energetic the beta decay the shorter is its half-life, the rate relationships do not show the clear regularities of the alpha-decay dependence on energy and atomic number.

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The first quantitative rate theory of beta decay was given by Enrico Fermi in 1934, and the essentials of this theory form the basis of modern theory. As an example, in the simplest beta-decay process, a free neutron decays into a proton, a negative electron, and an antineutrino: n → p + e− + ν. The weak interaction responsible for this process, in which there is a change of species (n to p) by a nucleon with creation of electron and antineutrino, is characterized in Fermi theory by a universal constant, g. The sharing of energy between electron and antineutrino is governed by statistical probability laws giving a probability factor for each particle proportional to the square of its linear momentum (defined by mass times velocity for speeds much less than the speed of light and by a more complicated, relativistic relation for faster speeds). The overall probability law from Fermi theory gives the probability per unit time per unit electron energy interval, P(W), as follows:in which W is the electron energy in relativistic units (W = 1 + E/m0c2) and W0 is the maximum (W0 = 1 + Qβ/m0c2), m0 the rest mass of the electron, c the speed of light, and hPlanck’s constant. This rate law expresses the neutron beta-decay spectrum in good agreement with experiment, the spectrum falling to zero at lowest energies by the factor W and falling to zero at the maximum energy by virtue of the factor (W0 − W)2.

Beta Minus Mechanic

In Fermi’s original formulation, the spins of an emitted beta and neutrino are opposing and so cancel to zero. Later work showed that neutron beta decay partly proceeds with the 1/2 ℏ spins of beta and neutrino adding to one unit of ℏ. The former process is known as Fermi decay (F) and the latter Gamow–Teller (GT) decay, after George Gamow and Edward Teller, the physicists who first proposed it. The interaction constants are determined to be in the ratio gGT2/gF2 = 1.4. Thus, g2 in equation (7) should be replaced by (gF2 + gGT2).

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The scientific world was shaken in 1957 by the measurement in beta decay of maximum violation of the law of conservation ofparity. The meaning of this nonconservation in the case of neutron beta decay considered above is that the preferred direction of electron emission is opposite to the direction of the neutron spin. By means of a magnetic field and low temperature it is possible to cause neutrons in cobalt-60 and other nuclei, or free neutrons, to have their spins set preferentially in the up direction perpendicular to the plane of the coil generating the magnetic field. The fact that beta decay prefers the down direction for spin means that the reflection of the experiment as seen in a mirror parallel to the coil represents an unphysical situation: conservation of parity, obeyed by most physical processes, demands that experiments with positions reversed by mirror reflection should also occur. Further consequences of parity violation in beta decay are that spins of emitted neutrinos and electrons are directed along the direction of flight, totally so for neutrinos and partially so by the ratio of electron speed to the speed of light for electrons.

The overall half-life for beta decay of the free neutron, measured as 12 minutes, may be related to the interaction constants g2 (equal to gF2 + gGT2) by integrating (summing) probability expression (7) over all possible electron energies from zero to the maximum. The result for the decay constant isin which W0 is the maximum beta-particle energy in relativistic units (W0 = 1 + Qβ/m0c2), with m0 the rest mass of the electron, c the speed of light, and h Planck’s constant. The best g value from decay rates is approximately 10−49 erg per cubic centimetre. As may be noted from equation (8), there is a limiting fifth-power energy dependence for highest decay energies.

In the case of a decaying neutron not free but bound within a nucleus, the above formulas must be modified. First, as the nuclear chargeZ increases, the relative probability of low-energy electron emission increases by virtue of the coulombic attraction. For positron emission, which is energetically impossible for free protons but can occur for bound protons in proton-rich nuclei, the nuclear coulomb charge suppresses lower energy positrons from the shape given by equation (7). This equation can be corrected by a factor F(Z,W) depending on the daughter atomic number Z and electron energy W. The factor can be calculated quantum mechanically. The coulomb charge also affects the overall rate expression (8) such that it can no longer be expressed as an algebraic function, but tables are available for analysis of beta decay rates. The rates are analyzed in terms of a function f(Z,Qβ) calculated by integration of equation (7) with correction factor F(Z,W).

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Approximate expressions for the f functions usable for decay energies Q between 0.1 MeV and 10 MeV, in which Q is measured in MeV, and Z is the atomic number of the daughter nucleus, are as follows (the symbol ≈ means approximately equal to):

Beta Minus Mechanic

For electron capture, a much weaker dependence on energy is found:

The basic beta decay rate expression obeyed by the class of so-called superallowed transitions, including decay of the neutron and several light nuclei is

Like the ground-to-ground alpha transitions of even–even nuclei, the superallowed beta transitions obey the basic rate law, but most beta transitions go much more slowly. The extra retardation is explained in terms of mismatched orbitals of neutrons and protons involved in the transition. For the superallowed transitions the orbitals in initial and final states are almost the same. Most of them occur between mirror nuclei, with one more or less neutron than protons; i.e., beta-minus decay of hydrogen-3, electron capture of beryllium-7 and positron emission of carbon-11, oxygen-15, neon-19, . . . titanium-43.

The nuclear retardation of beta decay rates below those of the superallowed class may be expressed in a fundamental way by multiplying the right side of equation (9) by the square of a nuclear matrix element (a quantity of quantum mechanics), which may range from unity down to zero depending on the degree of mismatch of initial and final nuclear states of internal motion. A more usual way of expressing the nuclear factor of the beta rate is the log ft value, in which f refers to the function f(Z,Qβ). Because the half-life is inversely proportional to the decay constant λ, the product fβt1⁄2 will be a measure of (inversely proportional to) the square of the nuclear matrix element. For the log ft value, the beta half-life is taken in seconds, and the ordinary logarithm to the base 10 is used. The superallowed transitions have log ft values in the range of 3 to 3.5. Beta log ft values are known up to as large as ∼ 23 in the case of indium-115. There is some correlation of log ft values with spin changes between parent and daughter nucleons, the indium-115 decay involving a spin change of four, whereas the superallowed transitions all have spin changes of zero or one.

In the first three chapters, the author presented the caste system in the Brave New World. The Caste System starts from Alphas, the best type of person, to Betas, Gammas, Deltas, and Epsilons, the worst caste to be.
The narrator makes the comment “They were Alphas, of course; but even Alphas have been well conditioned” because the students rose automatically and at once together (Huxley 26).

Beta Minus Emission

Beta
The director and the students passed through a room where 'Elementary Class Consciousness' was taking place, the voice said, “Alpha children wear grey. They work much harder than we do, because they’re so frightfully clever” (Huxley 27).

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The author explains, “a young Beta Minus mechanic was busy with screwdriver and spanner on the blood-surrogate pump of a passing bottle” (Huxley 14).
In 'Elementary Class Consciousness', the voice states, “I’m really awfully glad I’m a Beta, because I don’t work so hard.” (Huxley 27)
The voice in 'Elementary Class Conscious' is talking in the perspective of a Beta saying “Gammas are stupid. They all wear green,” (Huxley 27).

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During the hypnopaedic lessons, the narrator says, “Delta children wear khaki. Oh no, I don’t want to play with Delta children.” (Huxley 27)
Mr. Foster explains to the students passing through with the Director of Hatcheries and Conditioning, “But in Epsilons,’ said Mr. Foster very justly, ‘we don’t need human intelligence.”’ (Huxley 15)

Beta Minus Decay Formula

The importance of the above quotes is to show that within the Brave New World the ability to think does not exist due to the conditioning. A repetitive tactic is used to brainwash each class to think specific ways of each other. Each Class is predestined through conditioning to be one type of person who only can perform one job. Society in the Brave New World knows nothing of free will or the ability to think. The people are conditioned to appreciate the class they are created to be apart of in order to keep stability alive. If the people know nothing of other options, they have no desire to be something else because they only want to be apart of what they know. The World State creates an innate dislike for other classes to prevent intermingle because it could lead to thinking. Thinking will potentially result in revolt against the world state.

Beta Minus Decay

In a subpage below labeled Divergent, the caste system of the World State is compared to the caste system of Divergent.