During beta decay, one of two down quarks changes into an up quark by emitting a W - boson (carries away a negative charge). Only Q-values greater than zero (reactions that release energy) occur spontaneously. Nuclear charge distribution measurements may solve outstanding puzzle Legal. This tunneling process is alpha decay. However Wu, who was female, was not awarded the Nobel prize.[19]. Beta decay is a consequence of the weak force, which is characterized by relatively lengthy decay times. A particular type of radioactivity is known as beta-decay, which occurs in three forms known as beta-minus decay, beta-plus decay and electron capture. Particle physics: 7 Beta-decay at the level of quarks and leptons This is the Fermi-Kurie relation. Z Nuclear stability and nuclear equations (video) | Khan Academy (parallel) or Alpha decay | Definition, Example, & Facts | Britannica Both beta-plus and beta-minus, if allowed, always dominate electron capture since electron capture involves the relatively rare occurrence of a sizable overlap between electron and proton wavefunctions. In these expression we collected in the constant C various parameters deriving from the Fermi Golden Rule and density of states calculations, since we want to highlight only the dependence on the energy and momentum. [41] The resulting nucleus - 163Ho - is stable only in the fully ionized state and will decay via electron capture into 163Dy in the neutral state. (where we took \(T_{e} \approx p c\) in the relativistic limit for high electron speed). Similarly, if a neutron is converted to a proton, it is known as decay. Although neutral 163Dy is a stable isotope, the fully ionized 163Dy66+ undergoes decay into the K and L shells with a half-life of 47days. The higher the energy of the particles, the higher their polarization. In recognition of their theoretical work, Lee and Yang were awarded the Nobel Prize for Physics in 1957. {\displaystyle \eta =\pm Ze^{2}c/\hbar p} This content is excluded from the Creative Commons license. When there are too many neutrons related to the protons, negative beta decay occurs; when there are too many protons related to the neutrons, positive beta decay takes place. Corrections? \[_Z^AX\Rightarrow _{Z-1}^AX'+e^+ +v\] Beta Decay - Definition, Examples, Types, Fermi's Theory of Beta Decay This page titled 7.2: Beta Decay is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Paola Cappellaro (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Beta decay is a type of radioactive nuclear decay. In this process, a proton-rich nucleus can also reduce its nuclear charge by one unit by absorbing an . The two particles share the \(Q\) energy: For simplicity we assume that the mass of the neutrino is zero (its much smaller than the electron mass and of the kinetic mass of the neutrino itself). Parity (physics) - Wikipedia Beta Decay - PHYSICS CALCULATIONS To link to this Beta Decay page, copy the following code to your . For example, a neutrons beta decay converts itself into a proton by emitting an electron following the anti-neutrino. Beta particle - Wikipedia In order to reach that minimum, unstable nuclides undergo beta decay to transform excess protons in neutrons (and vice-versa). Beta decay occurs when an atom has either too many protons or too many neutrons in its nucleus. , In this example, a proton of carbon is converted into a neutron and the emitted beta particle is a positron. The exception to this rule involves electron capture. K-electron capture was first observed in 1937 by Luis Alvarez, in the nuclide 48V. To maintain the conservation of charge, the nucleus in the process also produces an electron and an antineutrino. We will see how we can reproduce these plots by analyzing the QM theory of beta decay. Beta decay is a radioactive decay in which a beta ray is emitted from an atomic nucleus. e The energy released in a nuclear transformation is typically referred to as the Q-value of the reaction. 7.1: Gamma Decay - Physics LibreTexts Approximating the associated wavefunctions to be spherically symmetric, the Fermi function can be analytically calculated to be:[30]. For many years it was actually believed to have zero mass. S=1 When beta decay particles carry no angular momentum (L = 0), the decay is referred to as "allowed", otherwise it is "forbidden". (anti-parallel). As the neutrino is hard to detect, initially the beta decay seemed to violate energy conservation. The proton stays in the nucleus and the electron leaves the . Let us familiarize ourselves with beta decay and its process by reading the article. Beta Decay. 2 Alpha and beta decay are generally slower processes than gamma decay. Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz, Visit BYJUS for all Physics related queries and study materials, Your Mobile number and Email id will not be published. \[ n \Rightarrow p^+ + e^- + \bar{v}\] Beta decay breaks conservation of momentum? - Physics Stack Exchange Click Start Quiz to begin! Book: Spiral Modern Physics (D'Alessandris), { "7.1:_The_Simplified_Nuclear_Potential_Well" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.2:_Radioactivity_Terminology" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.3:_Alpha_and_Beta_Decay" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.4:_Fission_and_Fusion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.5:_Nuclear_Physics_(Activities)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.A:_Alpha_Decay_(Project)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.A:_Radioactive_Chains_(Project)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7.A:_Relativistic_Baseball_(Project)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "1:_The_Special_Theory_of_Relativity_-_Kinematics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "2:_The_Special_Theory_of_Relativity_-_Dynamics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3:_Spacetime_and_General_Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "4:_The_Photon" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "5:_Matter_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "6:_The_Schrodinger_Equation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "7:_Nuclear_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "8:_Misc_-_Semiconductors_and_Cosmology" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", Appendix : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()" }, [ "article:topic", "authorname:dalessandrisp", "alpha decay", "Beta decay", "license:ccbyncsa", "showtoc:no", "licenseversion:40" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FModern_Physics%2FBook%253A_Spiral_Modern_Physics_(D'Alessandris)%2F7%253A_Nuclear_Physics%2F7.3%253A_Alpha_and_Beta_Decay, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\). \[ p^+ + e^- \Rightarrow n+v\], Generically, electron capture can be written as In 1900, Becquerel measured the mass-to-charge ratio (m/e) for beta particles by the method of J.J.Thomson used to study cathode rays and identify the electron. The half life for the latter is 4750 years. In the case of 187Re, the maximum speed of the beta particle is only 9.8% of the speed of light. The difference between the spectrum of the \(\beta^{\pm}\) particles is due to the Coulomb repulsion or attraction from the nucleus. Then we can take the relativistic expression, \[E^{2}=p^{2} c^{2}+m^{2} c^{4} \quad \rightarrow \quad E=T_{e}+m_{e} c^{2} \quad \text { with } T_{e}=\sqrt{p_{e}^{2} c^{2}+m_{e}^{2} c^{4}}-m_{e} c^{2} \nonumber\]. The neutron can decay by this reaction both inside the nucleus and as a free particle. 7.1: Gamma Decay. What is the initial power output of this sample? Another possibility is that a fully ionized atom undergoes greatly accelerated decay, as observed for 187Re by Bosch et al., also at Darmstadt. +decay generally occurs in proton-rich nuclei. The weak force is one of the four fundamental forces that govern all matter in the universe. resulting in a Q-value of: Figure 7.2.1: Beta decay schematics (CC BY-NC-ND; Paola Cappellaro) {\displaystyle m_{N}\left({\ce {^{\mathit {A}}_{\mathit {Z}}X}}\right)} resulting in a Q-value of: \[ Q = (m_{X,atomic}c^2 - Zm_e c^2) - (m_{X',atomic}c^2 - (Z-1)m_ec^2) - (m_ec^2)\], \[ Q = m_{X,atomic}c^2 - Zm_e c^2 - m_{X',atomic}c^2 + (Z-1)m_ec^2 - m_ec^2\], \[Q = (m_{X, atomic} - m_{X',atomic} - 2m_e)c^2\], Electron capture involves a proton in the nucleus absorbing an inner shell electron: / In beta plus decay, the proton disintegrates to yield a neutron causing a decrease in the atomic number of the radioactive sample. = Calculate the Q value for this decay. Quantum field theory gives a unification of e.m. and weak force (electro-weak interaction) with one coupling constant e. The interaction responsible for the creation of the electron and neutrino in the beta decay is called the weak interaction and its one of the four fundamental interactions (together with gravitation, electromagnetism and the strong interaction that keeps nucleons and quarks together). Usually, the Fermi-Kurie plot is used to infer by linear regression the maximum electron energy (or Q) by finding the straight line intercept. Beta particles can therefore be emitted with any kinetic energy ranging from 0 to Q. which sees the emission of a positron (the electron anti-particle) and a neutrino; and the electron capture: \[{ }_{Z}^{A} X_{N}+e^{-} \rightarrow{ }_{Z-1}^{A} X_{N+1}^{\prime}+\nu \nonumber\], \[\ce{ p + e^{-} \rightarrow n+\nu} \nonumber\]. The mass of the nucleus mN is related to the standard atomic mass m by, Because the reaction will proceed only when the Qvalue is positive, decay can occur when the mass of atom AZX is greater than the mass of atom AZ+1X. The overall energy of the nucleus would be reduced (and its stability increased) if the stray neutron at the top of the neutron well could somehow transform itself into a proton and jump down to the lower energy state in the proton well. In the process of course some energy is released that is carried away by a photon. This transition ( - decay) can be characterized as: Radioactive decay - Nuclear reactions - Higher Physics Revision - BBC A neutrinos behaviour is the same as the antineutrinos. Neil Spooner. The kinetic energy (equal to the \(Q\)) is shared by the neutrino and the electron (we neglect any recoil of the massive nucleus). Using the generic equation for electron capture, Because the binding energy of the electron is much less than the mass of the electron, nuclei that can undergo + decay can always also undergo electron capture, but the reverse is not true. 1. Half-lives for beta decay are never shorter than a few milliseconds. where (E) is the total density of states. The neutrino and beta particle (\(\beta^{\pm}\)) share the energy. Weak nuclear force | New Scientist a process that competes with, or substitutes, the positron emission. Beta decay just changes neutron to proton or, in the case of positive beta decay (electron capture) proton to neutron so the number of individual quarks doesn't change. There are two other types of reactions, the \(\beta^{+}\) reaction, \[\ce{ ^{A}_{Z} X_{N} -> _{Z-1}^{A} X_{N+1}^{\prime} + e^{+} + \nu } \nonumber\]. Note that free neutron decay is different from nuclear beta decay where the original neutron is not free and is bound to a nucleus. To convert atomic masses to nuclear masses, multiples of the electron mass must be subtracted from each term. Electron capture is a competing (simultaneous) decay process for all nuclei that can undergo + decay. All rights reserved. When a W+ boson is emitted, it decays into a positron and an electron neutrino: In all cases where +decay (positron emission) of a nucleus is allowed energetically, so too is electron capture allowed. As another example, consider 18F, which consists of 9 neutrons and 9 protons. This is because the atom will be left in an excited state after capturing the electron, and the binding energy of the captured innermost electron is significant. In electron capture, an electron orbiting around the nucleus combines with a nuclear proton to produce a neutron, which remains in the nucleus, and a neutrino, which is emitted. However, in a few cases of odd-proton, odd-neutron radionuclides, it may be energetically favorable for the radionuclide to decay to an even-proton, even-neutron isobar either by undergoing beta-positive or beta-negative decay. PDF BETA DECAY - Department of Physics There are two forms of beta decay, decay and + decay, which produce electrons and positrons respectively. the kinetic energy of the resulting proton and nucleus (in the beta-decay version . In the process the nucleus emits a beta particle (either an electron or a positron) and quasi-massless particle, the neutrino. 0 Notice that these distributions (as well as the decay rate below) are the product of three terms: These three terms reflect the three ingredients that determine the spectrum and decay rate of in beta decay processes. 1 Thus, F(Z, Q) is different, depending on the type of decay. He suggested that this "neutron" was also emitted during beta decay (thus accounting for the known missing energy, momentum, and angular momentum), but it had simply not yet been observed. which converts a proton into a neutron with the emission of an electron and an anti-neutrino. In this example, the total decay energy is 1.16 MeV, so the antineutrino has the remaining energy: 1.16MeV 0.40MeV = 0.76MeV. . In beta decay, one of the down quarks that composes a neutron (two down and one up quarks) in C-14 decays via the weak interaction into an up quark, leaving a proton (two up and one down quarks). Beta decay - Wikipedia From 1920 to 1927, Charles Drummond Ellis (along with Chadwick and colleagues) further established that the beta decay spectrum is continuous. The W boson from the weak interaction quickly decays into an electron and an anti-neutrino. Beta decay is a nuclear decay process where an unstable nucleus transmutes and ejects particles to become more stable. Thus, in practice, we need to integrate the density of states over all possible momentum of the outgoing electron/positron. [2] ( Beta decay was named (1899) by Ernest Rutherford when he observed that radioactivity was not a simple phenomenon. Gamma decay is the third type of radioactive decay. Introducing an extra particle in the process allows one to respect conservation of energy. He called the less penetrating rays alpha and the more penetrating rays beta. 1 The beta decay is a radioactive decay in which a proton in a nucleus is converted into a neutron (or vice-versa). However, the kinetic energy distribution, or spectrum, of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background. The Fermi function that appears in the beta spectrum formula accounts for the Coulomb attraction / repulsion between the emitted beta and the final state nucleus. 2 [39] In this type of beta decay, in essence all of the neutron decay energy is carried off by the antineutrino. One of the examples of beta decay is the , The beta particle is a high-speed electron when it is a . As an example, the beta decay spectrum of 210Bi (originally called RaE) is shown to the right. Energy and momentum are definitely conserved in beta decay. The weak nuclear force is the fundamental force responsible for radioactive beta decay. @psbarbeau @DukeResearch @SloanFoundation. If the proton and neutron are part of an atomic nucleus, the above described decay processes transmute one chemical element into another. This difference goes into the conversion of a proton into a neutron, a positron and a neutrino. beta decay, any of three processes of radioactive disintegration by which some unstable atomic nuclei spontaneously dissipate excess energy and undergo a change of one unit of positive charge without any change in mass number. When L > 0, the decay is referred to as "forbidden". There is no increase in mass number because a proton and a neutron have the same mass. In other words, the total energy released is the mass energy of the initial nucleus, minus the mass energy of the final nucleus, electron, and antineutrino. \[_Z^A X \Rightarrow _{Z+1}^AX' + e^- + \bar{v}\] In 1900, Paul Villard identified a still more penetrating type of radiation, which Rutherford identified as a fundamentally new type in 1903 and termed gamma rays. [34][35] It is a straight line for allowed transitions and some forbidden transitions, in accord with the Fermi beta-decay theory. In comparison with other forms of radioactivity, such as gamma or alpha decay, beta decay is a relatively slow process. Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. {\displaystyle p={\sqrt {(E/c)^{2}-(mc)^{2}}}} 2 Half-life | Definition & Facts | Britannica This is a process during which a nucleus captures one of its atomic electrons, resulting in the emission of a neutrino: An example of electron capture is one of the decay modes of krypton-81 into bromine-81: All emitted neutrinos are of the same energy. As in positron emission, the nuclear positive charge and hence the atomic number decreases by one unit, and the mass number remains the same. Other decay modes, which are rare, are known as bound state decay and double beta decay. There are about 350 known beta-decay stable nuclides. , \[ \begin{array}{lcc} \text{beta}^- \text{decay} & _{36}^{81}Kr \Rightarrow _{37}^{81}Rb + e^- + \bar{v} & Q =(m_{Kr} - m_{Rb})c^2 \\ \text{beta}^+ \text{decay} & _{36}^{81}Kr \Rightarrow _{35}^{81}Br + e^+ + \bar{v} & Q =(m_{Kr} - m_{Br} - 2m_{e^-})c^2 \\ \text{electron capture} & _{36}^{81}Kr + e^- \Rightarrow _{35}^{81}Br + v & Q = (m_{Kr} - m_{Br})c^2 \end{array}]. The extracted value of "Vud" from nuclear beta decays seems to be substantially smaller than what is required by the Standard Model of Particle Physics, the commonly-acknowledged best theory for . Antineutrino is the antimatter counterpart of neutrino. In a famous letter written in 1930, Wolfgang Pauli attempted to resolve the beta-particle energy conundrum by suggesting that, in addition to electrons and protons, atomic nuclei also contained an extremely light neutral particle, which he called the neutron. In nuclei for which both decay and decay are possible, the rarer decay process is effectively impossible to observe. = For forbidden decays, orbital angular momentum must also be taken into consideration. m {2}\): : Beta decay spectra: Distribution of momentum (top plots) and kinetic energy (bottom) for \(\beta^{-} \) (left) and \( \beta^{+}\) (right) decay. I = J . Fermis theory of beta decay or Fermis interaction illustrates beta decay by Enrico Fermi in 1933. so all leptons have assigned a value of +1, antileptons 1, and non-leptonic particles 0. In studying the gamma decay we calculated the density of states, as required by the Fermis Golden Rule. Generically, \[Q =(m_{X,atomic}c^2 - Zm_ec^2)-(m_{X,atomic}c^2 - (Z-2)m_e c^2) - (m_{He, atomic} c^2 - 2m_ec^2)\], \[Q =m_{X,atomic}c^2 - Zm_ec^2 - m_{X,atomic}c^2 - (Z-2)m_e c^2 - m_{He, atomic} c^2 - 2m_ec^2 \], \[Q = (m_{X,atomic} - m_{X,atomic} - m_{He, atomic} c^2\]. Examples of beta minus decay include the decay of 14C into 14N and it usually occurs in neutron-rich nuclei. In gamma decay process we have seen how the e.m. field is described as an operator that can create (or destroy) photons. The selection rules for the Lth forbidden transitions are: A very small minority of free neutron decays (about four per million) are so-called "two-body decays", in which the proton, electron and antineutrino are produced, but the electron fails to gain the 13.6 eV energy necessary to escape the proton, and therefore simply remains bound to it, as a neutral hydrogen atom. Electron capture is a process in which a parent nucleus captures one of its orbital electrons and emits a neutrino.Electron capture, also known as inverse beta decay, is sometimes included as a type of beta decay because the basic nuclear process, mediated by the weak interaction, is the same. Beta-decay occurs via weak interaction. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. is the mass of the electron antineutrino. Let us know if you have suggestions to improve this article (requires login). For all odd mass numbers A, there is only one known beta-stable isobar. Required fields are marked *, \(\begin{array}{l}_{6}^{10}\textrm{C} \rightarrow _{5}^{10}\textrm{B} + _{1}^{0}\textrm{e}^+\end{array} \), \(\begin{array}{l}_{Z}^{A}\textrm{X} \rightarrow _{Z+1}^{A}\textrm{Y} + e^{-} + \bar{\nu }\end{array} \), \(\begin{array}{l}N = p + e^{-} + v^-\end{array} \), \(\begin{array}{l}_{Z}^{A}\textrm{X} \rightarrow _{Z-1}^{A}\textrm{Y} + e^{+} + {\nu }\end{array} \), \(\begin{array}{l}P = n + e^+ + v \end{array} \). Most neutrino physicists believe that neutrinoless double beta decay has never been observed. Beta Decay - an overview | ScienceDirect Topics Cobalt-60 is a nuclide that decays in the following manner: 60 Co 60 Ni + + neutrino. The Beta-decay process is the process of emission of an electron or positron from a radioactive nucleus. This was later explained by the proton-neutron model of the nucleus. {\displaystyle \Delta J=0} [44] Thus, decay is usually studied only for beta stable nuclei. In 1931, Enrico Fermi renamed Pauli's "neutron" the "neutrino" ('little neutral one' in Italian). This will be proportional to the rate of emission calculated from the Fermi Golden Rule, times the density of states: \[N(p)=C F(Z, Q)\left|V_{f i}\right|^{2} \frac{p^{2}}{c^{2}}[Q-T]^{2}=C F(Z, Q)\left|V_{f i}\right|^{2} \frac{p^{2}}{c^{2}}\left[Q-\left(\sqrt{p_{e}^{2} c^{2}+m_{e}^{2} c^{4}}-m_{e} c^{2}\right)\right]^{2} \nonumber\], \[N\left(T_{e}\right)=\frac{C}{c^{5}} F(Z, Q)\left|V_{f i}\right|^{2}\left[Q-T_{e}\right]^{2} \sqrt{T_{e}^{2}+2 T_{e} m_{e} c^{2}}\left(T_{e}+m_{e} c^{2}\right) \nonumber\]. Besides energy, there are other conserved quantities: \[Q_{\beta^{-}}=\left[m_{N}\left({ }^{A} X\right)-m_{N}\left({ }_{Z+1}^{A} X^{\prime}\right)-m_{e}\right] c^{2}. / \[V_{i f}=\left\langle\psi_{f}\left|\mathcal{H}_{i n t}\right| \psi_{i}\right\rangle \nonumber\], \[V_{i f}=g \int d^{3} \vec{x} \Psi_{p}^{*}(\vec{x})\left[\Psi_{e}^{*}(\vec{x}) \Psi_{\bar{\nu}}^{*}(\vec{x})\right] \Psi_{n}(\vec{x}) \nonumber\]. Beta Decay is a type of radioactive decay in which a proton is transformed into a neutron or vice versa inside the nucleus of the radioactive sample. In beta plus decay, shown in Fig. For each element, the lighter isotopes, those deficient in neutrons, generally tend toward stability by positron emission or electron capture, whereas the heavier isotopes, those rich in neutrons, usually approach stability by electron emission. {\textstyle I={\frac {1}{2}}} Another example is when the free neutron (10n) decays by decay into a proton (p): At the fundamental level (as depicted in the Feynman diagram on the right), this is caused by the conversion of the negatively charged (.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1/3 e) down quark to the positively charged (+2/3 e) up quark by emission of a W boson; the W boson subsequently decays into an electron and an electron antineutrino: In +decay, or positron emission, the weak interaction converts an atomic nucleus into a nucleus with atomic number decreased by one, while emitting a positron (e+) and an electron neutrino (e). Recall the mass chain and Beta decay plots of Fig.