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Beta Decay

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Radioactive decay occurs because some nuclides are not stable. Note that in alpha decay the parent nucleus reverts to a daughter nucleus that is down 2 units in neutron number N and to the left 2 units in atomic number Z. In many cases alpha decay leaves the daughter nucleus farther from the line of stability than the parent. Unstable nuclei may move closer to the line of stability by undergoing beta decay. The simplest example of beta decay is the decay of a free neutron.

Definition

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Beta ($\beta$) decay is a process in which an electron is emitted by unstable nucleus. We know that a nucleus contain only protons and neutrons. Then how it is possible to emit the electrons? The reason is that, when a neutron is changed to the proton within the nucleus, emission of electrons take place. These electrons are emitted during the beta decay. Beta decays take place when the ratio of protons and neutrons is not optimal. Beta decay tends to allow the nucleus to approach the optimal proton/neutron ratio.

Neutron $\rightarrow $Proton + Emitted electron

Equation

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Beta decay is classified as negative and positive beta decay. If the number of neutrons is higher than that of protons negative beta decay occurs, if the number of protons is higher than that of neutron positive beta decay occurs. As a result, the atomic number of the atoms are changed but the mass number is same. Atomic number decreases in the positive beta decay, whereas the atomic number increases in the negative beta decay. During the decay process,the neutrino is emitted in the positive decay and anti neutrino is emitted in the negative beta decay. The general representations of negative and positive beta decay are:

Negative beta decay:

$_{Z}^{A}\textrm{X} \rightarrow _{Z+1}^{A}\textrm{Y}$ + $\beta ^{-}$ + $\bar{\nu }$

Positive beta decay:

$_{Z}^{A}\textrm{X} \rightarrow _{Z-1}^{A}\textrm{Y}$ + $\beta ^{+}$ + $\nu$


Examples

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Some examples of beta decay are given below:

1. Decay of carbon-14

$_{6}^{14}\textrm{C} \rightarrow _{7}^{14}\textrm{N}$ +$\beta ^{-}$ + $\bar{\nu }$

2. Decay of cobalt-60

$_{27}^{60}\textrm{Co} \rightarrow _{28}^{60}\textrm{Ni}$ + $\beta ^{-}$ + $\bar{\nu }$

3. Decay of radium-228

$_{88}^{228}\textrm{Ra} \rightarrow _{89}^{228}\textrm{Ac}$ + $\beta ^{-}$ + $\bar{\nu }$

Fermi Theory 

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The beta decay theory of Fermi explains the origins for either a negative beta particle or positive beta particle from a decaying nucleus. However, an additional mystery to beta particle radiation was the broad range of energies that a beta particle could possess from near zero to a maximum energy when these were emitted from a particular radioactive atom. When an unstable nucleus emits radiation it decays from a higher energy state to a nucleus with a lower energy state and the energy difference in these two states should exactly correspond to the sum of the energies of the radiations emitted by the decaying nucleus. This could easily be observed when alpha particles or gamma radiation were emitted from nuclides with discrete energies that corresponded to the energy transitions of the parent and daughter nuclides. The emission of a beta particle from a nucleus that could possess any energy between zero and maximum value would appear to contradict the laws of conservation of energy, except that Wolfgang Pauli had proposed in 1930 the existence of a neutral particle of near zero rest mass that would share the decay energy with the beta particle. Pauli called this particle the "neutron", as this was prior to the time when the neutron was discovered and prior to Fermi's beta decay theory (1934). Fermi coined Pauli's neutral particle as the "neutrino" from the Italian meaning " little neutral one". The Fermi beta decay including the accompanying neutrino ($\nu$) can be written as follows:

n → $p^{+}$ + $\beta^{-}$ + $\bar{\nu}$

$p^{+}$ → n + $\beta^{+}$ + $\nu$

Inverse Beta Decay

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The inverse beta decay is a form of radioactive decay, in which a proton is suddenly converts to a neutron, positron and a neutrino. Mathematically, it can be represented as,

p → n + $e^{+}$ + $\nu_{e}$

The decay of radioactive N-13 to C-13 is an example of inverse beta decay. The decay process is given as follows:

$_{7}^{13}\textrm{N} \rightarrow _{6}^{13}\textrm{C}$ + $e^{+}$ + $\nu _{e}$


Types 

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Nuclear $\beta$ decay occurs in three ways, $\beta^{-}$, $\beta^{+}$ and electron capture (EC). In these decays, a nuclear neutron (or proton) changes in to a nuclear proton (or neutron) with the ejection of a neutrino (or antineutrino) and an electron (or positron). In electron capture, an orbital electron is captured by the nucleus, changing a proton into a neutron with the emission of a neutrino. The total number of nucleons, A, in the nucleus does not change in these decays, only the relative number of neutrons and protons. In $\beta^{+}$ and $\beta^{-}$ decays, the decay energy is shared between the emitted electron, the neutrino and the recoiling daughter nucleus.Thus the energy spectrum of the emitted electrons and neutrinos is continuous, ranging from zero to the decay energy. In the case of EC decay, all the decay energy is carried away by the neutrino which is emitted. Neutron-rich nuclei decay by $\beta^{-}$ decay, whereas proton-rich nuclei decay by $\beta^{+}$ or EC decay. $\beta^{+}$ decay is favored in the light nuclei and requires the decay energy to be greater than 1.02MeV, whereas EC decay is found mostly in the heavier nuclei.