# Beta decay

Radioactive disintegration with the emission of an electron or positron accompanied by an uncharged antineutrino or neutrino. The mass number of the nucleus remains unchanged but the atomic number is increased by one or decreased by one depending on whether an electron or positron is emitted.

$\beta^-$ decay

$\beta^-$ radioactivity occurs when a nucleus emits a negative electron from an unstable radioactive nucleus. This happens when the nuclide has an excess of neutrons. Theoretical considerations (the fact that there are radionuclides which decay by both positron and negatron emission and the de Broglie wavelength of MeV electrons is much larger than nuclear dimensions), however, do not allow the existence of a negative electron in the nucleus. For this reason the beta particle is postulated to arise from the nuclear transformation of a neutron into a proton through the reaction

$n \to p + \betaâ�� + \bar{\nu}$

where $\bar{\nu}$ is an anti-neutrino. The ejected high energy electron from the nucleus and denoted by $\beta^-$ to distinguish it from other electrons denoted by $e^-$. Beta emission differs from alpha emission in that beta particles have a continuous spectrum of energies between zero and some maximum value, the endpoint energy, characteristic of that nuclide. The fact that the beta particles are not mono-energetic but have a continuous energy distribution up to a definite maximum or endpoint energy, implies that there is another particle taking part i.e. the neutrino ν. This endpoint energy corresponds to the mass difference between the parent nucleus and the daughter as required by conservation of energy. The average energy of the beta particle is approximately 1/3 of the maximum energy.

More precisely, the “neutrino” emitted in $\beta^-$ decay is the anti-neutrino (with the neutrino being emitted in $\beta^+$ decay). The neutrino has zero charge and almost zero mass. The maximum energies of the beta particles range from 10 keV to 4 MeV. Although $\beta^-$ particles have a greater range than alpha particles, thin layers of water, glass, metal, etc. can stop them.

The $\beta^-$ decay process can be described by:

$\beta^- decay: {}_Z^AP \to [{}_{Z+1}^{A}D]^+ + \beta^- + \bar{\nu}$

Immediately following the decay by beta emission, the daughter atom has the same number of orbital electrons as the parent atom and is thus positively charged. Very quickly, however, the daughter atom acquires an electron from the surrounding medium to become electrical neutral. Beta radiation can be an external radiation hazard. Beta particles with less than about 200 keV have limited penetration range in tissue. However, beta particles can also give rise to Bremsstrahlung radiation which is highly penetrating.

$\beta^+$ decay

In nuclides where the neutron to proton ratio is low, and alpha emission is not energetically possible, the nucleus may become more stable by the emission of a positron (a positively charged electron). Within the nucleus a proton is converted into a neutron, a positron, and a neutrino i.e.

$n \to p + \beta+ + \nu$

Similarly to the $\beta^-$, the positron $\beta^+$ is continuously distributed in energy up to a characteristic maximum or endpoint energy. The positron, after being emitted from the nucleus, undergoes strong electrostatic attraction with the atomic electrons. The positron and negative electrons annihilate each other and result in two photons (gamma rays) each with energy of 0.511 MeV moving in opposite directions. The radiation hazard from positrons is similar to that from $\beta^-$ particles. In addition, the gamma radiation resulting from the positron-electron annihilation presents an external radiation hazard. The $\beta^+$ decay process can be described by:

$\beta^+ decay: {}_Z^AP \to [{}_{Z-1}^{A}D]^- + \beta^+ + \nu$

Immediately following the decay by positron emission, the daughter atom has the same number of orbital electrons as the parent atom and is thus negatively charged. Very quickly, however, the daughter atom loses the electron from the surrounding medium to become electrical neutral.

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