Question

What is beta decay? Write a brief account of ß-particle spectrum.

Answer 1

Beta decay: The emission of electron (ß-particle) from the nucleus of an atom is called ß-decay. It is believed that emission of an electron by the nucleus is due to transformation of a neutron into a proton and an electron. When a neutron changes into a proton, a ß-particle is ejected whereas a proton remains in the nucleus. The emission of ß-particle, therefore:

• increases the atomic number by one and
• keeps the mass number unaffected.

The energy of ß-disintegration is provided by the difference between the mass of the parent nucleus and the sum of the masses by the daughter nucleus and ß-particles. The ß-disintegration energy is thus given by:

E_ß = _ZM_n^A - [_Z+1M_n^A + m_e] ..........(1)

where

M_n = mass of nucleus

m_e = mass of electron

(A, Z) and (A, Z + l) = mass number of atom i.e. number of parent and daughter nuclei.

Theory of ß-particle Spectra

According to Eq. (1) the same mass disappears during the emission of a ß-particle and all ß-particles must be emitted with the same energy. But actually it is found that

(1) ß-particle emitted by a radioactive substance has a continuous energy range, extending from zero to a certain maximum. The upper energy level is called the end point energy and is the characteristic of nature of ß-emitter Fig. shows the spectrum of the ß-particles emitted with end point energy 1.17 MeV.

(2) Every ß-particle energy distribution curve has a well defined maximum whose height and position depend upon the nature of ß-emitter.

Pauli suggested that in ß-particle disintegration, another particle neutrino was simultaneously emitted along with ß-particle. The neutrino is supposed to be fundamental particle having:

(i) zero charge

(ii) zero rest mass, and

(iii) a spin of \(\frac{1}{2} . \frac{h}{2\pi}\)

A ß-decay can thus be represented as

n → p + e- + v (neutrino)

Under neutrino hypothesis, each ß-decay is accompanied by discrete energy E_ß which corresponds to the end point energy in the continuous ß-particles spectrum. The disintegration energy is shared by ß-particle, neutrino and the recoil nucleus in a continuous range of different ways. The neutrino may take any amount of the available ß-disintegration energy so that the energy left at the disposal of the ß-particle will be different for each disintegration. Thus ß-particles of all possible energies extending from zero to a certain maximum (end point energy) shall be emitted. Thus Pauli's neutrino hypothesis satisfactorily explains the continuous energy range of ß-particle spectrum.

It was found late that ß-decay is accompanied by two kinds of neutrinos, the neutrino (v) and antineutrino \(\overrightarrow v\). In ordinary ß-decay, it is an antineutrino that is emitted.

n → p + e^- + \(\overrightarrow v\)