IGNOU MPH 17 2026 - Obtain an expression of momentum distribution of -particles in th

Question

Obtain an expression of momentum distribution of $\beta$ -particles in the momentum range $p_\beta$ to $(p_\beta + dp_\beta)$ , considering the Coulomb correction term. Also, derive the energy distribution function to get the shape of the $\beta$ -decay spectrum.

19 Jan 2026

Answer :

Word Count : 307

For β-decay, consider an electron (or β-particle) emitted from a nucleus. The number of electrons emitted with momentum in the range (p_\beta) to (p_\beta + dp_\beta) is proportional to the phase space available and the Coulomb correction from the nuclear charge. The momentum distribution can be written as: [ dN(p_\beta) \propto F(Z, E_\beta), p_\beta^2 , dp_\beta , (E_0 - E_\beta)^2 ] where: * (p_\beta) is the β-particle momentum, (dp_\beta) its small interval, * (E_\beta = \sqrt{p_\beta^2 c^2 + m_\beta^2 c^4}) is the total energy of the β-particle, * (E_0) is the total energy available (end-point energy), * (F(Z, E_\beta)) is the Fermi function, representing the Coulomb correction due to the nuclear charge (Z). For an allowed transition, the Fermi function (F(Z, E_\beta)) approximately

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