Chapter 30, Problem 35P

To determine

Total energy released by the decay of nucleus in β⁺ decay.

Answer to Problem 35P

Solution:

$(M_P-M_D-2M_e)c^2$

Explanation of Solution

Given Info:

A nucleus decays by β⁺ decay. Mass of electron is equal to positron.

Formula Used:

Energy is given by

$E=m{c}^2$

Inβ⁺decay the proton inside the radioactive nucleus converts to neutron and releases a positron and an electron neutrino.

The balanced equation for β⁺decay can be expressed as

${}_Z{}^{A}N\to {}_{Z-1}{}^{A}N{}^{\text{'}}+e^{+}+v_e$

The energy corresponding to the above balanced equation can be expressed as

$(M_P-M_D-2M_e)c^2$

As mass of electron is equal to mass of positron.