Question

A neutron decays to a proton and an electron. Find the fraction of energy gone to proton if total energy released is $k.m_p=1836m_e$

• A. $\frac{1}{1836}$
• B. $\frac{1836}{1837}$
• C. $\frac{1835}{1837}$
• D. $\frac{1}{1837}$

Answer 1

Answer: (D)

$\frac{1}{1837}$

$0=1836v_1+v_2$ or $v_1=\frac{v_2}{1836}$

total $KE=\frac{1}{2}$ [1836 $v_1^2+v_2^2$]

$=\frac{1}{2}[\frac{v_2^2}{1836}+v_2^2]$

$\frac{K_P}{K_T}=\frac{\frac{1}{2}{v}_2^2\times \frac{1}{1836}}{\frac{1}{2}{v}_2^2\times \frac{1837}{1836}}=\frac{1}{1837}$.