Question

The minimum frequency of a $\gamma$-ray that causes a deuteron to disintegrate into a proton and a neutron is $(m_d=2.0141amu,m_p=1.0078amu,m_n=1.0087amu.)$

• A. $2.7\times {10}^{20}Hz$
• B. $5.4\times {10}^{20}Hz$
• C. $10.8\times {10}^{20}Hz$
• D. $21.6\times {10}^{20}Hz$

Answer 1

The correct option is B $5.4\times {10}^{20}Hz$

$D\to n+p$
$\Delta m=m_p+m_n-m_d$
$=1.0087+1.0078-2.0141)amu=2.4\times {10}^{-3}amu$

Energy required $=\Delta m{c}^2$
$E/amu=931Mev$

Energy $=931(2.4\times {10}^{-3})=2.2344MeV$
$hv=2.23MeV$
$v=5.4\times {10}^{20}Hz$