Question

A nucleus with mass number 220 initially at rest emits an $\alpha$ -particle. If the Q value of the reaction is 5.5 MeV. Calculate the kinetic energy of the $\alpha$ -particle

• A. 4.4 MeV
• B. 5.4 MeV
• C. 5.6 MeV
• D. 6.5 MeV

Answer 1

The correct option is B 5.4 MeV



Q-value of the reaction is 5.5 eV i.e. $k_1+k_2=5.5MeV$ ……(i)
By conservation of linear momentum $p_1=p_2\Rightarrow \sqrt{2\left(216\right)k_1}=\sqrt{2\left(4\right)k_2}\Rightarrow k_2=54k_1$ ……(ii)
On solving equation (i) and (ii) we get $k_2=5.4$ MeV.