question_answer

A nucleus with mass number 220 initially at rest emits an a-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the a-particle [IIT JEE (Screening) 2003]

A)            4.4 MeV                                 

B)            5.4 MeV

C)            5.6 MeV                                 

D)            6.5 MeV

Correct Answer: B

Solution :

                   Q-value of the reaction is 5.5 eV  i.e. \[{{k}_{1}}+{{k}_{2}}=5.5\,MeV\]                                           ??(i) By conservation of linear momentum \[{{p}_{1}}={{p}_{2}}\Rightarrow \sqrt{2(216){{k}_{1}}}=\sqrt{2(4){{k}_{2}}}\] Þ  k2 = 54 k1                                                           ??(ii) On solving equation (i) and (ii) we get k2 = 5.4 MeV.