Atoms And Nuclei Question 384

Question: In an $ \alpha $ -decay the kinetic energy of $ \alpha $ -particle is 48 MeV and Q-value of the reaction is 50 MeV. The mass number of the mother nucleus is (Assume that daughter nucleus is in ground state)

Options:

A) 96

B) 100

C) 104

D) 110

Show Answer

Answer:

Correct Answer: B

Solution:

  • We have $ {K_{\alpha }}=\frac{m_{y}}{m_{y}+{m_{\alpha }}}.Q $
    $ \Rightarrow ,{K_{\alpha }}=\frac{A-4}{A}.Q\Rightarrow 48=\frac{A-4}{4}.50\Rightarrow A=100 $


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