question_answer

An alpha-particle of mass m suffers I-dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is:

A) 2 m                  

B) 3.5 m

C) 1.5 m               

D) 4 m

Correct Answer: D

Solution :

(I) \[m\,{{\nu }_{o}}=-m{{\nu }_{1}}+m{{\nu }_{2}}\]

(ii) \[{{\nu }_{o}}={{\nu }_{1}}+{{\nu }_{2}}\]

\[\frac{2m{{\nu }_{0}}}{m+M}={{\nu }_{2}}\]

\[K{{E}_{f}}=\frac{1}{2}m\nu _{1}^{2}=\frac{1}{2}m\left( \frac{M-m}{M+m} \right)\nu _{0}^{2}\]

\[=\frac{36}{100}\times \frac{1}{2}m\nu _{0}^{2}\]

\[\Rightarrow \]   m = 4 m.