Question

An alpha-particle of mass m suffers 1-dimensional elastic coolision 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. 4 m
• B. 3.5 m
• C. 2 m
• D. 1.5 m

Answer 1

Answer: (A)

4 m

Answer 2

$mv _{0}= mv _{2}- mv _{1}$
$\frac{1}{2} mV _{1}^{2}=0.36 \times \frac{1}{2} mV _{0}^{2}$
$v _{1}=0.6 v _{0}$
$\frac{1}{2} M V _{2}^{2}=0.64 \times \frac{1}{2} mV _{0}^{2}$
$V _{2}=\sqrt{\frac{ m }{ M }} \times 0.8 V _{0}$
$mV _{0}=\sqrt{ m M } \times 0.8 V _{0}- m \times 0.6 V _{0}$
$\Rightarrow 1.6 m =0.8 \sqrt{ mM }$
$4 m ^{2}= mM$