Question

An alpha particle collides elastically with a stationary nucleus and continues moving at an angle of ${60}^0$ with respect to the original direction of motion. The nucleus recoils at an angle of ${30}^0$ with respect to this direction. Mass number of the nucleus is :

• A. 3
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

4

Given collision of $\alpha$-particle with nucleus is elastic.

Mass of $\alpha$ particle$=4$ units

mass of neucleus$=$m

Given $\theta ={60}^o$

$\varphi ={30}^o$

$\varphi +\theta ={90}^o$

as we know that when a particle moving with velocity v colloid obliquely & elastically with a particle of same mass and at rest then after collision angle between their velocities is $\frac{\pi }{2}$

$\Rightarrow$ Mass of $\alpha$ particle$=$mass of nucleus

$m=4$ unit.