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Q.

A stream of particles $α -$ particles encounters a stationary unknown nucleus in a cloud chamber. After a collision, the two nuclei are scattered in mutually perpendicular directions. If some kinetic energy is lost in the collision, the unknown nucleus must be

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a

a nucleus lighter than an $α -$ particle

b

A proton

c

an $α -$ particle

d

a nucleus heavier than an $α -$ particle

answer is D.

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Detailed Solution

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$\begin{array}{l} \bar{P_{α}} = \bar{P_{α}^{'}} + \bar{P} \\ θ = 90^{0} \\ \Rightarrow P_{α}^{2} = {(P_{α}^{'})}^{2} + P^{2} \\ D i v i d i n g w i t h 2 m_{α} \\ \Rightarrow \frac{P_{α}^{2}}{2 m_{α}} = \frac{{(P_{α}^{'})}^{2}}{2 m_{α}} + \frac{P^{2}}{2 m_{α}} \\ \frac{P^{2}}{2 m_{α}} s h o u l d b e s u m o f \frac{p^{2}}{2 m} a n d l o s t k i n e t i c e n e r g y \end{array}$

Where m is mass of unknown nucleus $∴ m > m_{α}$

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