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${90^o}$ ના ખૂણે પ્રકીર્ણન પામતા કણો $56$ હોય, તો ${60^o}$ ના ખૂણે કેટલા કણો પ્રકીર્ણન પામે?

A

$224$

B

$256$

C

$98$

D

$108$

Solution

$N \propto \frac{1}{{{{\sin }^4}(\theta /2)}}$

$⇒\frac{{{N_2}}}{{{N_1}}} = {\left[ {\frac{{\sin \left( {\frac{{{\theta _1}}}{2}} \right)}}{{\sin \left( {\frac{{{\theta _2}}}{2}} \right)}}} \right]^4}$

$\Rightarrow$ $\frac{{{N_2}}}{{{N_1}}} = {\left[ {\frac{{\sin \left( {\frac{{90^\circ }}{2}} \right)}}{{\sin \left( {\frac{{60^\circ }}{2}} \right)}}} \right]^4} = {\left[ {\frac{{\sin 45^\circ }}{{\sin 30^\circ }}} \right]^4} = 4$

${N_2} = 4{N_1} = 4 \times 56 $

$\therefore {N_2} = 224$

Standard 12
Physics

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