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  • In Rutherford scattering experiment, the number of particles scattered at <img alt="\mathrm{60^{o}\: is\: 5

In Rutherford scattering experiment, the number of \alpha -particles scattered at \mathrm{60^{o}\: is\: 5 \times10^{6}.}The number of \alpha -particles scattered at \mathrm{120^{o}} will be
 

Option: 1

15\times10^{6}


Option: 2

3/5\times10^{6}


Option: 3

5/9\times10^{6}


Option: 4

None of these


Answers (1)

best_answer

Number of \alpha-particles scattered at angle

\mathrm{ N \propto \frac{1}{\sin ^4 \frac{\theta}{2}} }

\mathrm{ \therefore \frac{N_2}{N_1}=\left(\frac{\sin \frac{\theta_1}{2}}{\sin \frac{\theta_2}{2}}\right)^4 }

\mathrm{ \text { or } \quad N_2=5 \times 10^6 \times\left(\frac{\sin \frac{60^{\circ}}{2}}{\sin \frac{120^{\circ}}{2}}\right)^4=\frac{5}{9} \times 10^6}

Hence option 3 is correct.




 

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