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  • In a Rutherford experiment, the number of particles scattered at angle are 28 per minute then numbe

In a Rutherford experiment, the number of particles scattered at 90^{\circ} angle are 28 per minute then number of scattered particles at an angle 60^{\circ}\; \mathrm{ and }\; 120^{\circ} will be

 

Option: 1

117 perminute, 25 per minute


Option: 2

50 per minute, 12.5 per minute


Option: 3

100 per minute, 200 per minute


Option: 4

112 per minute, 12.4 per minute


Answers (1)

No. of particles scattered through an angle

\begin{aligned} & \theta=\mathrm{N}(\theta)=\frac{\mathrm{k} z^2}{\sin ^4\left(\frac{\theta}{2}\right)(\mathrm{K} . \mathrm{E} .)^2} \\ \\& \therefore \quad 28=\frac{4 \mathrm{kz}^2}{(\mathrm{~K} . \mathrm{E} .)^2} \text { for } \theta=90^{\circ} \quad \therefore \quad \frac{\mathrm{kz}^2}{(\mathrm{~K} . \mathrm{E} .)^2}=\frac{28}{4}=7 \end{aligned}

\begin{aligned} & \therefore \quad \mathrm{N}\left(60^{\circ}\right)=\frac{7}{\sin ^4\left(\frac{60^{\circ}}{2}\right)}=16 \times 7=112 \text { per minute } \\ \\& \mathrm{N}\left(120^{\circ}\right)=\frac{7}{\sin ^4\left(\frac{120^{\circ}}{2}\right)}=12.4 \text { per minute } \end{aligned}

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Kshitij

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