Question

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

• A. 117 per minute, 25 per minute
• B. 50 per minute, 12.5 per minute
• C. 100 per minute, 200 per minute
• D. 112 per minute, 12.4 per minute

Answer 1

The correct option is D 112 per minute, 12.4 per minute

No. of particles scattered through an angle, $\theta =N\left(\theta \right)=\frac{k{Z}^2}{si{n}^4\left(\frac{\theta }{2}\right)(K.E.{)}^2}$
$\therefore 28=\frac{4kc{z}^2}{(K.E.{)}^2}for\theta ={90}^{\circ }\therefore \frac{k{z}^2}{(K.E.{)}^2}=\frac{28}{4}=7$

$\therefore N\left({60}^{\circ }\right)=\frac{7}{si{n}^4\left(\frac{{60}^{\circ }}{2}\right)}=16\times 7=112/min$

$N\left({120}^{\circ }\right)=\frac{7}{si{n}^4\left(\frac{{120}^{\circ }}{2}\right)}=12.4/min$