Question

In Rutherford's experiment, number of particles scattered at $90^{\circ }$ angle are $x$ per second. Number particles scattered per second at angle $60^{\circ }$ is

• A. x
• B. 4 x
• C. 8 x
• D. 16 x

Answer 1

Answer: (B)

$N(\theta )\propto \frac{Z^2}{{\sin }^4\left(\frac{\theta }{2}\right)E^2}$
or $N(\theta )\propto \frac{1}{{\sin }^4\left(\frac{\theta }{2}\right)}$
$\theta =60^{\circ }$ and $90^{\circ }$
$\therefore \frac{N(90)}{N(60)}\propto \frac{{\sin }^{4}30}{{\sin }^{4}45}$
$N\left(90^{\circ }\right)=x$
$N\left(60^{\circ }\right)=4x$