Question

A proton and an alpha particle having the same kinetic energy are in turn allowed to pass through a uniform magnetic field perpendicular to the direction of motion. The ratio of the radii of their path is

• A. 1:4
• B.
• C. 1:1
• D. 1:2

Answer 1

The correct option is (D) 1 : 1

We have to find the ratio of the radii of the both particles

We know,

Relation between the mass is $m_{\alpha }=4m_p$

Relation between the charge = $q_{\alpha }=2q_p$

According to the question, the kinetic energy of both the particles are same

Now radius of the circular path $r=\frac{mv}{Bq}=\frac{\sqrt{2mK}}{Bq}$

So we can write

$\frac{r_p}{r_{\alpha }}=\sqrt{\frac{m_p}{m_{\alpha }}}\times \frac{q_{\alpha }}{q_p}=\sqrt{\frac{1}{4}}\times \frac{2}{1}=\frac{1}{1}$

Hence the ration is $1:1$