Question

A proton and an $\alpha$ - particle, moving with the same velocity, enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and $\alpha$ - particle is

• A. 1 : 2
• B. 1 : 4
• C. 1 : 16
• D. 4 : 1

Answer 1

Answer: (A)

The centripetal force to the two types of particles is provided by magnetic force.
Alpha particles are highly ionizing form of particle radiation which have low penetration. They consist of two protons and two neutrons bound together identical to helium nucleus. Also proton is ${ }_{1} H ^{1}$. Hence,
$m_{\alpha}=4 m_{p}$ and $ q_{\alpha}=2 q_{p}$
When proton and $\alpha$-particle describe circular paths then centripetal and centrifugal forces balance each other
$ \frac{m v^{2}}{r} =q v B $
$ \Rightarrow \frac{r_{p}}{r_{\alpha}} =\frac{m_{p} v}{e B} \times \frac{2 e B}{4 m_{p} v} $
$ \frac{2 m_{p}}{4 m_{p}} =\frac{1}{2} $
$ \therefore r_{p}: r_{\alpha}=1: 2 $