Question

A proton, a deuteron and an $\alpha$ particle having same momentum enter a uniform magnetic field at right angles to the field. The ratio of their angular momentum with respect to their corresponding centres during their motion in the magnetic field is

• A. 2:2:1
• B. 2:1:3
• C. 4:1:2
• D. 4:2:1

Answer 1

The correct option is A

2:2:1

We know that, $L=Pr=P\left(\frac{mv}{qB}\right)=\frac{P^2}{qB}$
$\Rightarrow L\propto \frac{1}{q}$
Now, charge on a proton = +e
Charge on a deuteron = +e
Charge on an $\alpha$ particle = +2e
Hence, the ratio of their angular momentum will be 2:2:1.