Question

A narrow beam of protons and deuterons, each having the same momentum, enters a region of uniform magnetic field directed perpendicular to their direction of momentum. The ratio of the radii of the circular paths described by them is

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

Answer 1

Answer: (B)

Charge on deutron $\left(q_d\right)=$ charge on proton $\left(q_p\right)$
$q_d=q_p$
Radius of circular path $(r)=\frac{P}{Bq}\left(\therefore qvB=\frac{m{v}^2}{r}\right)$
$r\propto \frac{1}{q}[$ for constant momentum $(P)]$
So, $\frac{r_p}{r_d}=\frac{q_d}{q_p}=\frac{q_p}{q_p}=1$
Hence, $r_p;r_d=1:1$