Question

A stream of protons and $\alpha$-particles of equal momenta enter a uniform magnetic field perpendicularly.The radii of their orbits are in the ratio

• A. 1:1
• B. 1:2
• C. 2:1
• D. 4;1

Answer 1

The correct option is C 2:1

The radius of circular orbit of charged particle projected perpendicular to magnetic field is given by :

$r=\frac{mv}{qB}$

given proton and $\alpha$ particle have equal momenta

$r\propto \frac{1}{q}$

$\frac{r_{proton}}{r_{\alpha }}=\frac{q_2}{q_1}$

Charge on $\alpha$ particles $=2e$

Charge on proton $=e$

$\frac{r_{proton}}{r_{\alpha }}=\frac{2}{1}$.