Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic fi

Question

Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths $r_H : r_\alpha$ will be :

Accepted Answer

The radius of the path is $r = \frac{p}{qB}$. For hydrogen, $q_H = e$. For $\alpha$-particle, $q_\alpha = 2e$. Thus, $\frac{r_H}{r_\alpha} = \frac{p/eB}{p/2eB} = \frac{2}{1}$.

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