Ionized hydrogen atoms and -particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths will be [2019]

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Solution

Q.
Ionized hydrogen atoms and $α$ -particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths $r_{H} : r_{α}$ will be [2019]

1 1 : 4

2 2 : 1

3 1 : 2

4 4 : 1

Ans.
(2)

As, $r = \frac{m v}{q B} = \frac{p}{q B}$

For given $p$ and $B,$ $r \propto \frac{1}{q}$ $\Rightarrow \frac{r_{H}}{r_{α}} = \frac{q_{α}}{q_{H}} = \frac{2}{1}$

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