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An electron and an alpha particle enter a uniform magnetic field normally. If the force on the electron is twice the force of the alpha particle, then the ratio of the speeds of the alpha particle and the electron is

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1 : 1

1 : 2

1 : 3

1 : 4

answer is D.

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Detailed Solution

Force on a charged particle in a magnetic field

$F = q v B$

$g i v e n F o r c e o n e l e c t r o n i s t w i c e t h e a l p h a p a r t i c l e$

$\frac{F_{e}}{F_{α}} = \frac{q_{e}}{q_{α}} \frac{v_{e}}{v_{α_{}}}$

$\frac{2}{1} = \frac{1}{2} \frac{v_{e}}{v_{α}}; \frac{v_{e}}{v_{α}} = \frac{4}{1}$

$\frac{v_{α}}{v_{e}} = \frac{1}{4}$

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