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Question

The radius of an α-particle moving in a circle in a constant magnetic field is half of the radius of an electron moving in circular path in the same field. The de Broglie wavelength of α-particle is x times that of the electrons. Find x (an integer).

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Solution

Radius of a charged particle in a magnetic field is given by : R=mVqB
momentum = p=mV=RqB
It is given that radius of alpha particle is half of electron.
We know that the charge of an alpha particle is twice of that of an electron.
Therefore momentum remains same for both electron and alpha particle .
de Broglie wavelength = hp
Since momentum is same, ratio of wavelengths is 1 .

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