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Question

An αparticle and a proton are fired through the same magnetic field which is perpendicular to their velocity vectors. The αparticle and the proton move such that radius of curvature of their paths is same. Find the ratio of their de Broglie wavelengths :

A
2:3
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B
3:4
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C
5:7
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D
1:2
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Solution

The correct option is D 1:2
Magnetic force, FB=q(v×B)=qvBsinθ

As magnetic field is perpendicular to velocity so θ=90o so FB=qvB

or, mv2r=qvB or mv=qBr

So, momentum p=mv=qBr

de Broglie wavelength for proton , λp=hpp=hqpBrp and

de Broglie wavelength for alpha particle , λα=hpα=hqαBrα

Given, rαrp=1 and qα=2qp

Thus, λαλp=rpqprαqα=1/2

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