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Question

The ratio of de-Broglie wavelength of a α particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal each other assuming the field induction vector B is perpendicular to the velocity vectors of the αparticle and the proton, is

A
1
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B
1/4
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C
1/2
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D
2
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Solution

The correct option is C 1/2
When a charged particle of charge q, mass m enters perpendicularly to the magnetic induction B of a magnetic field, it will experience a magnetic force
F=q(v×B)=q vBsin90o=q vB that provide a centripetal acceleration v2r
qvB=mv2rmv=qBr
The de-Broglie wavelength λ=hmv=hqBr
λαparticleλproton=qρrpqαrα
Since rαrp=1 and qαqp=2
λαλ=1/2
Hence (C) is correct.

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