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Question

Find the ratio of de-Broglie wavelength of an αparticle to that of a proton. The proton is subjected to double the strength of magnetic field that of αparticle so that the radii of their path are equal to each other. Assume the field induction B perpendicular to velocity vector of the αparticle.

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

The correct option is A 1:1
As, radius of path

r=mVqB

mV=qBr

De-Broglie wavelength is given by

λ=hmV

λ1mV

λ1qBr

λαλp=qpBprpqαBαrα

Given :Bp=2Bα and rp=rα

Also, qp=+e, qα=+2e

λαλp=(+e)(2B)×r(+2e)(B)×r=11

Hence, option (A) is correct.

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