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Question

A proton accelerated through a potential V has de-Broglie wavelength λ. Then the de-Broglie wavelength of an α-particle, when accelerated through the same potential V is :

A
λ2
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B
λ2
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C
λ22
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D
λ8
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Solution

The correct option is C λ22
As de-Broglie wavelength is given by λ=hmv=h2m(K.E)
λ=h2mqV where v= accelerating potential

q=charge
λp=h2mpqpv

α=4He++

rqα=2qp
mα=4mp

λα at same accelerating potential

λα=h2×4mp×2qp×v

λα=h2mpqpv×8=λp22

Given λp=λ

λα=λ22.

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