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Question

A proton has kinetic energy E=100keV which is equal to that of a proton. The wavelength of photon is λ2 and that the proton is λ1. The ratio of λ2/λ1 is proportional to

A
E2
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B
E1/2
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C
E1
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D
E1/2
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Solution

The correct option is B E1/2
Here, kinetic energy of proton = energy of photon
So, E=hcλ2
or λ2=hc/E
If p be the momentum of proton, then E=p22m or p=2mE
From De Broglie hypothesis, wavelength of proton is λ1=hp=h2mE
Thus, λ2λ1=hcE×2mEh=c2mE1/2E1/2

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