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Q.

The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let λ1, be the de-Broglie wavelength of the proton and λ2, be the wavelength of the photon. The ratio λ1/λ2 is proportional to

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a

E0

b

E1/2

c

E−1

d

E−2

answer is B.

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Detailed Solution

We know that λ=hmv=hp  Here 12mv2=p22m=E or p=2mE λ1=h2mE and λ2=hcE therefore λ1λ2=h2mE×Ehc=E1/22mc or λ1λ2∝E1/2
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The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let λ1, be the de-Broglie wavelength of the proton and λ2, be the wavelength of the photon. The ratio λ1/λ2 is proportional to