The energy of a photons is equal to the kinetic energy of a proton. If λ1 is the de-Broglie wavelength of a proton, λ2 the wavelength associated with the photon, and if the energy of the photon is E, then (λ1/λ2) is proportional to:
E4
E1/2
E2
E
A
E4
B
E1/2
C
E
D
E2
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Solution
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Given : Eproton=Ephoton=E
de-Broglie wavelength of the proton λ1=hp where p=√2mE
⟹λ1=h√2mE .......(1)
Wavelength associated with photon is λ2
∴E=hcλ2⟹λ2=hcE .........(2)
∴λ1λ2=h√2mEhcE=√Ec√2m
⟹λ1λ2∝E1/2
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