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Question

The de-Broglie wavelength of an electron is the same as that of a 50keV X-ray photon. The ratio of the energy of the photon to the kinetic energy of the electron is (the energy equivalent of electron mass is 0.5MeV):
  1. 1:20
  2. 50:1
  3. 20:1
  4. 1:50

A
1:50
B
1:20
C
20:1
D
50:1
Solution
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Energy of X-ray photon Ephoton=50keV=5×104eV
Energy equivalent of electron mass is 0.5MeV i.e mc2=0.5MeV=5×105eV ......(1)
Wavelength of the photon λphoton=hcE=12425×104 nm=0.0248 nm
de-Broglie wavelength of the electron λ=λphoton=0.0248 nm

Kinetic energy of electron Eelectron=h22m×λ2=h2c22(mc2)λ2 (E=p22m)

Kinetic energy of electron Eelectron=(1242)22(5×105)×(0.0248)2 eV=2.51×103eV
EphotonEelectron=5×1042.51×103=20

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