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 Multiple Choice QuestionsMultiple Choice Questions

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91.

The de-Broglie wavelength of an electron is the same as that of a 50 keV 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 0.5 MeV)

  • 1 : 50

  • 1 : 20

  • 20 : 1

  • 50 : 1


C.

20 : 1

de-Broglie wavelength λ = h2mK

The kinetic energy of the electron

          Kelectron = 12m . h2λ2           ......(i)

where h = Planck Constant

          λ = wavelength

The photon energy

           Ephoton = hcλ                    .......(ii)

From Eqs. (ii) and (i), we get

    EphotonKelectron = hc/λh2/2m . λ2 = hc . λ2 × 2mh2 . λwhere m = 0.5 MeV = 5 × 105 eVhλc = 50 × 103 eV = 2mλch      = 2mh/λc = 2 × 5 × 10550 × 103         m = h      = 20 : 1


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92.

Consider two particles of different masses. In which of the following situations the heavier of the two particles will have smaller de-Broglie wavelength ?

  • Both have a free fall through the same height

  • Both move with the same kinetic energy

  • Both move with the same linear momentum

  • Both move with the same speed


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