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KVPY2016PhysicsDual Nature of Matter

Photons of wavelength are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius R by a perpendicular magnetic field having a magnitude B . The work function of the metal is (Where symbols have their usual meanings) -

Options

  1. Ahc - m _ e + e ² ~B ² R ² 2 ~m _ e
  2. Bhc +2 ~m _ e ( eBR 2 ~m _ e )²
  3. Chc - m _ c C ²- e ² ~B ² R ² 2 ~m _ e
  4. Dhc -2 ~m _ c ( eBR 2 ~m _ e )²

Correct answer

D. hc -2 ~m _ c ( eBR 2 ~m _ e )²

Step-by-step solution

aligned R &= mv qB V &= qBR m = eBR m _ e hc - = KE _ (Einstein photo electric equation) &= hc - KE _ &= hc - 1 2 ~m _ e ( eBR m _ e )² &= hc -2 ~m _ e ( eBR 2 ~m _ e )² aligned

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