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NEETPhysicsDual Nature of Matter

Light of frequency is incident on a photosensitive metal surface having work function ₀ . A photon has the same linear momentum as that of the fastest emitted photoelectron. The energy of this photon is : (Let m be the mass of the electron, c be the speed of light and h be Planck's constant)

Options

  1. A1 c 2m(h - ₀)
  2. Bc 2m(h - ₀)
  3. Cc m(h - ₀)
  4. D2mc(h - ₀)

Correct answer

B. c 2m(h - ₀)

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy K_ max of the emitted photoelectron is: K_ max = h - ₀ The linear momentum p_e of the fastest emitted photoelectron is: p_e = 2mK_ max = 2m(h - ₀) It is given that the photon has the same linear momentum as the fastest photoelectron, so: p_ ph = p_e = 2m(h - ₀) The energy E_ ph of a photon is related to its momentum by E_ ph = p_ ph c . Substituting the value of p_ ph : E_ ph = c 2m(h - ₀) Answer: c 2m(h - ₀)

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