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KCET2021PhysicsDual Nature of Matter

A proton moving with a momentum p₁ has a kinetic energy 1 / 8 th of its rest mass-energy. Another light photon having energy equal to the kinetic energy of the possesses a momentum p₂ . Then, the ratio p₁-p₂ p₁ is equal to

Options

  1. A1
  2. B1 / 4
  3. C1 / 2
  4. D3 / 4

Correct answer

D. 3 / 4

Step-by-step solution

For proton, v²= c² 4 ( v= c 2 ) aligned p₁ &= 2 m E_ k &= 2 m 1 8 m c² ( E_ k = 1 8 m c² ) p₁ &= m 2 aligned For photon, aligned & E= KE & h c = 1 8 m c² & p₂= h = m c 8 & p₁-p₂ p₁ = m c 2 - m c 8 m c 2 = 4-1 8 2= 3 4 aligned

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