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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Photoelectric Effect and Wave–Particle Duality

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Photoelectric Effect and Wave–Particle Duality

The equation E = pc holds true

The equation E=pcE = pc holds true

Options

  1. Afor an electron but not for a photon
  2. Bfor a photon but not for an electron
  3. Cfor both an electron and a photon
  4. Dfor neither an electron nor a photon

Correct answer

B. for a photon but not for an electron

Step-by-step solution

The relativistic relation between energy EE and momentum pp for a particle of rest mass m0m_0 is given by

E2=p2c2+m02c4E^2 = p^2c^2 + m_0^2c^4

For a photon, the rest mass m0=0m_0 = 0. Substituting this in the equation, we get

E2=p2c2⇒E=pcE^2 = p^2c^2 \Rightarrow E = pc

For an electron, the rest mass m0≠0m_0 \neq 0. Therefore, m02c4>0m_0^2c^4 > 0, which gives

E=p2c2+m02c4>pcE = \sqrt{p^2c^2 + m_0^2c^4} > pc

Thus, the equation E=pcE = pc holds true for a photon but not for an electron.
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