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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
The Special Theory of Relativity

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Special Theory of Relativity

Calculate the kinetic energy, in electronvolts, of an electron that...

Calculate the kinetic energy, in electronvolts, of an electron that has a mass equal to twice its rest mass.

Options

  1. A255×103255 \times 10^3
  2. B511×103511 \times 10^3
  3. C511511
  4. D1022×1031022 \times 10^3

Correct answer

B. 511×103511 \times 10^3

Step-by-step solution

Total energy of a relativistic particle is given by E=mc2E = mc^2.

Given that the mass of the electron is twice its rest mass, m=2m0m = 2m_0.

Total energy E=2m0c2E = 2m_0c^2.

Kinetic energy KK is the difference between the total energy and the rest mass energy:

K=E−m0c2K = E - m_0c^2

K=2m0c2−m0c2=m0c2K = 2m_0c^2 - m_0c^2 = m_0c^2

The rest mass energy of an electron is m0c2≈0.511 MeV=511×103 eVm_0c^2 \approx 0.511 \text{ MeV} = 511 \times 10^3 \text{ eV}.

Therefore, the kinetic energy of the electron is 511×103 eV511 \times 10^3 \text{ eV}.
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