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QPage 458: Q27: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q27 Solution: What is the kinetic energy of an electron in electron volts…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently substitute the relativistic mass $m$ directly into the classical formula $K = \frac{1}{2}mv^2$ or incorrectly assume $K = \gamma m_0 c^2$ without subtracting the rest energy. Always use the definition $K = (\gamma - 1)m_0 c^2$ to correctly isolate the kinetic component from the total relativistic energy.

What is the kinetic energy of an electron in electron volts with mass equal to double its rest mass?

Step-by-Step Verified Solution

**Answer:** KE = 0.511 MeV. **Step-by-Step Explanation:** If mass = 2m02m_0, then γm0=2m0⇒γ=2\gamma m_0 = 2m_0 \Rightarrow \gamma = 2. K=(γ−1)m0c2=(2−1)×0.511=0.511K = (\gamma - 1)m_0c^2 = (2-1) \times 0.511 = 0.511 MeV.

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