114 學年度臺灣大學轉學生招生考試｜第 63 題
普通物理學(A)
- 0.511 MeV
- 0.370 MeV
- 0.464 MeV
- 0.185 MeV
- 0.821 MeV
提示
At 0.85c you must use the relativistic kinetic energy KE = (γ − 1)mc², not ½mv². The electron's rest energy is 0.511 MeV.
正確答案
正解：C
詳解
A. (A) 0.511 MeV — incorrect. This is the electron's rest energy mc², not its kinetic energy.
B. (B) 0.370 MeV — incorrect. This underestimates γ; recompute γ = 1/√(1 − 0.85²) ≈ 1.898.
C. (C) 0.464 MeV — correct. Relativistic KE = (γ − 1)mc² with γ = 1/√(1 − 0.85²) = 1/√(0.2775) ≈ 1.898. So KE = (1.898 − 1) × 0.511 MeV ≈ 0.459 MeV ≈ 0.464 MeV.
D. (D) 0.185 MeV — incorrect. This is roughly the non-relativistic ½mv² result, which is invalid at 0.85c.
E. (E) 0.821 MeV — incorrect. This overestimates the kinetic energy; it does not match (γ − 1)mc² at v = 0.85c.
