114 學年度臺灣大學轉學生招生考試｜第 61 題
普通物理學(A)
- 4.1×102
- 4.1×103
- 4.1×104
- 4.1×105
- 4.1×106
提示
The photon and electron share the same momentum p = h/λ. Compare a photon's energy (E = pc) with a non-relativistic electron's energy (E = p²/2m); the ratio reduces to 2mcλ/h.
正確答案
正解：D
詳解
A. (A) 4.1×10² — incorrect. Three orders of magnitude too small; check the powers of ten in 2mcλ/h.
B. (B) 4.1×10³ — incorrect. Two orders of magnitude too small.
C. (C) 4.1×10⁴ — incorrect. One order of magnitude too small.
D. (D) 4.1×10⁵ — correct. With equal momentum p = h/λ: KE_ph = pc and KE_e = p²/2m, so the ratio = pc/(p²/2m) = 2mc/p = 2mcλ/h = (2 × 9.11×10⁻³¹ × 3×10⁸ × 500×10⁻⁹)/6.63×10⁻³⁴ ≈ 4.1×10⁵. The photon carries far more energy than the equally-momentum electron.
E. (E) 4.1×10⁶ — incorrect. One order of magnitude too large.
