114 學年度臺灣大學轉學生招生考試｜第 59 題
普通物理學(A)
- 2.3×1049
- 2.3×1019
- 2.3×109
- 2.3×1029
- 2.3×1039
提示
Both forces fall off as 1/r², so the separation cancels in the ratio. Compute kₑe² divided by G·mₑ·m_p — the answer is a famously huge pure number.
正確答案
正解：E
詳解
A. (A) 2.3×10⁴⁹ — incorrect. Ten orders of magnitude too large; the exponent does not work out to 49.
B. (B) 2.3×10¹⁹ — incorrect. This is closer to the electron–electron-style ratios people half-remember, but here one mass is the proton's, giving ~10³⁹.
C. (C) 2.3×10⁹ — incorrect. Far too small; this ignores how extraordinarily weak gravity is relative to the Coulomb force.
D. (D) 2.3×10²⁹ — incorrect. Ten orders of magnitude too small.
E. (E) 2.3×10³⁹ — correct. The r² cancels: ratio = kₑe²/(G mₑ m_p) = (8.99×10⁹ × (1.6×10⁻¹⁹)²)/(6.67×10⁻¹¹ × 9.11×10⁻³¹ × 1.67×10⁻²⁷) ≈ 2.3×10³⁹, the classic measure of how vastly weaker gravity is than electromagnetism.
