【DSE 物理公式表】 放射現象和核能 Radioactivity and Nuclear Energy ＋失分位一文睇清

扣除背景計數率

★ C_net = C_measured − C_background

由探測器讀數求源本身引致的淨計數率，再比較衰變前後的比例。

Subtract background to obtain the source’s net count rate before comparing decay ratios.

不能直接把含背景讀數減半；量度條件須保持一致，計數亦有隨機波動。

Do not halve a reading that includes background. Keep measurement conditions fixed and allow for random counting fluctuations.

半衰期：逐次減半

★ N / N₀ = (½)^t / T_½

★ A / A₀ = C_net / C_net,0 = N / N₀

對單一核素求經過若干個半衰期後的剩餘比例；計數率比例另須探測效率及幾何條件不變。

Find the remaining fraction for a single radionuclide. Count-rate ratios also require unchanged detection efficiency and geometry.

剩餘比例不等於已衰變比例；經過兩個半衰期仍有四分之一未衰變。

The remaining fraction differs from the decayed fraction. One quarter remains after two half-lives.

指數衰變、活度與衰變常數

N = N₀ e^−k t

T_½ = ln 2 / k

A = k N

求任意時間的未衰變原子核數或反推年代；k 是衰變常數，A 是每單位時間的衰變數。

Find the undecayed nuclei at any time or infer an age. k is the decay constant; A is the decay rate.

定年時不要對調現時與初始讀數；N 是原子核數目，不是摩爾數。k 與 t 的單位須配對，求 Bq 時 k 用 s⁻¹。 [R9]

Do not interchange current and initial readings in dating. N counts nuclei, not moles. Match units of k and t; for Bq, use k in s⁻¹.

核方程的守恆關係

★ 核子數：ΣA_before = ΣA_after

★ 電荷數：ΣZ_before = ΣZ_after

配平 α、β⁻ 衰變及核反應；α 粒子的 A = 4、Z = 2，β⁻ 粒子的 A = 0、Z = −1。

Balance alpha/beta-minus decay and nuclear reactions: an alpha particle has A = 4, Z = 2; a beta-minus particle has A = 0, Z = −1.

β⁻ 衰變後子核的 Z 增加 1、A 不變；不要因為放出電子就把子核 Z 減 1。

In beta-minus decay, the daughter’s Z increases by 1 while A stays unchanged; electron emission does not decrease daughter Z.

質能關係與核能釋放

ΔE = Δm c²

計算核反應釋出的能量時，Δm = 反應前總靜止質量 − 反應後總靜止質量；c 是真空光速。

For released nuclear energy, Δm is total rest mass before minus total rest mass after; c is the speed of light in vacuum.

須計齊所有反應粒子的質量，不能把整個 α 粒子的質量當作質量差；留意 u 與 kg、J 與 MeV 的換算。 [R10]

Account for all reaction particles; do not treat an alpha particle’s entire mass as the mass difference. Convert correctly between u and kg, and J and MeV.