HKDSE Physics – Radiation and Radioactivity

HKDSE Physics
Chapter 1: Radiation and Radioactivity | 輻射與放射現象

Billy Sir’s Smart Notes: Master Ionizing Radiation, Decay Equations, and Half-Life.
由中大物理系碩士 Billy Sir 編寫，助你極速掌握電離輻射、衰變方程及半衰期。

1. Basics of Radiation | 輻射基礎

Nuclear Radiation (核輻射): Particles or electromagnetic waves emitted from the unstable nucleus of an atom during radioactive decay. (放射性衰變期間從不穩定原子核發出的粒子或電磁波。)

Ionizing Radiation (電離輻射): Radiation with enough energy to remove electrons from atoms, creating ions. (具有足夠能量將電子從原子中移除並產生離子的輻射。)

☢️ Detection & Background Radiation | 探測與背景輻射

GM Tube (Geiger-Müller Tube / 蓋革-米勒管): A common device used to detect ionizing radiation. It counts the number of ionizing events. (常用於探測電離輻射的儀器，計算電離事件的次數。)
Background Radiation (背景輻射): The low-level ionizing radiation present in the environment at all times (e.g., from radon gas, cosmic rays, rocks, and food). (環境中時刻存在的低水平電離輻射，例如來自氡氣、宇宙射線、岩石和食物。)

Note: When measuring the activity of a source, the background count rate must be subtracted from the measured count rate! (注意：測量放射源活度時，必須從量度得的計數率中減去背景計數率！)

2. Comparing Types of Radiation | 輻射種類比較

Property (性質)	Alpha (\(\alpha\)) \| 阿爾法	Beta (\(\beta\)) \| 貝他	Gamma (\(\gamma\)) \| 伽馬	X-ray \| X射線
Nature (本質)	Helium nucleus (2p, 2n) 氦原子核	Fast-moving electron 高速電子	High-frequency EM wave 高頻電磁波	High-frequency EM wave 高頻電磁波
Mass (質量)	~ 4 u (Heavy)	~ 1/1836 u (Very light)	0	0
Charge (電荷)	+2e	-1e	0 (Neutral)	0 (Neutral)
Speed (速率)	~ 0.1 c	Up to ~ 0.9 c	c (Speed of light)	c (Speed of light)
Ionizing Power (電離能力)	Very High 極高	Moderate 中等	Low 低	Low 低
Range in Air (空氣中射程)	A few cm 幾厘米	A few meters 幾米	Infinite (follows inverse square law) 無限遠	Infinite 無限遠
Penetrating Power (穿透能力)	Stopped by a sheet of paper 被紙張阻擋	Stopped by ~5 mm of Aluminium 被 5 mm 鋁板阻擋	Reduced by thick Lead / Concrete 被厚鉛/混凝土減弱	Reduced by Lead 被鉛減弱

3. Radioactive Decay & Activity | 放射性衰變與活度

Radioactive decay is a spontaneous and random process. 放射性衰變是一個自發且隨機的過程。

📉 Activity & Exponential Equations | 活度與指數方程

Activity (\(A\)) / 活度: The number of disintegrations per second. Unit: Becquerel (Bq). (每秒衰變的次數。單位：貝可)
Decay Constant (\(k\)) / 衰變常數: The probability of decay of a nucleus per unit time. (原子核在單位時間內衰變的概率。)

$$ A = k N $$

Because the decay rate is proportional to the number of undecayed nuclei (\(N\)), the decay follows an exponential law: (由於衰變率與未衰變原子核數目成正比，衰變遵循指數定律：)

N = N_0 e^{-kt} \quad \text{and} \quad A = A_0 e^{-kt}

\(N_0\) and \(A_0\) are the initial number of nuclei and initial activity at \(t = 0\).

4. Half-Life | 半衰期

The Half-life (\(t_{1/2}\)) is the time taken for half of the radioactive nuclei in a sample to decay, or for the activity to fall to half of its initial value. 半衰期是指樣本中一半的放射性原子核發生衰變，或活度降至初始值一半所需的時間。

⏱️ Relating Half-Life and Decay Constant | 半衰期與衰變常數的關係

By substituting \( N = \frac{N_0}{2} \) into the exponential equation when \( t = t_{1/2} \), we get: (將 \( N = \frac{N_0}{2} \) 代入指數方程，可得：)

t_{1/2} = \frac{\ln 2}{k} \approx \frac{0.693}{k}

A larger decay constant (\(k\)) means a shorter half-life (decays faster). (衰變常數越大，半衰期越短，衰變越快。)
After \(n\) half-lives, the remaining fraction of undecayed nuclei is \( \left(\frac{1}{2}\right)^n \). (經過 \(n\) 個半衰期後，剩餘未衰變原子核的比例為 \( \left(\frac{1}{2}\right)^n \)。)

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