Alpha, Beta, Gamma Decay — Revision Notes

⚡ 30-Second Revision

Alpha Decay — $^A_Z\text{X} \rightarrow ^{A-4}_{Z-2}\text{Y} + ^4_2\text{He}$. A decreases by 4, Z decreases by 2. High ionizing, low penetrating. Positively charged.
Beta-minus Decay — $^A_Z\text{X} \rightarrow ^A_{Z+1}\text{Y} + e^- + \bar{\nu}_e$. A unchanged, Z increases by 1. Moderate ionizing, moderate penetrating. Negatively charged.
Beta-plus Decay — $^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + e^+ + \nu_e$. A unchanged, Z decreases by 1. Moderate ionizing, moderate penetrating. Positively charged.
Electron Capture — $^A_Z\text{X} + e^- \rightarrow ^A_{Z-1}\text{Y} + \nu_e$. A unchanged, Z decreases by 1. No particle emission, only X-rays/Auger electrons.
Gamma Decay — $^A_Z\text{X}^* \rightarrow ^A_Z\text{X} + \gamma$. A unchanged, Z unchanged. Low ionizing, high penetrating. No charge, no mass (photon). De-excitation process.
Conservation Laws — A, Z (charge), energy, momentum are conserved in all decays.

2-Minute Revision

Radioactive decay is how unstable nuclei achieve stability by emitting radiation. There are three main types: alpha, beta, and gamma decay.

Alpha decay involves emitting an alpha particle (a helium nucleus, $^4_2\text{He}$). This reduces the mass number (A) by 4 and the atomic number (Z) by 2, transforming the element. Alpha particles are heavy, positively charged, have very high ionizing power, and very low penetrating power.

Beta decay involves a nucleon transformation. Beta-minus decay ($e^-$) occurs when a neutron becomes a proton, emitting an electron and an antineutrino. A remains constant, Z increases by 1. Beta-plus decay ($e^+$) occurs when a proton becomes a neutron, emitting a positron and a neutrino. A remains constant, Z decreases by 1. Beta particles are light, charged, have moderate ionizing and penetrating power.

Gamma decay involves an excited nucleus releasing excess energy as a gamma ray (high-energy photon). Neither A nor Z changes; the nucleus simply de-excites. Gamma rays are uncharged, massless, have very low ionizing power, and very high penetrating power. They are often emitted after alpha or beta decay. All decays conserve mass number, atomic number (charge), energy, and momentum.

5-Minute Revision

Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a more stable one, accompanied by the emission of radiation. This process is governed by the fundamental forces and is independent of external factors like temperature or pressure.

**Alpha ($\alpha$) Decay**: This occurs primarily in very heavy nuclei. An alpha particle, which is a helium nucleus ($^4_2\text{He}$), is emitted. The parent nucleus $^A_Z\text{X}$ transforms into a daughter nucleus $^{A-4}_{Z-2}\text{Y}$.

This means the mass number (A) decreases by 4, and the atomic number (Z) decreases by 2. Alpha particles are positively charged (+2e), relatively massive, have very high ionizing power (due to strong interaction with matter), and consequently, very low penetrating power (stopped by paper).

Example: $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\text{He}$.

**Beta ($\beta$) Decay**: This involves the transformation of a nucleon within the nucleus, mediated by the weak nuclear force. The mass number (A) remains unchanged in both types of beta decay. * **Beta-minus ($\beta^-$) Decay**: Occurs in neutron-rich nuclei.

A neutron converts into a proton, an electron ($e^-$ or $^0_{-1}\beta$), and an antineutrino ($\bar{\nu}_e$). The atomic number (Z) increases by 1. Equation: $^A_Z\text{X} \rightarrow ^A_{Z+1}\text{Y} + e^- + \bar{\nu}_e$.

Example: $^{14}_6\text{C} \rightarrow ^{14}_7\text{N} + e^- + \bar{\nu}_e$. * **Beta-plus ($\beta^+$) Decay**: Occurs in proton-rich nuclei. A proton converts into a neutron, a positron ($e^+$ or $^0_{+1}\beta$), and a neutrino ($\nu_e$).

The atomic number (Z) decreases by 1. Equation: $^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + e^+ + \nu_e$. Example: $^{15}_8\text{O} \rightarrow ^{15}_7\text{N} + e^+ + \nu_e$. Beta particles are light, charged ($pm$e), have moderate ionizing power, and moderate penetrating power (stopped by aluminum).

Neutrinos/antineutrinos are essential for conserving energy, momentum, and angular momentum.

**Gamma ($\gamma$) Decay**: This usually follows alpha or beta decay when the daughter nucleus is left in an excited energy state. The nucleus releases its excess energy by emitting a high-energy photon called a gamma ray.

Neither the mass number (A) nor the atomic number (Z) changes. Equation: $^A_Z\text{X}^* \rightarrow ^A_Z\text{X} + \gamma$. Gamma rays are uncharged, massless, have very low ionizing power, and consequently, very high penetrating power (require thick lead/concrete shielding).

They are undeflected by electric or magnetic fields.

Key Properties Comparison: Alpha particles are most ionizing and least penetrating. Gamma rays are least ionizing and most penetrating. Beta particles are intermediate. All decay processes must adhere to the conservation laws of mass number, atomic number (charge), energy, and momentum.

Prelims Revision Notes

Alpha, Beta, Gamma Decay: NEET Revision Notes

1. Alpha ($\alpha$) Decay:

Emitted Particle — Alpha particle ($^4_2\text{He}$ nucleus, 2 protons, 2 neutrons).
Charge — +2e.
Mass — $\approx 4$ amu.
Effect on Nucleus

* Mass Number (A): Decreases by 4 ($A \rightarrow A-4$). * Atomic Number (Z): Decreases by 2 ($Z \rightarrow Z-2$).

Equation — $^A_Z\text{X} \rightarrow ^{A-4}_{Z-2}\text{Y} + ^4_2\text{He}$.
Properties — Highest ionizing power, lowest penetrating power (stopped by paper). Deflected by E and B fields.

2. Beta ($\beta$) Decay:

**Beta-minus ($\beta^-$) Decay:**

* Mechanism: Neutron ($n$) transforms to Proton ($p$). ($n \rightarrow p + e^- + \bar{\nu}_e$). * Emitted Particles: Electron ($e^-$ or $^0_{-1}\beta$) and Antineutrino ($\bar{\nu}_e$). * **Charge of $e^-$**: -e. * Effect on Nucleus: * Mass Number (A): Unchanged ($A \rightarrow A$). * Atomic Number (Z): Increases by 1 ($Z \rightarrow Z+1$). * Equation: $^A_Z\text{X} \rightarrow ^A_{Z+1}\text{Y} + e^- + \bar{\nu}_e$.

**Beta-plus ($\beta^+$) Decay:**

* Mechanism: Proton ($p$) transforms to Neutron ($n$). ($p \rightarrow n + e^+ + \nu_e$). * Emitted Particles: Positron ($e^+$ or $^0_{+1}\beta$) and Neutrino ($\nu_e$). * **Charge of $e^+$**: +e. * Effect on Nucleus: * Mass Number (A): Unchanged ($A \rightarrow A$). * Atomic Number (Z): Decreases by 1 ($Z \rightarrow Z-1$). * Equation: $^A_Z\text{X} \rightarrow ^A_{Z-1}\text{Y} + e^+ + \nu_e$.

Electron Capture (EC): — (Alternative to $\beta^+$)

* Mechanism: Nucleus captures an inner atomic electron. ($p + e^- \rightarrow n + \nu_e$). * Effect on Nucleus: A unchanged, Z decreases by 1. (Same as $\beta^+$). * Emitted: Neutrino, characteristic X-rays (from electron shell rearrangement).

Properties of Beta Particles — Moderate ionizing power, moderate penetrating power (stopped by aluminum). Deflected by E and B fields (opposite directions for $e^-$ and $e^+$).

3. Gamma ($\gamma$) Decay:

Emitted Particle — Gamma ray (high-energy photon).
Charge — 0.
Mass — 0.
Effect on Nucleus

* Mass Number (A): Unchanged ($A \rightarrow A$). * Atomic Number (Z): Unchanged ($Z \rightarrow Z$). * Only energy state changes (de-excitation).

Equation — $^A_Z\text{X}^* \rightarrow ^A_Z\text{X} + \gamma$ (where $^*$ denotes excited state).
Properties — Lowest ionizing power, highest penetrating power (requires thick lead/concrete). Undeflected by E and B fields.

4. Conservation Laws (Crucial for all decays):

Mass Number (A) — Total nucleons conserved.
Atomic Number (Z) — Total charge conserved.
Energy — Total energy (mass-energy + kinetic energy) conserved (Q-value).
Momentum — Total linear and angular momentum conserved (role of neutrinos/antineutrinos).

5. Relative Properties Summary:

Property	Alpha ($\alpha$)	Beta ($\beta$)	Gamma ($\gamma$)
Ionizing Power	Very High	Moderate	Low
Penetrating Power	Very Low	Moderate	Very High
Deflection in E/B	Yes	Yes	No
Nature	He nucleus	Electron/Positron	Photon

Vyyuha Quick Recall

Alpha: A-4, Z-2. (Heavy, Helium nucleus) Beta-minus: A-same, Z+1. (Neutron to Proton, Electron) Beta-plus: A-same, Z-1. (Proton to Neutron, Positron) Gamma: A-same, Z-same. (Energy release, Photon)

Penetrating Power Order: Alpha < Beta < Gamma (APBG) Ionizing Power Order: Alpha > Beta > Gamma (AIBG)