Login Free Test Start Mock

Physics · Nuclei

Radioactivity — Alpha, Beta, and Gamma Decay

Radioactivity is the phenomenon in which an unstable nucleus spontaneously transforms by giving out radiation. Following NCERT §13.6 and NIOS §26.3, this page covers the three decay modes that occur in nature — alpha, beta and gamma — together with their decay equations, the displacement law, the Q-value, and penetrating power. These are recurring, high-yield ideas in the NEET Nuclei chapter, and the displacement-law questions are almost always solvable in seconds once the rules are fixed.

What Radioactivity Is

Radioactivity was discovered in 1896 by A. H. Becquerel, who found that uranium salts emitted a penetrating radiation able to fog a photographic plate even through black paper and a silver sheet. Subsequent experiments established that the effect was a nuclear phenomenon: an unstable nucleus undergoes a spontaneous transformation called radioactive decay. Marie and Pierre Curie extended the work by isolating two far more active elements, radium and polonium, from uranium ore.

In 1899 Rutherford analysed the Becquerel rays and identified two distinct components, the alpha particles and the beta rays; the third component, gamma rays, was later established by P. Villard. The defining feature of the process is that it is spontaneous — the decay rate is independent of external factors such as temperature and pressure — and that in alpha or beta emission a nucleus of one element is converted into a nucleus of a new element.

Heavier nuclei face an intense electrostatic repulsion among their protons. Neutrons act as the binding "glue", but beyond a point even extra neutrons cannot keep such nuclei stable. To reach a more stable configuration the nucleus disintegrates, emitting alpha and beta particles along with gamma rays.

Radioactivity is the phenomenon in which nuclei of a given species transform by giving out α, β or γ rays. Alpha rays are helium nuclei, beta rays are electrons (or positrons), and gamma rays are electromagnetic radiation of wavelengths shorter than X-rays.

The Three Decay Modes

Three types of radioactive decay occur in nature. In alpha decay a helium nucleus $^{4}_{2}\mathrm{He}$ is emitted. In beta decay, electrons or positrons — particles with the same mass as the electron but opposite charge — are emitted. In gamma decay, high-energy photons (hundreds of keV or more) are emitted. In every nuclear disintegration both the charge number $Z$ and the mass number $A$ are conserved, and this single rule is what lets us predict the daughter nucleus.

The three decay equations α ᴬ₂Xᴢ → ᴬ⁻⁴ Y (Z−2) + ⁴₂He A − 4, Z − 2 β⁻ ᴬZX → ᴬ(Z+1)Y + e⁻ + ν̄ same A, Z + 1 β⁺ ᴬZX → ᴬ(Z−1)Y + e⁺ + ν same A, Z − 1 γ (ᴬZX)* → ᴬZX + γ no change in A or Z
The three nuclear transformations. The asterisk marks an excited nucleus. Both $A$ and $Z$ are conserved on each side.
Decay Emitted particle Change in A Change in Z Penetrating power
Alpha Helium nucleus ⁴₂He −4 −2 Lowest — stopped by 0.02 mm Al
Beta-minus (β⁻) Electron e⁻ + antineutrino 0 +1 ~100× alpha; few mm of Al
Beta-plus (β⁺) Positron e⁺ + neutrino 0 −1 Similar to β⁻
Gamma High-energy photon γ 0 0 Highest — several cm of iron/lead

Alpha Decay

In alpha decay the nucleus emits an alpha particle, which is a helium nucleus $^{4}_{2}\mathrm{He}$ made of two protons and two neutrons. Because two protons and two neutrons leave together, the parent's mass number drops by 4 and its atomic number drops by 2. The general transformation is written

$$^{A}_{Z}X \;\longrightarrow\; ^{A-4}_{Z-2}Y \;+\; ^{4}_{2}\mathrm{He}$$

The daughter $Y$ is a new element two places lower in the periodic table. Alpha particles are charged, so they deflect in electric and magnetic fields. They have a very high ionizing power — a single alpha particle can ionize thousands of gas atoms before it is absorbed — but a correspondingly low penetrating power, being stopped by an aluminium sheet about 0.02 mm thick. The energies of the emitted alpha particles are characteristic of the emitting nucleus.

Worked example

Uranium $^{238}_{92}\mathrm{U}$ undergoes alpha decay. Identify the daughter nucleus.

Mass number: $238 - 4 = 234$. Atomic number: $92 - 2 = 90$, which is thorium. The product is $^{234}_{90}\mathrm{Th}$, conserving both $A$ and $Z$ across the equation $^{238}_{92}\mathrm{U} \to {}^{234}_{90}\mathrm{Th} + {}^{4}_{2}\mathrm{He}$.

Beta Decay (β⁻ and β⁺)

Beta particles originate in the nucleus through the conversion of a neutron into a proton, or a proton into a neutron. There are two varieties. In beta-minus (β⁻) decay, a neutron becomes a proton, emitting an electron and an antineutrino:

$$n \;\longrightarrow\; p + e^{-} + \bar{\nu}, \qquad ^{A}_{Z}X \;\longrightarrow\; ^{\;\;A}_{Z+1}Y + e^{-} + \bar{\nu}$$

Since one neutron has turned into one proton, the atomic number rises by 1 while the mass number is unchanged. The same conversion happens to a free neutron, which is unstable and decays into a proton, an electron and an antineutrino with a mean life of about 1000 s; inside a stable nucleus, however, the neutron does not decay.

In beta-plus (β⁺) decay, a proton becomes a neutron, emitting a positron and a neutrino:

$$p \;\longrightarrow\; n + e^{+} + \nu, \qquad ^{A}_{Z}X \;\longrightarrow\; ^{\;\;A}_{Z-1}Y + e^{+} + \nu$$

Here the atomic number falls by 1 and the mass number again stays the same. The positron is the antiparticle of the electron: identical in mass, equal and opposite in charge. When a positron meets an electron the pair annihilates, releasing energy as gamma-ray photons. Beta particles deflect in electric and magnetic fields, ionize gas atoms far less strongly than alpha particles, and are roughly 100 times more penetrating, passing through a few millimetres of aluminium.

NEET Trap

Mixing up the displacement rules — and forgetting the antineutrino

The most common error in displacement-law questions is misremembering how $Z$ shifts. Fix the four rules in this order: α gives $A-4$, $Z-2$; β⁻ keeps $A$ the same and pushes $Z+1$; β⁺ keeps $A$ the same and pushes $Z-1$; γ changes neither $A$ nor $Z$. A second trap is leaving out the (anti)neutrino — β⁻ emits an antineutrino ($\bar{\nu}$) and β⁺ emits a neutrino ($\nu$). When you balance a decay equation, balance only $A$ and $Z$; the neutrino carries no charge and effectively no mass number.

α: $A{-}4$, $Z{-}2$ · β⁻: same $A$, $Z{+}1$ · β⁺: same $A$, $Z{-}1$ · γ: no change in $A$ or $Z$.

→
Keep going

Once you can name the daughter nucleus, the next step is timing the decay. See Radioactive Decay & Half-Life for the decay law, decay constant and half-life.

Gamma Decay

After an alpha or beta emission, the daughter nucleus is frequently left in an excited state, marked with an asterisk. It returns to a lower-energy state by releasing the surplus energy as a high-frequency electromagnetic photon — a gamma ray:

$$(^{A}_{Z}X)^{*} \;\longrightarrow\; ^{A}_{Z}X \;+\; \gamma$$

Because only the energy state changes and not the composition, gamma emission leaves both $A$ and $Z$ unchanged — no new element is formed. Gamma rays are not deflected by electric or magnetic fields, travel at the speed of light, and have the greatest penetrating power of the three, passing through several centimetres of iron and lead. Their ionizing power, by contrast, is the smallest. High-energy ("hard") gamma rays are used in the radiotherapy of malignant cells.

The Q-value of a Decay

The energy released in a nuclear process is its Q-value, defined as the final kinetic energy minus the initial kinetic energy. By conservation of mass–energy this can equally be written in terms of masses:

$$Q = \big(\text{sum of initial masses} - \text{sum of final masses}\big)c^{2}$$

A spontaneous decay requires $Q > 0$, meaning the combined mass of the products is less than the mass of the parent; the missing mass appears as the kinetic energy of the products and any emitted photon. If $Q$ were negative the decay could not occur on its own. This is why radioactivity always moves a nucleus toward a more tightly bound, lower-mass configuration.

A decay-chain segment on an N versus Z plot Atomic number Z (protons) → Neutron number N → parent α (Z−2, N−2) β⁻ (Z+1, N−1) α moves the nucleus down and to the left; β⁻ moves it down and to the right.
A segment of a decay chain on the N–Z plane. An alpha step removes two protons and two neutrons; a β⁻ step converts a neutron into a proton, so N falls by 1 as Z rises by 1.

Penetrating and Ionizing Power

The three radiations differ sharply in how far they travel and how strongly they ionize matter. Alpha particles are the most strongly ionizing but the least penetrating; gamma rays are the opposite, deeply penetrating but weakly ionizing; beta particles sit in between on both counts. This inverse relationship is a frequent qualitative-question target.

Penetration comparison of alpha, beta and gamma source paper Al sheet thick Pb α β γ
Penetration in increasing order: alpha is stopped by paper or a 0.02 mm aluminium sheet, beta by a few millimetres of aluminium, and gamma needs several centimetres of iron or lead. Ionizing power runs in the reverse order.

Displacement-law Practice

The displacement law is simply conservation of $A$ and $Z$ applied repeatedly along a decay sequence. To track a chain, apply the per-step rules in turn and balance the totals at the end. The worked example below mirrors the structure of the NEET 2024 chain question.

Worked example

A nucleus $^{A}_{Z}X$ undergoes the sequence: α, then β⁺, then β⁻, then β⁻. By how much do $A$ and $Z$ change in total?

Track each step. α: $A-4$, $Z-2$. β⁺: $A$ unchanged, $Z-1$. β⁻: $A$ unchanged, $Z+1$. β⁻: $A$ unchanged, $Z+1$. Net change in mass number: $-4$. Net change in atomic number: $-2-1+1+1 = -1$. So the final product has mass number $A-4$ and atomic number $Z-1$.

Quick Recap

Radioactivity — Alpha, Beta, and Gamma Decay

  • Radioactivity is the spontaneous decay of an unstable nucleus into a more stable one, emitting α, β or γ radiation; both $A$ and $Z$ are always conserved.
  • Alpha: emits $^{4}_{2}\mathrm{He}$; $A \to A-4$, $Z \to Z-2$. Highest ionizing, lowest penetrating power.
  • Beta-minus: $n \to p + e^{-} + \bar{\nu}$; $A$ unchanged, $Z \to Z+1$. Beta-plus: $p \to n + e^{+} + \nu$; $A$ unchanged, $Z \to Z-1$.
  • Gamma: excited nucleus emits a photon; no change in $A$ or $Z$. Highest penetrating, lowest ionizing power.
  • The Q-value is $(\Sigma m_\text{initial} - \Sigma m_\text{final})c^2$; a decay is spontaneous only when $Q > 0$.

NEET PYQ Snapshot — Radioactivity: Alpha, Beta, and Gamma Decay

Real NEET questions on decay equations and the displacement law. Half-life numericals are covered on the sibling Half-Life page.

NEET 2022

In the given nuclear reaction, the element X is: $^{22}_{11}\mathrm{Na} \to X + e^{+} + \nu$.

  • (1) $^{23}_{10}\mathrm{Ne}$
  • (2) $^{22}_{10}\mathrm{Ne}$
  • (3) $^{22}_{12}\mathrm{Mg}$
  • (4) $^{23}_{11}\mathrm{Na}$
Answer: (2) $^{22}_{10}\mathrm{Ne}$

This is a β⁺ emission. Conserving atomic number: $11 = Z + 1 \Rightarrow Z = 10$ (neon). Conserving mass number: $22 = A + 0 \Rightarrow A = 22$. Hence $X = {}^{22}_{10}\mathrm{Ne}$.

NEET 2021

A radioactive nucleus $^{A}_{Z}X$ decays in the sequence $^{A}_{Z}X \to {}_{Z-1}B \to {}_{Z-3}C \to {}_{Z-2}D$. The possible decay particles in the sequence are:

  • (1) β⁻, α, β⁺
  • (2) α, β⁻, β⁺
  • (3) α, β⁺, β⁻
  • (4) β⁺, α, β⁻
Answer: (4) β⁺, α, β⁻

Step 1: $Z \to Z-1$ means β⁺ decay (atomic number falls by 1). Step 2: $Z-1 \to Z-3$ is a drop of 2, which is α decay. Step 3: $Z-3 \to Z-2$ is a rise of 1, which is β⁻ decay. Order: β⁺, α, β⁻.

NEET 2024

$^{290}_{82}X \xrightarrow{\alpha} Y \xrightarrow{e^{+}(\beta^{+})} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q$. The mass number and atomic number of the product Q respectively are:

  • (1) 280, 81
  • (2) 286, 80
  • (3) 288, 82
  • (4) 286, 81
Answer: (4) 286, 81

Start at $A = 290$, $Z = 82$. α: $A \to 286$, $Z \to 80$. β⁺: $A = 286$, $Z \to 79$. β⁻: $A = 286$, $Z \to 80$. β⁻ (e⁻): $A = 286$, $Z \to 81$. Final Q has mass number 286 and atomic number 81.

FAQs — Radioactivity: Alpha, Beta, and Gamma Decay

Quick answers to the displacement-law and decay-mode doubts that recur most in NEET prep.

How do the mass number and atomic number change in alpha, beta-minus and gamma decay?
In alpha decay the nucleus emits a helium nucleus, so the mass number falls by 4 and the atomic number falls by 2. In beta-minus decay a neutron becomes a proton, so the atomic number rises by 1 while the mass number is unchanged. In gamma decay an excited nucleus releases a high-energy photon, so neither the mass number nor the atomic number changes.
Why is an antineutrino emitted in beta-minus decay?
A free neutron decays into a proton, an electron and an antineutrino. The antineutrino is a nearly massless, chargeless particle that carries away the balance of energy and momentum. Its emission is why the emitted electrons show a continuous range of energies rather than a single fixed value, and it is needed to conserve energy, momentum and lepton number.
How does beta-plus decay differ from beta-minus decay?
In beta-minus decay a neutron converts into a proton, emitting an electron and an antineutrino, so the atomic number increases by 1. In beta-plus decay a proton converts into a neutron, emitting a positron and a neutrino, so the atomic number decreases by 1. In both cases the mass number stays the same because the total number of nucleons does not change.
What is the Q-value of a radioactive decay?
The Q-value is the energy released in a nuclear process, equal to the final kinetic energy minus the initial kinetic energy. Equivalently, by mass-energy conservation, Q equals the sum of the initial masses minus the sum of the final masses, multiplied by c squared. A decay is spontaneous only when Q is positive, meaning the products are lighter than the parent.
Why does gamma decay usually follow alpha or beta decay?
After an alpha or beta emission, the daughter nucleus is often left in an excited energy state. It then drops to a lower state by releasing the surplus energy as a gamma-ray photon. Because gamma emission only changes the energy state and not the composition, the mass number and atomic number remain the same.
Which radiation has the greatest penetrating power and which has the greatest ionizing power?
Gamma rays have the greatest penetrating power, passing through several centimetres of iron and lead, while alpha particles are stopped by a 0.02 mm aluminium sheet. The order is reversed for ionizing power: alpha particles ionize most strongly, beta particles much less, and gamma rays the least.
Related Topics
Nuclei — Chapter Home All subtopics in the NEET Nuclei chapter. Radioactive Decay & Half-Life The decay law, decay constant and half-life numericals. Nuclear Binding Energy Why decay moves nuclei toward tighter binding. Atomic Masses & Nuclear Composition Protons, neutrons and the A, Z, N notation. Nuclear Fission Heavy nuclei splitting into intermediate fragments. Nuclear Fusion Light nuclei combining to power the stars.