22.3.1 Alpha Decay | Nuclear Physics | Physics 12

Alpha decay is a type of radioactive decay in which an unstable nucleus spontaneously emits an alpha particle ( $_{2}^{4} He$ ) to become a more stable daughter nucleus.

The Alpha Particle

An alpha particle is identical to a helium-4 nucleus:

Composed of 2 protons and 2 neutrons
Charge: $+ 2 e$
Mass: $\approx 4 u$
High ionizing power (due to large charge and mass)
Low penetrating power (stopped by a few centimetres of air or a sheet of paper)

General Equation for Alpha Decay

When a parent nucleus $_{Z}^{A} X$ undergoes alpha decay:

$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He + Q$

where:

$Y$ is the daughter nucleus
The mass number $A$ decreases by 4
The atomic number $Z$ decreases by 2 (the element moves two places to the left in the periodic table)
$Q$ is the energy released (Q-value)

Example — Uranium-238 decay:

$_{92}^{238} U \to_{90}^{234} Th +_{2}^{4} He + Q$

Q-Value and Energy Released

The Q-value is the energy released during alpha decay, calculated from the mass defect:

$Q = [m (X) - m (Y) - m (α)] c^{2}$

If $Q > 0$ : decay is spontaneous (exothermic) — the parent is heavier than the products.
If $Q < 0$ : decay cannot occur spontaneously.

The Q-value is shared as kinetic energy between the alpha particle and the recoiling daughter nucleus. By conservation of linear momentum, the daughter nucleus recoils in the opposite direction, so the alpha particle receives slightly less than the full Q-value:

$Q = K E_{α} + K E_{daughter}$

Since $m_{daughter} ≫ m_{α}$ , the alpha particle carries away most of the kinetic energy.

Why Heavy Nuclei Undergo Alpha Decay

In heavy nuclei (large $Z$ ):

The long-range electrostatic (Coulomb) repulsion between the many protons is very large.
The short-range strong nuclear force cannot fully overcome this repulsion across the large nuclear volume.
Emitting an alpha particle reduces both $Z$ and $A$ , decreasing Coulomb repulsion and moving the nucleus toward greater stability.

This is why alpha decay is predominantly observed in heavy nuclei with $Z > 82$ (beyond lead in the periodic table).

Spontaneous and Random Nature

Alpha decay is:

Spontaneous: it occurs without any external trigger; the rate is unaffected by temperature, pressure, or chemical state.
Random: it is impossible to predict which specific nucleus will decay next; only the probability (decay constant $λ$ ) can be stated.

Alpha decay is a type of radioactive decay in which an unstable nucleus spontaneously emits an alpha particle ( $_{2}^{4} He$ ) to become a more stable daughter nucleus.

The Alpha Particle

An alpha particle is identical to a helium-4 nucleus:

Composed of 2 protons and 2 neutrons
Charge: $+ 2 e$
Mass: $\approx 4 u$
High ionizing power (due to large charge and mass)
Low penetrating power (stopped by a few centimetres of air or a sheet of paper)

General Equation for Alpha Decay

When a parent nucleus $_{Z}^{A} X$ undergoes alpha decay:

$_{Z}^{A} X \to_{Z - 2}^{A - 4} Y +_{2}^{4} He + Q$

where:

$Y$ is the daughter nucleus
The mass number $A$ decreases by 4
The atomic number $Z$ decreases by 2 (the element moves two places to the left in the periodic table)
$Q$ is the energy released (Q-value)

Example — Uranium-238 decay:

$_{92}^{238} U \to_{90}^{234} Th +_{2}^{4} He + Q$

Q-Value and Energy Released

The Q-value is the energy released during alpha decay, calculated from the mass defect:

$Q = [m (X) - m (Y) - m (α)] c^{2}$

If $Q > 0$ : decay is spontaneous (exothermic) — the parent is heavier than the products.
If $Q < 0$ : decay cannot occur spontaneously.

$Q = K E_{α} + K E_{daughter}$

Since $m_{daughter} ≫ m_{α}$ , the alpha particle carries away most of the kinetic energy.

Why Heavy Nuclei Undergo Alpha Decay

In heavy nuclei (large $Z$ ):

The long-range electrostatic (Coulomb) repulsion between the many protons is very large.
The short-range strong nuclear force cannot fully overcome this repulsion across the large nuclear volume.
Emitting an alpha particle reduces both $Z$ and $A$ , decreasing Coulomb repulsion and moving the nucleus toward greater stability.

This is why alpha decay is predominantly observed in heavy nuclei with $Z > 82$ (beyond lead in the periodic table).

Spontaneous and Random Nature

Alpha decay is:

Spontaneous: it occurs without any external trigger; the rate is unaffected by temperature, pressure, or chemical state.
Random: it is impossible to predict which specific nucleus will decay next; only the probability (decay constant $λ$ ) can be stated.