Alpha Decay: Heavy Nuclei, Helium Nuclei, and Energy Release

What alpha decay is (and what is emitted)

In alpha decay, an unstable nucleus emits an alpha particle, which is a tightly bound helium-4 nucleus made of 2 protons and 2 neutrons. Because the emitted particle carries away two protons and two neutrons, the parent nucleus changes in a very specific way:

• Mass number decreases by 4: A → A − 4
• Atomic number decreases by 2: Z → Z − 2

Written generically:

^A_Z X  →  ^(A−4)_(Z−2) Y  +  ^4_2 He   (alpha particle)

Alpha decay is most common in very heavy nuclides (typically high-Z nuclei). In these nuclei, the strong nuclear force still binds nearby nucleons, but the large number of protons increases electrostatic repulsion, making it favorable to reduce Z by emitting an alpha particle.

How to balance alpha-decay equations and predict the daughter nuclide

Balancing alpha decay is a bookkeeping procedure: you conserve mass number A and atomic number Z. The alpha particle always contributes A = 4 and Z = 2.

Step-by-step procedure

1. Write the parent nucleus in nuclear notation: ^A_Z X.

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2. Subtract 4 from A to get the daughter mass number: A_d = A − 4.

3. Subtract 2 from Z to get the daughter atomic number: Z_d = Z − 2.

4. Identify the daughter element by its atomic number Z_d (from the periodic table). Keep the same element symbol only if Z is unchanged (it is not in alpha decay), so the element always changes.

5. Check conservation: confirm that A_parent = A_d + 4 and Z_parent = Z_d + 2.

Worked examples

Example 1: Uranium-238

^238_92 U  →  ^234_90 Th  +  ^4_2 He

• A: 238 → 234 (subtract 4)
• Z: 92 → 90 (subtract 2), element with Z=90 is thorium (Th)

Example 2: Polonium-210

^210_84 Po  →  ^206_82 Pb  +  ^4_2 He

• Z: 84 → 82, element with Z=82 is lead (Pb)

Example 3: Unknown daughter identification

If you are told:

^226_88 Ra  →  daughter  +  ^4_2 He

Compute daughter numbers:

• A_d = 226 − 4 = 222
• Z_d = 88 − 2 = 86 → element Z=86 is radon (Rn)

^226_88 Ra  →  ^222_86 Rn  +  ^4_2 He

Common balancing mistakes to avoid

• Subtracting 2 from A instead of 4. Remember: alpha contains 4 nucleons.
• Forgetting the element changes. Since Z decreases by 2, the daughter is a different element.
• Mixing up symbols: ^4_2He is the alpha particle; it is not an electron or a generic “helium atom.” (It is a nucleus; it will quickly capture electrons from matter to become neutral helium.)

Energy release and the barrier picture (why alpha decay can happen at all)

Inside a nucleus, the alpha particle is strongly attracted by the nuclear force when it is very close to other nucleons. However, once it tries to leave, it faces an opposing effect: the Coulomb repulsion barrier between the positively charged alpha particle (charge +2e) and the positively charged daughter nucleus.

Classically, if the alpha particle’s kinetic energy were less than the height of this barrier, it could not escape. Yet alpha decay occurs because the alpha particle behaves quantum mechanically: it has a nonzero probability to tunnel through the barrier. Two qualitative consequences follow:

• Heavier nuclei tend to alpha-decay more readily because large Z increases the Coulomb repulsion and changes the barrier shape; small changes in barrier width/height can strongly affect tunneling probability.
• Alpha decay rates vary enormously among nuclides because tunneling probability is extremely sensitive to the alpha particle energy and the barrier geometry.

Why alpha particles have discrete (not continuous) energies

In a given alpha decay, the parent nucleus transforms into a specific daughter nucleus, often into a specific energy state of that daughter. The energy available to the products (often called the Q-value) is fixed by the difference in nuclear masses/energies between initial and final states. Because the initial and final nuclear states are quantized, the released energy is also quantized.

As a result, alpha particles from a particular nuclide are emitted with one or a few discrete kinetic energies (lines), not a broad continuous spectrum. If the daughter is left in an excited state, some energy goes into that excitation, and the alpha particle comes out with a correspondingly lower discrete energy; the daughter may then emit a gamma ray to de-excite.

Interaction with matter: why alpha radiation is highly ionizing and short-ranged

Alpha particles are relatively massive (compared with electrons) and carry a +2 charge. When they pass through matter, they interact strongly with electrons in atoms, producing dense ionization along a short track.

Key qualitative features

• High ionization density: Many ion pairs per unit path length. This is why alpha radiation can cause significant damage to biological tissue if it deposits energy inside the body.
• Short range: Because they lose energy quickly, alpha particles travel only a short distance—typically a few centimeters in air and a very small distance in tissue (on the order of tens of micrometers, depending on energy).
• Easy shielding: A sheet of paper, the outer dead layer of skin, or a thin plastic layer can stop most alpha particles. The main requirement is to prevent the alpha emitter from being in direct contact with sensitive tissue.

External vs internal exposure: why the risk changes

External exposure to alpha emitters is usually low risk because alpha particles cannot penetrate far enough to reach living cells beneath the outer skin layer (and they are stopped by clothing or air gaps).

Internal exposure can be high risk if alpha-emitting material is inhaled, ingested, or enters through a wound. In that case, the alpha particles deposit their energy directly in nearby living tissue over a very short range, producing intense local ionization. This is why contamination control (preventing intake) is often more important than thick external shielding for alpha sources.

Practical implications for handling alpha sources

• Focus on containment: sealed sources, glove boxes, fume hoods, and good hygiene reduce internal exposure risk.
• Simple barriers are effective for external shielding, but do not rely on shielding alone if there is a contamination pathway.
• Distance and airflow matter: even though range in air is short, airborne particles can be inhaled if the source is dispersible.