Alpha Decay: Radioactive Process and Equations

Alpha decay is a radioactive process in which an unstable nucleus emits an alpha particle (a helium-4 nucleus, ⁴₂He), so that the atomic number decreases by 2 and the mass number by 4. In brief: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He, with an energy release (Q value) of 4.27 MeV, and the alpha particles can be stopped by a sheet of paper or the outer layer of the skin.

Alpha decay is the typical way for heavy nuclei (Z > 82) to become more stable, and it is the source of radon in homes and of the heat in some space probes. This article explains how to write balanced nuclear equations for alpha decay, how to calculate the energy released, what alpha particles are like, and the quantum-mechanical explanation of the process, with tables and worked examples.

What happens in alpha decay?

A heavy nucleus has too many protons and neutrons to be stable, because the repulsion between the protons becomes large compared with the short-range strong force. It emits a cluster of two protons and two neutrons, which is a very stable combination (the binding energy of helium-4 is high for such a light nucleus). The nucleus becomes smaller, and the number of both protons and neutrons decreases by two. The alpha particle takes most of the energy released, and the daughter nucleus recoils.

How do you write the equations?

The general equation is:

AZX → A−4Z−2Y + 42He

1. Subtract 4 from the mass number and 2 from the atomic number of the parent.
2. Identify the daughter from its new atomic number, using the periodic table.
3. Check that the sums of the mass numbers and of the atomic numbers are equal on both sides.

Examples: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He; ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He; ²⁴¹₉₅Am → ²³⁷₉₃Np + ⁴₂He.

Examples of alpha emitters

A pattern called the Geiger–Nuttall law can be seen: the higher the energy of the alpha particle, the shorter the half-life. Between ²³⁸U (4.27 MeV) and ²¹⁰Po (5.41 MeV), the half-life changes from billions of years to months.

How much energy is released?

The Q value of the decay is the difference between the mass of the parent atom and the sum of the masses of the daughter and the alpha particle (helium-4 atom), converted into energy: Q = [m(parent) − m(daughter) − m(⁴He)] × 931.494 MeV/u. It is shared between the alpha particle and the daughter in the inverse ratio of their masses, because of the conservation of momentum, so the alpha particle gets about (A − 4)/A of Q.

Worked example: uranium-238

1. m(²³⁸U) = 238.050788 u; m(²³⁴Th) = 234.043601 u; m(⁴He) = 4.002603 u.
2. Δm = 238.050788 − 234.043601 − 4.002603 = 0.004584 u.
3. Q = 0.004584 × 931.494 = 4.27 MeV.
4. Alpha energy ≈ 4.27 × 234/238 = 4.20 MeV, and the thorium nucleus carries 0.07 MeV.
5. The speed of the alpha particle: KE = 4.20 MeV = 6.73 × 10⁻¹³ J, v = √(2KE/m) = √(2 × 6.73 × 10⁻¹³ / 6.645 × 10⁻²⁷) = 1.42 × 10⁷ m/s, about 5 % of the speed of light.

What are the properties of alpha radiation?

• Charge and mass: +2 and 4 u (about 7300 times the mass of an electron).
• Penetration: low. The range in air is only 3–7 cm, and the particles are stopped by a sheet of paper or by the dead outer layer of human skin.
• Ionization: very high, since the particle is slow, heavy and doubly charged. It leaves a dense track of ions.
• Hazard: low outside the body, but very high when an alpha emitter is inhaled or ingested, because all of the energy is deposited in a small volume of tissue. For this reason the radiation weighting factor of alpha particles is 20, compared with 1 for gamma rays and beta particles.
• Deflection: alpha particles are deflected only slightly in a magnetic or electric field, and toward the negative plate.

Why does alpha decay occur?

Classically, an alpha particle inside the nucleus does not have enough energy to climb over the Coulomb barrier that surrounds it, which is about 25–30 MeV for heavy nuclei, while the particles emitted have energies of only 4–9 MeV. George Gamow explained in 1928 that the particle can pass through the barrier by quantum tunneling. The probability depends extremely strongly on the energy and the width of the barrier, which explains why half-lives range over more than 20 orders of magnitude, from less than a microsecond to billions of years.

Where are alpha emitters used?

• Smoke detectors: a tiny amount (about 0.3 µg) of americium-241 ionizes the air in a chamber, and smoke particles reduce the current, which sets off the alarm.
• Power sources: plutonium-238 (half-life 87.7 years) in radioisotope thermoelectric generators that power space probes such as Voyager and Curiosity.
• Static eliminators: polonium-210 sources ionize air to remove static charge.
• Radiotherapy: targeted alpha therapy with radium-223 for bone metastases.
• Radon hazard: radon-222 from the decay of uranium in rock accumulates in basements, and after inhalation its short-lived alpha-emitting daughters irradiate lung tissue. It is estimated to be the second leading cause of lung cancer after smoking.

How was alpha radiation discovered?

Ernest Rutherford distinguished in 1899 two types of radiation from uranium, which he named alpha and beta. In 1908 he and Thomas Royds showed that alpha particles are helium nuclei: alpha particles were collected in a thin-walled glass tube, and the spectrum of helium appeared in the tube after a few days. Rutherford received the Nobel Prize in Chemistry in 1908 for his research on the disintegration of the elements. Marie and Pierre Curie discovered polonium and radium in 1898 by following the alpha activity of pitchblende.

Which mistakes are common?

• Subtracting the wrong numbers: A decreases by 4 and Z by 2.
• Calling alpha radiation an electromagnetic wave: it is a stream of helium nuclei.
• Assuming that alpha radiation is harmless because it is stopped by paper: inside the body it is very damaging.
• Forgetting the recoil of the daughter: the alpha particle does not get all of Q.
• Mixing up the daughter element: use the new atomic number to name it.