11.1 - Radiation, antiparticles and decay equations

Particles, photons and antiparticles

Can a particle have exactly the electron's mass but a positive charge? The positron does. Carl Anderson's discovery of it in 1932 established that the electron has an antiparticle; a positive particle is not automatically a proton.

Radiation emitted by nuclei can consist of particles or electromagnetic radiation. The labels describe very different objects:

Here $e=1.60\times10^{-19}\,\mathrm C$ and $1\,\mathrm u=1.66\times10^{-27}\,\mathrm{kg}$ are supplied data-sheet values. A helium nucleus is not a neutral helium atom: an alpha particle has no two bound electrons cancelling its nuclear charge.

A photon is a quantum, or packet, of electromagnetic energy. Treat that as a model of how radiation transfers energy, rather than a little material ball. Zero rest mass does not mean zero energy or no physical effects. You will calculate photon energies in the A Level quantum lessons.

An antiparticle has the same mass as its corresponding particle but opposite electric charge. For an electron the antiparticle is the positron: its charge is $+e$, and its mass is $9.11\times10^{-31}\,\mathrm{kg}$. An antiproton likewise has the proton's mass and charge $-e$. A neutron and an antineutron are both electrically neutral; charge alone does not distinguish a neutral particle from its antiparticle. You do not need their other distinguishing properties here.

Match the particle and antiparticle without confusing electron mass with proton mass.

Nucleon number and charge in decay equations

A nuclear decay changes a parent nucleus into a daughter nucleus and emitted radiation. Two checks make the notation manageable: the total nucleon number and total electric charge must each agree on the two sides.

For a nucleus, the lower number $Z$ is its proton number and therefore its charge in units of $e$. For an emitted electron or positron, the lower number represents charge in units of $e$, not a count of protons inside that particle. The upper number is the nucleon count, which is zero for an electron, positron or photon.

The neutrino and antineutrino are electrically neutral, non-nucleon particles emitted in beta decay. The bar distinguishes the antineutrino from the neutrino; do not treat them as interchangeable. Their role in the energy balance comes in the next part.

Alpha decay

Losing two protons and two neutrons reduces the parent's nucleon number by 4 and proton number by 2. For example,

The upper numbers give $226=222+4$, and the lower numbers give $88=86+2$. A different proton number means a different element.

Beta-minus decay

A neutron changes into a proton while an electron and an electron antineutrino are emitted. One nucleon remains one nucleon, so $A$ stays constant; the nucleus gains one proton, so its $Z$ rises by 1:

The nuclear charge increases, but total charge does not: $6=7-1+0$. The emitted negative electron balances the extra positive nuclear charge.

Beta-plus decay

In a suitable nucleus, a proton changes into a neutron while a positron and an electron neutrino are emitted. Again $A$ stays constant, while $Z$ falls by 1:

The charge check is $9=8+1+0$. Whether such a change is energetically possible depends on the nucleus; a free proton does not simply undergo spontaneous beta-plus decay.

These are relations to understand and reproduce, rather than equations supplied on the data sheet. A gamma photon may also be emitted when an excited daughter nucleus loses energy. Gamma emission changes neither its proton number nor its nucleon number.