Beta-plus decay: an up quark becomes a down quark

By the end of this lesson

By the end you can describe beta-plus decay at the quark level, write the quark equation, check its charge balance, and say how it differs from beta-minus decay.

The mirror image of beta-minus

In beta-plus decay a proton turns into a neutron and a positron is emitted:

$\text{p} \rightarrow \text{n} + \text{e}^+ + \nu_e$

At the quark level, one up quark becomes a down quark:

$\text{u} \rightarrow \text{d} + \text{e}^+ + \nu_e$

Since a proton is $\text{u}\,\text{u}\,\text{d}$ and a neutron is $\text{u}\,\text{d}\,\text{d}$ , changing one $\text{u}$ into a $\text{d}$ converts the proton into a neutron.

The charge has to balance

	before	after
quarks and leptons	$\text{u} = +\tfrac{2}{3}$	$\text{d} = -\tfrac{1}{3}$ , $\text{e}^+ = +1$ , $\nu_e = 0$
total	$+\tfrac{2}{3}$	$-\tfrac{1}{3} + 1 = +\tfrac{2}{3}$

Both sides give $+\tfrac{2}{3}$ , so charge is conserved. The positron carries the charge that would otherwise be missing when the quark loses $1$ unit.

As in beta-minus decay, the neutrino carries no charge and almost no mass; it conserves energy, momentum and lepton number.

Why beta-plus decay needs energy from the nucleus

A free proton cannot decay into a neutron, because a neutron is slightly heavier than a proton. Making a heavier particle from a lighter one needs energy.

Inside a nucleus, that energy can come from the binding energy released when the whole nucleus moves to a more stable state. This is why beta-plus decay is only seen in proton-rich (neutron-deficient) nuclei, and why it does not happen to protons on their own.

Worked example: Example: writing a beta-plus decay

Sodium-22 decays by beta-plus emission to neon-22. Write the decay equation and state which quark changes.

Have a go first?

Check 1 — the quark change

Multiple choiceQuestion 1 · Recall

Multiple choiceQuestion 2 · Recall

Answer the 2 questions above to continue.