Writing alpha and beta decay equations

Each decay changes the parent nucleus in a fixed way, so you can write the equation from the pattern rather than from memory of individual nuclides:

The syllabus form for alpha decay is, for example,

$^{238}_{92}\text{U} \rightarrow {}^{234}_{90}\text{Th} + {}^{4}_{2}\alpha$

Beta decay keeps $A$ the same because the nucleon count does not change: in beta-minus decay a neutron becomes a proton, and in beta-plus decay a proton becomes a neutron.

Follow the same three steps every time:

1. Write the parent and the emitted particle in nuclide notation.
2. Balance the nucleon numbers to get $A$ for the daughter.
3. Balance the proton numbers to get $Z$ for the daughter, then name the element from $Z$.

With an alpha particle emitted: $A$ falls by 4 and $Z$ falls by 2. With a beta-minus particle: $A$ is unchanged and $Z$ rises by 1. With a beta-plus particle: $A$ is unchanged and $Z$ falls by 1.

A gamma photon is written $^{0}_{0}\gamma$ and changes neither number, so it appears in an equation only when a nucleus de-excites after the main decay.