Mass number of a nucleus X is A and atomic number is Z.
Find mass number and atomic number of the new nucleus (say Y) after the
emission of m-alpha particles and n-beta particles.

By the emission of one alpha particle, atomic number decreases by 2 and by the
emission of one beta particle atomic number increases by 1. Therefore, the atomic number of
nucleus Y is $Z = Z - 2m+ n$
Further, by the emission of one alpha particle mass number decreases by 4 and by the emission
of beta particle, mass number does not change. Therefore, the mass number of Y is
$A\text{'} = A - 4m$