6 alpha particles and 4 beta particles are emitted.
Work Step by Step
The mass number decreases by 4 when an alpha particle is emitted and it doesn't change when beta particles are emitted. The change in mass number $\Delta A=208-232=-24$ A total of 6 (24/4) alpha particles must be emitted to balance the mass numbers. When an alpha particle is emitted, the atomic number decreases by two. When a beta particle is emitted, the atomic number increases by one. Therefore, we have $\Delta Z=$number of $\beta$-(2$\times$number of $\alpha$)=$82-90=-8$ $\implies$ number of $\beta$ particles emitted= $-8+(2\times6)=4$