Alpha rays emitted from a radioactive substance are

Consider the decay of a free neutron at rest: $n \rightarrow p + e^-$. Show that the two-body decay of this type must necessarily give an electron of fixed energy and,therefore,cannot account for the observed continuous energy distribution in the $\beta$-decay of a neutron or a nucleus.

Before the neutrino hypothesis,the beta decay process was thought to be the transition $n \to p + e^-$. If this were true,show that if the neutron was at rest,the proton and electron would emerge with fixed energies and calculate them. Experimentally,the electron energy was found to have a large range.

$A$ free neutron decays spontaneously into :

What is $\alpha-$,$\beta-$ and $\gamma-$decay? Write their general formulas.

When an element ${}_{90}^{232}Th$ decays into ${}_{82}^{208}Pb$, the number of $\alpha$ and $\beta^{-}$ particles emitted respectively are