Neutron rich, heavy nucleus: $\alpha$ or $\beta^-$ decay? Consider a theoretical nucleus that is both neutron rich and heavy e.g. $A=300$, $N=250$. Is it possible to say whether it is more likely to undergo $\beta^-$ decay or $\alpha$ decay (or even cluster decay or fission) or does this depend on the specific nature of the atom? Please can you explain your answer.
 A: It could be both!
Your hypothetical nucleus is beyond the neutron drip line and would decay by neutron emission.  However, consider the polonium isotopes, whose alpha-decay branching ratios are plotted below:

None is stable against alpha decay.
However most of the isotopes (and the long-lived isomers) with mass $190 < A < 209$ have a non-negligible branching ratio for both alpha decay and positron decay/electron capture. On the neutron-rich side, it seems that for whatever reason most of the isotopes decay overwhelmingly by either alpha or beta decay, but in $\rm^{219}Po$ the branching ratios for alpha and beta decay are different by only a factor of three.
For the proton-rich polonium isotopes, I don't really see a pattern in whether alpha decay or electron capture is the dominant decay method. For example I would have expected the most proton-rich poloniums to decay by electron capture and positron emission, but those with $A < 195$ (with the exception of $\rm^{188}Po$) are overwhelmingly alpha emitters. That suggests there's some complicated final-state stuff happening.
A: Usually a neutron heavy nucleus would do both. It might first undergo beta decay and turn some neutrons into protons. Then release bundle of those newly formed protons and some remaining neutrons.  
$$^{300}\mathrm{Sn} \to {}^{300}\mathrm{I} +2e^-+ 2\nu_e.$$
After this maybe 
$$^{300}\mathrm{I} \to {}^{296}\mathrm{Sn} + 2e^- + 2 \nu_e.$$
This process might continue for a while until the nucleus is stable.
