An atomic nucleus $A$ is composed of $84$ protons and $128$ neutrons. The nucleus $A$ emits an $\alpha$-particle and is transformed into a nucleus $\mathrm{B}$. What is the composition of $B$ ?

A certain nucleus $A$ (mass number $238$ and atomic number $92$) is radioactive and becomes a nucleus $,B$ (mass number $234$ and atomic number $90$ ) by the loss of a particle.

What particle was emitted ?

State whether the following nuclear disintegrations are allowed or not (star indicates an excited state). Given reason if it is not allowed.

${}_Z{}^A\mathrm{X}*\to {}_Z{}^A\mathrm{X}+\gamma$

State whether the following nuclear disintegrations are allowed or not (star indicates an excited state). Given reason if it is not allowed.

${}_Z{}^A\mathrm{X}\to {}_{Z-2}{}^A\mathrm{X}+{}_2{}^4\mathrm{He}$