Question

Write the law of radioactive decay. A radioactive nucleus is decaying in the following way. Determine the mass number and atomic number of final product $X_4$. When initial nucleus has mass number $A=238$ and atomic number $Z=92$.
${}_Z^{A}X\stackrel{\alpha }{\to }{X}_1\stackrel{{\beta }^{-}}{\to }{X}_2\stackrel{\alpha }{\to }{X}_3\stackrel{\gamma }{\to }{X}_4$.

Answer 1

In an $\alpha$ decay, there is decrease of atomic number by 2, and decrease in mass number by 4.

In a ${\beta }^{-}$ decay, there is increase in atomic number by 1, and no change in mass number.

In a $\gamma$ decay, there is no change in atomic or mass number of parent atom.

Hence the atomic number of $X_4$ is $92-2+1-2+0=89$

The mass number of $X_4$ is $238-4+0-4=230$