Bismuth ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ is known to be radioactive. The stability of ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ with respect to alpha, beta-plus and beta-minus decay is to be determined. The following atomic masses are known:
$\begin{array} { l l } { } _ { 2 } ^ { 4 } \mathrm { He } : & 4.002603 \mathrm { u } \ { } ^ { 208 } \mathrm { TI } : & 207.981998 \ { } ^ { 212 } \mathrm {~Pb} : & 211.991871 \ { } _ { 82 } ^ { 212 } \mathrm { Bi } : & 211.991255 \ { } _ { 83 } ^ { 212 } \mathrm { Po } : & 211.988842 \ { } ^ { 84 } & \ \text { The } { } _ { 83 } ^ { 212 } \text { Bi nucleus is } \end{array}$

Question

Quizplus · Accepted Answer

Alpha decay: ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ can decay to ${ } _ { 81 } ^ { 208 } \mathrm { Tl }$ by emitting an alpha particle (${ } _ { 2 } ^ { 4 } \mathrm { He }$). The mass of the initial state (${ } _ { 83 } ^ { 212 } \mathrm { Bi }$) is 211.991255 u, and the combined mass of the products (${ } _ { 81 } ^ { 208 } \mathrm { Tl }$ and ${ } _ { 2 } ^ { 4 } \mathrm { He }$) is 207.981998 u + 4.002603 u = 211.984601 u. Since the mass of the initial state is greater than the mass of the products, alpha decay is energetically possible.Beta-minus decay: ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ can decay to ${ } _ { 84 } ^ { 212 } \mathrm { Po }$ by emitting a beta-minus particle. The mass of the initial state is 211.991255 u, and the mass of the product (${ } _ { 84 } ^ { 212 } \mathrm { Po }$) is 211.988842 u. Since the mass of the initial state is greater than the mass of the product, beta-minus decay is energetically possible.Beta-plus decay: For ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ to undergo beta-plus decay, it would need to decay to ${ } _ { 82 } ^ { 212 } \mathrm { Pb }$, which has a mass of 211.991871 u. However, this process would require the initial mass to be greater than the final mass, which is not the case here. Therefore, beta-plus decay is not energetically favorable.Thus, ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$ is subject to alpha and beta-minus decay, but not beta-plus decay.

Bismuth 83212Bi{ } _ { 83 } ^ { 212 } \mathrm { Bi }83212​Bi

Bismuth ${ } _ { 83 } ^ { 212 } \mathrm { Bi }$