Bismuth ${}^{212}_{83}$ Bi is known to be radioactive.The stability of ${}^{212}_{83}$ Bi with respect to alpha,beta-plus and beta-minus decay is to be determined.The following atomic masses are known: ${}^{4}_{2}$ He: 4.002603 u $^{208}
_{81} T$l: 207.981998 u $^{212}
_{82} Pb$: 211.991871 u ${}^{212}_{83}$ Bi: 211.991255 u 212 84 Po: 211.988842 u The ${}^{212}_{83}$ Bi nucleus is

Question

Quizplus · Accepted Answer

To determine the stability of ${}^{212}_{83}$ Bi with respect to alpha, beta-plus, and beta-minus decay, we calculate the mass differences for each type of decay:1. **Alpha Decay**: ${}^{212}_{83}$ Bi decays into ${}^{208}_{81}$ Tl plus an alpha particle (${}^{4}_{2}$ He).   - Mass before decay: 211.991255 u   - Mass after decay: 207.981998 u (Tl) + 4.002603 u (He) = 211.984601 u   - Since the mass decreases, energy is released, and alpha decay is energetically possible.2. **Beta-Plus Decay**: ${}^{212}_{83}$ Bi decays into ${}^{212}_{82}$ Pb by emitting a positron.   - Mass before decay: 211.991255 u   - Mass after decay: 211.991871 u (Pb)   - Since the mass of the product is greater, beta-plus decay is not energetically favorable.3. **Beta-Minus Decay**: ${}^{212}_{83}$ Bi decays into ${}^{212}_{84}$ Po by emitting an electron.   - Mass before decay: 211.991255 u   - Mass after decay: 211.988842 u (Po)   - Since the mass decreases, energy is released, and beta-minus decay is energetically possible.Therefore, ${}^{212}_{83}$ Bi is subject to alpha or beta-minus decay, but not beta-plus decay.

Bismuth 83212{}^{212}_{83}83212​ Bi Is Known to Be Radioactive 83212{}^{212}_{83}83212​ Bi with Respect to Alpha,beta-Plus and Beta-Minus Decay Is to {}^{212}_{83}

Bismuth ${}^{212}_{83}$ Bi Is Known to Be Radioactive ${}^{212}_{83}$ Bi with Respect to Alpha,beta-Plus and Beta-Minus Decay Is to {}^{212}_{83}