JEE Physics 2023 Question with Solution

Given: The decay chain starts from $^{218}_{84}A$ and proceeds through $\alpha$, $\beta^-$, $\gamma$, $\alpha$, $\beta^+$ and $\gamma$ changes.

Find: The mass number and atomic number of $A_6$.

For each decay:

• In $\alpha$-decay, mass number decreases by $4$ and atomic number decreases by $2$.
• In $\beta^-$-decay, mass number remains unchanged and atomic number increases by $1$.
• In $\beta^+$-decay, mass number remains unchanged and atomic number decreases by $1$.
• In $\gamma$-decay, neither mass number nor atomic number changes.

Applying these step by step:

$${}^{218}_{84}A \xrightarrow{\alpha} {}^{214}_{82}A_1$$ $${}^{214}_{82}A_1 \xrightarrow{\beta^-} {}^{214}_{83}A_2$$ $${}^{214}_{83}A_2 \xrightarrow{\gamma} {}^{214}_{83}A_3$$ $${}^{214}_{83}A_3 \xrightarrow{\alpha} {}^{210}_{81}A_4$$ $${}^{210}_{81}A_4 \xrightarrow{\beta^+} {}^{210}_{80}A_5$$ $${}^{210}_{80}A_5 \xrightarrow{\gamma} {}^{210}_{80}A_6$$

So, the final nucleus $A_6$ has mass number $210$ and atomic number $80$.

Therefore, the correct option is C.

The solution labels the correct option as B, but its worked steps conclude $210$ and $80$, which matches option C.