Q 12-13-062JEE MainJEE Main 2023 (29 Jan, Shift 2)Medium
Substance $A$ has atomic mass number $16$ and half life of $1$ day. Another substance $B$ has atomic mass number $32$ and half life of $\frac12$ day. If both $A$ and $B$ simultaneously start undergoing radioactivity at the same time with initial mass $320\ \text{g}$ each, how many total atoms of $A$ and $B$ combined would be left after $2$ days?
Answer: (A) $3.38\times10^{24}$
$A$: 2 half-lives, $320\to80\ \text{g}$, i.e. $\dfrac{80}{16}=5$ mol.
$B$: 4 half-lives, $320\to20\ \text{g}$, i.e. $\dfrac{20}{32}=0.625$ mol.
Total $=5.625\times6.02\times10^{23}\approx3.38\times10^{24}$ atoms.
Solution by Sreeraj P, M.Sc Physics