Question

The decay constant for an $\alpha$-decay of ${Th}^{232}$ is $1.58\times {10}^{-10}{s}^{-1}$. How many $\alpha$-decays occur from $1$ $g$ sample in $365$ days?

• A. $2.89\times {10}^{19}$
• B. $1.298\times {10}^{19}$
• C. $8.219\times {10}^{19}$
• D. None of these

Answer 1

Answer: (B)

$1.298\times {10}^{19}$

$1g$ of ${}^{232}Th$ is $\frac{1}{232}\times 6023\times {10}^{23}$ atoms
now, 365 days $=31536000sec.N_{disintigrations}=N_P.Q_{\alpha }.t=\left(\frac{{6023\times 10}^{23}}{232}\right).158.31536000=1298\times {10}^{19}⟶option\left(B\right)$