Question

A radioactive substance has half-life $5760yrs$. A sample of $100mg$ containing substance is reduced to $25mg$ in:

• A. $280yrs$
• B. $1440yrs$
• C. $2880yrs$
• D. $11520yrs$

Answer 1

Answer: (D)

$11520yrs$

$K=\frac{0.693}{t_{1/2}}=\frac{0.693}{5760}=0.00012y{r}^{-1}$

Time, $t=\frac{2.303}{k}log\frac{[R{]}_o}{\left[R\right]}$

$t=\frac{2.303}{0.00012}log\frac{\left[100\right]}{\left[25\right]}$

$t=\frac{2.303}{0.00012}\times log4=11554yr$

Which is near about the $11520yrs$.