Question

The half life of polonium is 140 days. In what time will 15g of polonium be disintegrated out of its initial mass of 16 g?

• A. 230 days
• B. 560 days
• C. 730 days
• D. 160 days

Answer 1

Answer: (B)

560 days

$\begin{array}{c}\text{Given-}\ast \text{Half life}=140\text{days.}\\ \text{* Initial mass}=16g\\ \text{* Final mass}=1g\text{.}\\ \text{we have Final mass}=1g=16g\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\end{array}$

$\begin{array}{c}16g\frac{}{t_{1/2}}8g\frac{}{t_{1/2}}4g\frac{}{t_{1/2}}2g\frac{}{t_{1/2}}\lg \\ \text{so we get a time equivalent to}4\text{half lives,}\\ \Rightarrow t=4t_{112}=4\times 140=560\text{days.}\end{array}$