Question

Some amount of radioactive substance ($t_{\frac{1}{2}}=10$ days) is spread inside a room and consequently, the level of radiation becomes $50$ times the permissible level for normal occupancy of the room. The room would be safe for occupation after

• A. $20$days
• B. $34.8$ days
• C. $56.4$days
• D. $62.9$days

Answer 1

Answer: (C)

$56.4$days

Level of radiation above normal $=50$ times
Amount to the left $=1$

$\lambda =\frac{ln2}{10}$

Now,

$1=50e^{-\frac{ln2}{10}t}$

$ln\left(\frac{1}{50}\right)=-\frac{ln2}{10}t$

$\Rightarrow t=56.450$ days