Question

An accident occurs in a laboratory in which a large amount of a radioactive material, having a half life of 20 days, becomes embedded in the floor and walls so that the level of radiation is 32 times the permissible level. The laboratory can be safely occupied after:

• A. 20 days
• B. 32 days
• C. 64 days
• D. 100 days

Answer 1

The correct option is D 100 days

$A=A_o{\left(\frac{1}{2}\right)}^n$

$\frac{A}{A_o}=\frac{1}{32}={\frac{1}{2}}^n$

${\frac{1}{2}}^5={\frac{1}{2}}^n$

Hence

n=5

$t=5\times 20=100days$