Question

The half-life of a radioactive element is 6 months. The time taken to reduce its original concentration to its 1/16 value is:

• A. 1 year
• B. 16 years
• C. 2 years
• D. 8 years

Answer 1

Answer: (C)

2 years

Given: $t_{1/2}=6months$

$N=\frac{1}{16}{N}_o$

$t=\frac{2.303\times t_{1/2}}{0.693}log\frac{N_0}{N}$

$t=\frac{2.303\times 6}{0.693}log{2}^4$ months

$t\approx 24months=2years$

Option C is correct.