Question

Carbon $- 14$decays with half-life of about 5,800 years. In a sample of bone, the ratio of carbon $- 14$to carbon $- 12$is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about x centuries ago, where x is nearest to.

• A. $2 \times 58$
• B. 58
• C. 58/2
• D. $3 \times 58$

Answer 1

Answer: (A)

$2 \times 58$

Answer 2

To becomes $\frac{1}{4}$th, it requires time of two half lives

$i.e.,t = 2(T_{1/2}) = 2 \times 5800 = 2 \times 58$centuries.