Question

The half life of C-14 is 5600 years. A sample of freshly cut wood from a tree contains 10 mg of C-14. The amount left in the sample after 50000 years is (a - x) $\times$ 100. The value of (a - x) $\times$ 100 is :

• A. 1 mg
• B. 2 mg
• C. 3 mg
• D. 4 mg

Answer 1

Answer: (B)

2 mg

$t=\frac{2.303}{K}log\frac{a}{a-x}$
$K=\frac{0.693}{t_{1/2}}=\frac{0.693}{5600}$
or, $log\frac{a}{a-x}=\frac{50000\times 0.693}{5600\times 2.303}$
or, $log\frac{10}{a-x}=\frac{50000\times 0.693}{5600\times 2.303}$
or, (a - x) = 0.02 mg
$\therefore$ (a - x) $\times$ 100 = 0.02 $\times$ 100 = 2 mg