Question

C - 14 has a half life of 5760 years. 100 mg of sample containing C - 14 is reduced to 25 mg in :

• A. 11520 years
• B. 2880 years
• C. 1440 years
• D. 17280 years

Answer 1

The correct option is A 11520 years

For a first order reaction,

Rate constant $k=$ $\frac{0.693}{t_{1/2}}$

Given, $t_{1/2}=5760years$

$k=1.2\times {10}^{-4}$

Also, $t=$ $\frac{2.303}{k}\times log\frac{N_o}{N_t}$

$N_o=100mg$

$N_t=25mg$

Substituting the values we get, $t=11520$ years