Question

A 100g sample of Carbon-14 has a half-life of 5 years. How much Carbon-14 is left after 10 years?

Answer 1

Answer:  The carbon-14 left after 10 years is 25 g

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for rate constant

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{5years}=0.139years^{-1}$

b) for amount left after 10 years

$t=\frac{2.303}{k}\log\frac{a}{(a-x)}$

$10=\frac{2.303}{0.139}\log\frac{100}{(a-x)}$

$(a-x)=25g$

Thus carbon-14 left after 10 years is 25 g