Question

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?11440 years1430 years4750 years2375 years4290 years

Answer 1

Answer: 11440 years

Explanation:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{2.303}{k}\log\frac{100}{50}$

$t_{\frac{1}{2}}=\frac{0.69}{k}$

$5720years=\frac{0.69}{k}$

$\frac{0.69}{5720years}=1.2\times 10^{-4}years^{-1}$

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  = 100

x = amount decayed = 75

a - x = amount left after decay process  = 100 - 75 = 25

$t=\frac{2.303}{1.2\times 10^{-4}}\log\frac{100}{25}$

$t=11440years$

Thus the piece of wood is 11440 years old.