Question

the half life of radioactive decay of c14 is 5730 years.how much time it will take so that 25% of C14 was found in sample

Answer 1

half-life is 5730 years

for 25% undecay it requires two half lives. so total time for 25% of C14 was found in sample is 11460 years

Answer 2

It will take 11460 years so that 25% of C14 was found in sample

Explanation:

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

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

$k=\frac{0.693}{5730}=1.21\times 10^{-4}years^{-1}$

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 =$1.21\times 10^{-4}years^{-1}$

t = time of decomposition = ?

a = let initial amount of the reactant  =100

a - x = amount left after decay process= $\frac{25}{100}\times 100=25$

Putting in the values, we get:

$t=\frac{2.303}{1.21\times 10^{-4}}\log\frac{100}{25}$

$t=11460years$

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