Question

The half-life of the carbon isotope C-14 is approximately 5,715 years. What percent of a given amount remains after 300 years? Round your answer to two decimal places.

Answer 1

Answer: 96.34%

Explanation:

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

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

$k=\frac{0.693}{5715}=0.00012years^{-1}$

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 = time for decomposition = 300 years

a = let initial amount of the reactant  = 100

a - x = amount left after decay process = ?  

$300=\frac{2.303}{0.00012}\log\frac{100}{100-x}$

$x=3.66$

$(a-x)=100-3.66=96.34$

Thus 96.34 percent of a given amount remains after 300 years.