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Anna71 [15]
2 years ago
14

A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5

730 years. How old is the fossil? Express your answer with the appropriate units. View Available Hint(s) t t t = nothing nothing
Chemistry
1 answer:
Citrus2011 [14]2 years ago
5 0

Answer: 2948

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{0.69}{t_{\frac{1}{2}}}=\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 = age of sample  = ?

a = let initial amount of the reactant  = 100

a - x = amount left after decay process = \frac{70}{100}\times 100=70

t=\frac{2.303}{1.21\times 10^{-4}}\log\frac{100}{70}

t=2948years

Thus the fossil is 2948 years old.

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