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sergejj [24]
3 years ago
11

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-1

4, then how old is it?11440 years1430 years4750 years2375 years4290 years
Chemistry
1 answer:
Nadusha1986 [10]3 years ago
6 0

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.

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