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garri49 [273]
2 years ago
7

Carbon-14 is a radioactive isotope that decays according to first-order kinetics in a process that has a half-life of 5730 years

. If a sample containing carbon-14 now has 71% of its original concentration of carbon-14, how much time has passed in years? 4.09 ~ 103 years 5.73 x 103 years 2.38 x 103 years 2.83 x 103 years 3.52 * 104 years
Chemistry
1 answer:
Sliva [168]2 years ago
8 0

Answer : The time passed in years is 2.83\times 10^3\text{ years}

Explanation :

Half-life = 5730 years

First we have to calculate the rate constant, we use the formula :

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

k=\frac{0.693}{5730\text{ years}}

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

Now we have to calculate the time passed.

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}\text{ years}^{-1}

t = time passed by the sample  = ?

a = let initial amount of the reactant  = X g

a - x = amount left after decay process = 71\% \times (x)=\frac{71}{100}\times (X)=0.71Xg

Now put all the given values in above equation, we get

t=\frac{2.303}{1.21\times 10^{-4}}\log\frac{X}{0.71X}

t=2831.00\text{ years}=2.83\times 10^3\text{ years}

Therefore, the time passed in years is 2.83\times 10^3\text{ years}

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