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postnew [5]
2 years ago
9

The half-life for the (first order) radioactive decay of 14C is5730

Chemistry
1 answer:
Zielflug [23.3K]2 years ago
4 0

Answer:

The age of this archeological sample is 2737.53 years

Explanation:

Given that:

Half life = 5730  years

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

Where, k is rate constant

So,  

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

k=\frac{\ln\ 2}{5730}\ year^{-1}

The rate constant, k = 0.00012 year⁻¹

Using integrated rate law for first order kinetics as:

[A_t]=[A_0]e^{-kt}

Where,  

[A_t] is the concentration at time t

[A_0] is the initial concentration

Given that:

The rate constant, k = 0.00012 year⁻¹

It is given that 72 % of the 14C remains. So,

\frac {[A_t]}{[A_0]} = 0.72

Applying values as:-

\frac {[A_t]}{[A_0]}=e^{-k\times t}

0.72
=e^{-0.00012\times t}

\ln \left(0.72\right)=-0.00012t\ln \left(e\right)

\ln \left(0.72\right)=-0.00012t

t=2737.53\ years

The age of this archeological sample is 2737.53 years

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