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zavuch27 [327]
3 years ago
12

Carbon-14 has a half-life of 5,700 years.

Chemistry
1 answer:
Maksim231197 [3]3 years ago
5 0

Answer:

3.106\ \text{g}

Explanation:

t_{1/2} = Half-life of carbon = 5700 years

t = Time at which the remaining mass is to be found = 10400 years

m_0 = Initial mass of carbon = 11 g

Decay constant is given by

\lambda=\dfrac{\ln2}{t_{1/2}}

Amount of mass remaining is given by

m=m_0e^{-\lambda t}\\\Rightarrow m=m_0e^{-\dfrac{\ln2}{t_{1/2}} t}\\\Rightarrow m=11e^{-\dfrac{\ln 2}{5700}\times 10400}\\\Rightarrow m=3.106\ \text{g}

The amount of the substance that remains after 10400 years is 3.106\ \text{g}.

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