Question

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

Answer 1

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 $3.106\ \text{g}$.