Answer:
[tex]3.106\ \text{g}[/tex]
Explanation:
[tex]t_{1/2}[/tex] = Half-life of carbon = 5700 years
t = Time at which the remaining mass is to be found = 10400 years
[tex]m_0[/tex] = Initial mass of carbon = 11 g
Decay constant is given by
[tex]\lambda=\dfrac{\ln2}{t_{1/2}}[/tex]
Amount of mass remaining is given by
[tex]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}[/tex]
The amount of the substance that remains after 10400 years is [tex]3.106\ \text{g}[/tex].
