Question

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

A sample of carbon-14 has a mass of 11.0 g. How much of
this substance will remain after 10,400 years?

Answer 1

`3.106\ \text{g}`

Step-by-step 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=(\ln2)/(t_(1/2))`

Amount of mass remaining is given by

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

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