Carbon-14 has a half-life of 5730 years. How much of a 144 g sample of carbon-14 will remain after 1719 years?

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Answer 1 · 2017-08-05T09:28:03

The mass remaining is $=117g$

The half life of carbon- $14$ is $t_(1/2)=5730y$

This means that in $5730y$ , the initial amount of carbon $-14$ will be halved

The radioactive constant is

$lambda=ln2/t_(1/2)=ln2/5730=0.000121$

The fundamental decay equation is

$m=m_0e^(-lambdat)$

The initial amount of carbon $-14$ is $m_0=144g$

The time is $t=1719y$

Therefore

$m=144*e^(-0.000121*1719)=144*e^-0.208=117g$