Question

A 100 g sample of a radioactive isotope has a half life of 2 days. After 6 days how many grams of the original radioactive isotope are left?

Answer 1

The formula of decay has form $N(t) = N_0\cdot 2^{-t/T_{1/2}}$ , where $N_0$ is the initial number of atoms, $t$ is the time interval and $T_{1/2}$ is the half-life time.

Therefore, $\dfrac{N(t)}{N_0} = 2^{-t/T_{1/2}}$ .

In our case $t = 6^d, \; T_{1/2} = 2^d,$ so $\dfrac{N(t)}{N_0} = 2^{-6/2} = \dfrac18,$ so only one eighth of the initial number of radioactive atoms will be left. Therefore, only $100\cdot\dfrac18 = 12.5$ g will be left.