Question

a certain radioactive isotope has a half life of 7 days. if this isoptope has 16 grams how many grams will it have after the each of the following number of days? a.)7 days b.)14 days c.) 21 days d.)28 days

Answer 1

The half life formula is

`m=m_0((1)/(2))^{(t)/(th)}`

where m0 is the amount started with, m is the amount left after a time t and th is the half life.

In our case

`\begin{gathered} m_0=16\text{ gr} \\ t_h=7\text{ days} \end{gathered}`

Hence, we obtain:

a) After 7 days

`\begin{gathered} m=(16)((1)/(2))^{(7)/(7)} \\ m=16((1)/(2)) \\ m=8\text{ gr} \end{gathered}`

b) After 14 days