Question

How much of a 75 mg sample of will remain after 750 hours if the sample has a half-life of 7.5days?

Answer 1

Given,

`\begin{gathered} N_0=75\text{ mg} \\ t=750\text{ hrs} \\ t_{(1)/(2)}=7.5\text{ days=7.5}*24=180\text{ hrs} \end{gathered}`

The reaction constant λ is given as,

`\begin{gathered} \lambda=\frac{0.693}{t_{(1)/(2)}} \\ =\frac{0.693}{180\text{ hrs}} \\ =3.85*10^(-3)hr^(-1) \end{gathered}`

According to law of radioactive decay number of particle after time t is given as,

`N=N_0e^(-\lambda t)`

Substituting all known values,

`\begin{gathered} N=75\text{ mg}* e^{-(3.85*10^(-3)*750)} \\ =75\text{ mg}* e^(-2.8875) \\ =75\text{ mg}*0.0557 \\ =4.1775\text{ mg} \end{gathered}`

Therefore, 4.1775 mg of the sample will be left after 750 hrs.