Question

How much of a 500 g sample of potassium-42 is left after 62.0 hours if its half-life is 12.4hours?

Answer 1

Given the half life of the sample is 12.4 hrs.

Therefore, number of half life in 62.0 hrs is given as,

$\begin{gathered} n=\frac{62.0\text{ hrs}}{12.4\text{ hrs}} \\ =5 \end{gathered}$

The number of particle left after squence of half life is given as,

$N=\frac{N_0}{2^n}$

Here,

$\begin{gathered} n\text{ is the number of half life.} \\ N_0\text{ is the initial number of sample (in this case 500 g)} \\ N\text{ is the number of the sample left} \end{gathered}$

Substituting all known values,

$\begin{gathered} N=\frac{500\text{ g}}{2^5} \\ =\frac{500\text{ g}}{32} \\ =15.625\text{ g} \end{gathered}$

Therefore, after 62.0 hrs 15.625 g of the sample will be left over.