Question

Potassium-42 has a half-life of 12.4 hours. How much of a 746-gram sample will be left after 62 hours?

Answer 1

the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)

Explanation:

half life = 12.4 hours

initial amount = 746g

time elapsed = 62 hours

Using the half-life formula:

$\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = amount remaining} \\ N_0\text{ = initial amount = 746g} \\ t\text{ = 62 hours} \\ t_{\frac{1}{2}\text{ }}\text{ = 12.4 hours} \end{gathered}$

Substitute for the values:

$\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = }746(\frac{1}{2})^{\frac{62}{12.5}} \\ N(t)\text{ = }746(\frac{1}{2})^5 \\ N(t)\text{ = }746(\frac{1}{2^5}) \end{gathered}$$\begin{gathered} N(t)\text{ = }(\frac{746}{32})^{} \\ N(t)\text{ = }23.3125 \end{gathered}$

Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)