Question

A 2 mg sample of Au-198, which is sometimes used in medicine, has a half life of 2.7 days. Write an equation and then find the amount remaining after 5 days.Equation:Answer:

Answer 1

Answer:

The amount of Au-198 remaining after 5days is 0.554mg

Explanation:

Given:

initial amount of Au-198= 2mg

half-life = 2.7 days

To find:

Amount remaining after 5 days

To determine the amount remaining, we will apply the half-life formula:

$\begin{gathered} N(t)\text{ = N}_0(\frac{1}{2})^{\frac{t}{\frac{t1}{2}}} \\ where\text{ N\lparen t\rparen = amount remaining} \\ t\text{ = time} \\ t_{\frac{1}{2}}=\text{ half-life} \end{gathered}$

We will write the equation in terms of t. Substitute other values into the formula except the value of t:

$\begin{gathered} N(t)\text{ = 2\lparen}\frac{1}{2})^{\frac{t}{2.7}}\text{ \lparen the equation\rparen} \\ \end{gathered}$

To get the amount remaining after 5 days, we will substitute t with 5

$\begin{gathered} N(t)\text{ = 2\lparen}\frac{1}{2})^{\frac{5}{2.7}} \\ \\ N(t)\text{ = 2\lparen}\frac{1}{2})^{1.8519} \\ N(t)\text{ = 2\lparen0.2770\rparen} \\ N(t)\text{ = 0.554} \end{gathered}$

The amount of Au-198 remaining after 5days is 0.554mg