Question

sodium-24 has a half-life of 15 hours. after 45 hours, how much sodium-24 will remain of an original 50.0-g sample?
○ 5.56 g
○ 6.25 g
○ 16.7 g
○ 25.0 g

Explanation:

Step1: Determine number of half - lives

The half - life of Sodium - 24 is \(t_{1/2}=15\) hours. The total time elapsed \(t = 45\) hours. To find the number of half - lives \(n\), we use the formula \(n=\frac{t}{t_{1/2}}\).
Substituting the values, we get \(n=\frac{45}{15}=3\).

Step2: Use the radioactive decay formula

The formula for the amount of a radioactive substance remaining after \(n\) half - lives is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount and \(N\) is the remaining amount.
We know that \(N_0 = 50.0\) g and \(n = 3\). Substituting these values into the formula, we have \(N=50.0\times(\frac{1}{2})^3\).
First, calculate \((\frac{1}{2})^3=\frac{1}{8}\). Then, \(N = 50.0\times\frac{1}{8}=\frac{50.0}{8}=6.25\) g.

Answer:

6.25 g (Option: 6.25 g)