Answer:
6.2 g
Explanation:
In a first-order decay, the formula for the amount remaining after n half-lives is
[tex]N = \frac{N_{0}}{2^{n}}[/tex]
where
N₀ and N are the initial and final amounts of the substance
1. Calculate the number of half-lives.
If [tex]t_{\frac{1}{2}} = \text{3.8 da}[/tex]
[tex]n = \frac{t}{t_{\frac{1}{2}}} = \frac{\text{15.2 da}}{\text{3.8 da}}= \text{4.0}[/tex]
2. Calculate the final mass of the substance.
[tex]\text{N} = \frac{\text{100 g}}{2^{4.0}} = \frac{\text{100 g}}{16} = \text{6.2 g}[/tex]
