Question

The half life of radon-222 is 3.8 days. How Much of a 100g sample is left after 15.2 days

Answer 1

Answer:  

6.2 g  

Explanation:  

In a first-order decay, the formula for the amount remaining after n half-lives is  

$N = \frac{N_{0}}{2^{n}}$  

where  

N₀ and N are the initial and final amounts of the substance  

1. Calculate the number of half-lives.  

If $t_{\frac{1}{2}} = \text{3.8 da}$  

$n = \frac{t}{t_{\frac{1}{2}}} = \frac{\text{15.2 da}}{\text{3.8 da}}= \text{4.0}$

2. Calculate the final mass of the substance.  

$\text{N} = \frac{\text{100 g}}{2^{4.0}} = \frac{\text{100 g}}{16} = \text{6.2 g}$