Question

1. if the half - life of radon is 3.8 days and you start with 100 atoms, about how many remain after one week? * 4 points

decay of a radioactive substance
% of substance remaining
0 1 2 3 4 5 6 7 8 9 10
number of half lives
a. 25
b. 50
c. 12
d. 100

Explanation:

Step1: Calculate number of half - lives

One week has 7 days. The number of half - lives $n=\frac{7}{3.8}\approx1.84$.

Step2: Use decay formula

The formula for radioactive decay is $N = N_0\times(\frac{1}{2})^n$, where $N_0 = 100$ (initial number of atoms) and $n\approx1.84$. So $N=100\times(\frac{1}{2})^{1.84}$.
$(\frac{1}{2})^{1.84}\approx0.28$, and $N = 100\times0.28 = 28$. The closest value to 28 among the options is 25.

Answer:

A. 25