Question

question 22
1 pts
the half - life of an isotope is 1.4 years. if there are 25.0 g of the sample left after 2.8 years, how many grams were in the original sample?
200g
100g
25g
50g

Explanation:

Step1: Calculate number of half - lives

The half - life $t_{1/2}=1.4$ years and the time elapsed $t = 2.8$ years. The number of half - lives $n=\frac{t}{t_{1/2}}=\frac{2.8}{1.4}=2$.

Step2: Use the radioactive decay formula

The formula for radioactive decay is $N = N_0(\frac{1}{2})^n$, where $N$ is the final amount, $N_0$ is the initial amount, and $n$ is the number of half - lives. We know $N = 25.0$ g and $n = 2$. Rearranging the formula for $N_0$ gives $N_0=\frac{N}{(\frac{1}{2})^n}$. Substituting the values, we get $N_0=\frac{25}{(\frac{1}{2})^2}$.

Step3: Solve for the initial amount

$N_0=\frac{25}{\frac{1}{4}}=25\times4 = 100$ g.

Answer:

100g