a 60.0 - g sample of fermium - 253 was placed in a sealed vessel 9.0 days ago. only 7.5 g of this isotope is…

Explanation:

Step1: Determine the number of half - lives

The initial amount $N_0 = 60.0$ g and the final amount $N=7.5$ g. We use the formula $N = N_0\times\left(\frac{1}{2}\right)^n$, where $n$ is the number of half - lives. Substituting the values, we get $7.5=60\times\left(\frac{1}{2}\right)^n$. Then $\left(\frac{1}{2}\right)^n=\frac{7.5}{60}=\frac{1}{8}$. Since $\frac{1}{8}=\left(\frac{1}{2}\right)^3$, $n = 3$.

Step2: Calculate the half - life

We know that the time elapsed $t = 9.0$ days and $t=n\times t_{1/2}$, where $t_{1/2}$ is the half - life. Rearranging for $t_{1/2}$, we have $t_{1/2}=\frac{t}{n}$. Substituting $t = 9.0$ days and $n = 3$, we get $t_{1/2}=\frac{9}{3}=3.0$ days.

Answer:

3.0 days