Question

type the correct answer in the box. use numerals instead of words. fermium - 253 is a radioactive isotope of fermium that has a half - life of 3.0 days. a scientist obtained a sample that contained 216 micrograms of fermium - 253. complete the table to show how much fermium - 253 should remain in the sample at the indicated times after the scientist obtained the sample. time elapsed amount remaining 3.0 days μg 6.0 days μg 9.0 days μg

Explanation:

Step1: Recall half - life formula

The amount of a radioactive substance $A$ after $n$ half - lives, given an initial amount $A_0$ is $A = A_0\times(\frac{1}{2})^n$.

Step2: Calculate for 3.0 days

Since the half - life is 3.0 days, for $t = 3.0$ days, $n = 1$. Given $A_0=216$ micrograms. Then $A=216\times(\frac{1}{2})^1=\frac{216}{2}=108$ micrograms.

Step3: Calculate for 6.0 days

For $t = 6.0$ days, the number of half - lives $n=\frac{6.0}{3.0}=2$. Then $A = 216\times(\frac{1}{2})^2=216\times\frac{1}{4}=54$ micrograms.

Step4: Calculate for 9.0 days

For $t = 9.0$ days, the number of half - lives $n=\frac{9.0}{3.0}=3$. Then $A=216\times(\frac{1}{2})^3=216\times\frac{1}{8}=27$ micrograms.

Answer:

3.0 days: 108
6.0 days: 54
9.0 days: 27