type the correct answer in the box. use numerals instead of words. fermium - 253 is a radioactive isotope of…
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
Answer
Answer:
3.0 days: 108 6.0 days: 54 9.0 days: 27
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.