type the correct answer in the box. use numerals instead of words.\nfermium - 253 is a radioactive isotope…
type the correct answer in the box. use numerals instead of words.\nfermium - 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.\ncomplete the table to show how much fermium - 253 should remain in the sample at the indicated times after the scientist obtained the sample.\n| time elapsed | amount remaining |\n| ---- | ---- |\n| 3.0 days | μg |\n| 6.0 days | μg |\n| 9.0 days | μg |
Answer
Answer:
3.0 days: 108 6.0 days: 54 9.0 days: 27
Explanation:
Step1: Recall half - life concept
The amount of a radioactive substance after one half - life is half of the initial amount.
Step2: Calculate for 3.0 days
Initial amount $A_0 = 216$ micrograms. After $t = 3.0$ days (1 half - life), $A_1=\frac{A_0}{2}=\frac{216}{2}=108$ micrograms.
Step3: Calculate for 6.0 days
6.0 days is 2 half - lives. So $A_2=\frac{A_0}{2^2}=\frac{216}{4} = 54$ micrograms.
Step4: Calculate for 9.0 days
9.0 days is 3 half - lives. So $A_3=\frac{A_0}{2^3}=\frac{216}{8}=27$ micrograms.