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.\n| time elapsed | amount remaining |\n| ---- | ---- |\n| 3.0 days | μg |\n| 6.0 days | μg |\n| 9.0 days | μg |
Answer
Explanation:
Step1: Recall half - life formula
The amount of a radioactive substance $A$ after time $t$ with initial amount $A_0$ and half - life $T_{1/2}$ is given by $A = A_0\times\left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$. Here, $A_0 = 216$ micrograms and $T_{1/2}=3.0$ days.
Step2: Calculate amount at $t = 3.0$ days
Substitute $t = 3.0$ days into the formula: $A=216\times\left(\frac{1}{2}\right)^{\frac{3.0}{3.0}}=216\times\frac{1}{2}=108$ micrograms.
Step3: Calculate amount at $t = 6.0$ days
Substitute $t = 6.0$ days into the formula: $A = 216\times\left(\frac{1}{2}\right)^{\frac{6.0}{3.0}}=216\times\left(\frac{1}{2}\right)^2=216\times\frac{1}{4} = 54$ micrograms.
Step4: Calculate amount at $t = 9.0$ days
Substitute $t = 9.0$ days into the formula: $A=216\times\left(\frac{1}{2}\right)^{\frac{9.0}{3.0}}=216\times\left(\frac{1}{2}\right)^3=216\times\frac{1}{8}=27$ micrograms.
Answer:
| Time Elapsed | Amount Remaining |
|---|---|
| 3.0 days | 108 μg |
| 6.0 days | 54 μg |
| 9.0 days | 27 μg |