Question

fermium - 253 has a half - life of three days. a sample contains 400 g. how long will it take for the sample to decay to 100 g? number of half - lives 2 number of days 6 how many grams of fermium will remain after fifteen days? 50 25 12.5 6.25

Explanation:

Step1: Calculate number of half - lives

The half - life of fermium - 253 is 3 days. The time elapsed is 15 days. So the number of half - lives $n=\frac{15}{3}=5$.

Step2: Use decay formula

The initial amount of fermium $N_0 = 400$ g. The amount of a radioactive substance after $n$ half - lives is given by $N = N_0\times(\frac{1}{2})^n$. Substitute $N_0 = 400$ and $n = 5$ into the formula: $N=400\times(\frac{1}{2})^5$.

Step3: Calculate the remaining amount

$(\frac{1}{2})^5=\frac{1}{32}$, and $400\times\frac{1}{32}=12.5$ g.

Answer:

12.5