Fermium-253 has a half-life of 3.00 d.A sample of fermium contains 7.37 × 10⁷ nuclei.How long will it take for there to be only 3.36 × 10⁶ fermium nuclei in this sample?

Question

Quizplus · Accepted Answer

We can use the radioactive decay formula to solve this problem. Let N be the initial number of fermium nuclei and Nₒ be the final number of fermium nuclei. Then:

N = Nₒ e^(-kt)

where k is the decay constant and t is time. We can solve for k using the half-life:

t(1/2) = ln(2)/k
k = ln(2)/t(1/2)
k = ln(2)/3.00 d
k = 0.2315 d^(-1)

Substituting this into the radioactive decay formula and solving for t when N = 3.36 × 10^16 gives:

3.36 × 10^16 = 7.37 × 10^17 e^(-0.2315t)
t = (ln(7.37 × 10^17) - ln(3.36 × 10^16))/0.2315
t = 13.4 d

Therefore, the answer is C.

Fermium-253 Has a Half-Life of 3