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

Question

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

Quizplus · Accepted Answer

We can use the formula for exponential decay: N = N0 * (1/2)^(t/T), where N is the final number of nuclei, N0 is the initial number of nuclei, t is the time elapsed, and T is the half-life.

Plugging in the given values, we have:

3.36 × 10^11 = 7.37 × 10^11 * (1/2)^(t/3)

Simplifying:

(1/2)^(t/3) = 3.36/7.37
(1/2)^(t/3) = 0.456

Taking the logarithm of both sides (with base 1/2):

t/3 = log(0.456)
t = 3 * log(0.456) / log(1/2)

Using a calculator:

t ≈ 13.4 d

Therefore, the answer is C) 13.4 d.

Fermium-253 Has a Half-Life of 3