Fermium-253 has a half-life of 3.00 days.If a sample of fermium originally has 7.37 ×
Nuclei,how long will it take for there to be only 3.36 ×
Fermium-253 nuclei left in this sample?

Question

Fermium-253 has a half-life of 3.00 days.If a sample of fermium originally has 7.37 × 
Nuclei,how long will it take for there to be only 3.36 × 
Fermium-253 nuclei left in this sample?

Quizplus · Accepted Answer

We can use the half-life formula to solve for the time it takes for the number of nuclei to decrease from 7.37 × 10^6 to 3.36 × 10^6:

N = N0 (1/2)^(t/t1/2)

where N0 is the initial number of nuclei, N is the final number of nuclei, t is the time elapsed, and t1/2 is the half-life.

Substituting the given values, we get:

3.36 × 10^6 = 7.37 × 10^6 (1/2)^(t/3)

Taking the natural logarithm of both sides:

ln (3.36 × 10^6/7.37 × 10^6) = ln (1/2)^(t/3)

Simplifying:

ln (0.456) = -(t/3) ln (2)

Solving for t:

t = -(3/ln 2) ln (0.456)

t ≈ 13.4 days

Therefore, the answer is choice C, 13.4 days.

Fermium-253 Has a Half-Life of 3