Fermium-253 has a half-life of 3.00 days.If a sample of fermium originally has 7.37 × $10^7$ nuclei,how long will it take for there to be only 3.36 × $10^6$ fermium-253 nuclei left in this sample?

Question

Quizplus · Accepted Answer

We can use the equation for radioactive decay:

N = N0 * (1/2)^(t/T)

Where:
N0 = initial number of nuclei (7.37*10^7 in this case)
N = final number of nuclei (3.36*10^6 in this case)
T = half-life (3.00 days for Fermium-253)

Solving for t:

t = T * log(N/N0) / log(1/2)

t = 3.00 days * log(3.36*10^6 / 7.37*10^7) / log(1/2)

t = 13.4 days

Therefore, the answer is (C) 13.4 days.

Fermium-253 Has a Half-Life of 3 10710^7107 Nuclei,how Long Will It Take for There to Be Only

Fermium-253 Has a Half-Life of 3 $10^7$ Nuclei,how Long Will It Take for There to Be Only