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 radioactive decay formula to solve for the time required:

$N = N_0 (1/2)^{t/T_{1/2}}$

where:
$N_0$ = initial number of nuclei
$N$ = final number of nuclei
$t$ = time
$T_{1/2}$ = half-life

We can rearrange this equation to solve for time:

$t = (T_{1/2})\frac{\ln(N/N_0)}{\ln(1/2)}$

Plugging in the given values:

$t = (3.00	ext{ days})\frac{\ln(3.36	imes10^6/7.37	imes10^7)}{\ln(1/2)} \approx 13.4	ext{ days}$

Therefore, the best choice is C, which corresponds to 13.4 days.

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

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