The isotope
Has a half-life of 21 hours.If a sample initially contains exactly 10000 atoms of
,approximately how many of these atoms will remain after one week?
A)1250
B)78
C)39
D)0
E)None of these choices is correct.

Question

The isotope 
Has a half-life of 21 hours.If a sample initially contains exactly 10000 atoms of 
,approximately how many of these atoms will remain after one week?
A)1250 
B)78 
C)39 
D)0 
E)None of these choices is correct.

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for radioactive decay: N = N0 * 0.5^(t/T), where N is the final number of atoms, N0 is the initial number of atoms, t is the time passed, and T is the half-life.

In this case, we know that the half-life is 21 hours, which means that T = 21. We want to know how many atoms will remain after one week, which is 7 * 24 = 168 hours. So we plug in N0 = 10000, t = 168, and T = 21:

N = 10000 * 0.5^(168/21) = 10000 * 0.5^8 = 39.0625

Rounding this to the nearest whole number gives us approximately 39 atoms remaining, which is answer choice C.

The Isotope Has a Half-Life of 21 Hours.If a Sample Initially Contains