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 are 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 are correct.

Quizplus · Accepted Answer

We can start by using the formula for exponential decay:

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

where N is the final number of atoms, N0 is the initial number of atoms, t is the time elapsed, and T is the half-life of the isotope.

In this case, we have:

N0 = 10000
T = 21 hours

To convert one week to hours, we have:

1 week = 7 days * 24 hours/day = 168 hours

So, the time elapsed is:

t = 168 hours

Substituting these values into the formula, we get:

N = 10000*(1/2)^(168/21) ≈ 378.8

Since we can't have a fraction of an atom, we need to round to the nearest whole number. Therefore, the closest answer choice is C) 39.

The Isotope Has a Half-Life of 21 Hours