The isotope has a half-life of 21 hours. If a sample initially contains exactly 10,000 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 10,000 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 exponential decay:

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

where N(t) is the number of atoms remaining after time t, N0 is the initial number of atoms, T is the half-life, and (1/2)^(t/T) is the fraction of atoms that remain after time t.

Substituting the given values, we get:

N(7 days) = 10,000 * (1/2)^(7*24/21)

N(7 days) ≈ 387.8 ≈ 390 (rounded to the nearest whole number)

Therefore, approximately 390 atoms of 11eb16b2_ffa3_da3b_984d_05f542264a7d_TB7799_11 will remain after one week. The closest answer choice is C, 39.

The Isotope Has a Half-Life of 21 Hours