The isotope has a half-life of 7.5 seconds. If a sample contains 144 atoms of approximately how many such atoms were there present 30 seconds earlier? A)576 B)1152 C)2304 D)4320 E)4.30 × 10 ⁸

Question

Quizplus · Accepted Answer

Since the half-life of the isotope is 7.5 seconds, we can use the formula N = N0(1/2)^(t/t1/2), where N is the current number of atoms, N0 is the initial number of atoms, t is the time elapsed, and t1/2 is the half-life.

Plugging in the values, we get N = 144(1/2)^(30/7.5) = 144(1/2)^4 = 144/16 = 9. Therefore, approximately 9 atoms were present 30 seconds earlier.

To find the initial number of atoms, we can use the same formula with the given values of t and N. We get N0 = N(2)^(t/t1/2) = 144(2)^(30/7.5) = 144(2^4) = 144(16) = 2304. Therefore, approximately 2304 atoms were present 30 seconds earlier.

So the best choice is (C) 2304.

The Isotope Has a Half-Life of 7