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 × 10⁸

Question

Quizplus · Accepted Answer

We can use the formula for radioactive decay:

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

Where N0 is the initial number of atoms, N is the final number of atoms after time t has elapsed, T is the half-life of the isotope, and ^( ) indicates exponentiation (e.g. 2^3 = 8).

We are given N = 144 and T = 7.5 seconds. We want to solve for N0 when t = 30 seconds.

144 = N0 * (1/2)^(30/7.5)

144 = N0 * (1/2)^4

144 = N0 * 1/16

N0 = 144 * 16

N0 = 2304

Therefore, there were approximately 2304 atoms of the isotope present 30 seconds earlier. The closest choice is C.

The Isotope Has a Half-Life of 7