The isotope has a half-life of 7.5 seconds. If a sample contains 144 atoms of , approximately how many such atoms were present 30 seconds earlier? A) 576 B) 1152 C) 2304 D) 4320 E) 4.30 * 10⁸

Question

Quizplus · Accepted Answer

The number of remaining atoms after t seconds can be calculated using the formula.
N(t) = N0 (1/2)^(t/T)
where N0 is the initial number of atoms, T is the half-life, and t is the time elapsed.
In this case, N0 = 144, T = 7.5 sec and t = 30 sec.
N(30) = 144 (1/2)^(30/7.5) = 144 (1/2)^4 = 144/16 = 9
So, approximately 9 atoms of 11eb16b2_ffa3_da3d_984d_0372faa8756c_TB7799_11 were present 30 seconds earlier.
Therefore, the number of atoms present earlier = N(0) = N(30) x (2)^(30/T) = 9 x (2)^4 = 144, approximately.
Hence, the best choice is option C, 2304.

The Isotope Has a Half-Life of 7