Rubidium-87 decays by beta decay with a half-life of 4.9 * 10¹⁰ yr. How many ⁸⁷Rb atoms are in a moon rock sample that has a rubidium decay rate of 3,500 disintegrations per hour

Question

Quizplus · Accepted Answer

First, we need to use the half-life of Rubidium-87 to find the decay constant:

t1/2 = 4.9 x 10^10 years
λ = ln(2)/t1/2 = 0.01415 per year

Next, we can use the decay rate (the activity) to find the number of atoms:

activity = 3500 disintegrations per hour = 3500/3600 disintegrations per second
λN = activity
N = activity/λ

N = (3500/3600) / 0.01415 per year = 2.187 x 10^13 atoms

Therefore, the answer is 2.2 x 10^10 atoms, or choice C.

Rubidium-87 Decays by Beta Decay with a Half-Life of 4