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 calculate its decay constant.

t1/2 = 4.9 × 1010 years

λ = ln 2 / t1/2

λ = ln 2 / (4.9 × 1010 years)

λ = 1.413 × 10-11 year-1

Next, we can use the decay rate of the sample to calculate the number of Rb-87 atoms:

N = λ × N0

N0 = N / λ

N0 = (3,500 disintegrations/hour x 24 hours/day x 365 days/year) / (1.413 x 10-11 year-1)

N0 = 2.21 × 1018 Rb-87 atoms

Therefore, the number of Rb-87 atoms in the moon rock sample is 2.2 × 1018 atoms, which is closest to option C.

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