The rubidium isotope 87Rb is a β emitter that has a half-life of 4.9 ✕ 1010 y that decays into 87Sr. It is used to determine the age of rocks and fossils. Rocks containing the fossils of early animal have a ratio of 87Sr to 87Rb of 0.0040. Assuming that there was no 87Sr present when the rocks were formed, calculate the age of the fossils.

t = 39.04 1010 year

Explanation:

This is a nuclear disintegration exercise that is governed by the equation.

N = N0 e (-lam t)

The average life time is related to nuclear activity

T ½ = ln 2 / lam

Let's use these two equations for exercise, let's start by finding nuclear activity

Lam = ln 2 / T ½

Lam = ln 2 / 4.9 10 10

Lam = 0.14146 10-10 y-1

They tell us that the relationship atoms

No / N = 0.0040

Let's look

No / N = 1/0040

N/No = 250

Let's calculate the time

(-lam t) = ln (N / No)

, t = - 1 / lam ln (n / No)

t = - 1 / 0.14146 10-10 ln (250)

t = 39.04 1010 year