Problem: Rubidium-87 decays by β-particle production to strontium-87 with a half-life of 4.7 x 1010 years. What is the age of a rock sample that contains 109.7 μg of  87Rb and 3.1 μg of  87Sr? Assume that no 87Sr was present when the rock was formed. The atomic masses for   87Rb and 87Sr are 86.90919 u and 86.90888 u, respectively.

🤓 Based on our data, we think this question is relevant for Professor Chamberlain's class at UCD.

FREE Expert Solution

Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln [N]t=-kt+ln [N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:


t12=ln 2k


We first need to calculate for the decay constant using the given half-life of 87Rb, 4.7 x 1010 years:


k=ln 2t12=ln 24.7×1010 yr


k = 1.4748x10-11 yr-1



Calculate the initial amount of 87Rb atoms present:


initial amount of 87Rb = final amount of 87Rb + amount of 87Sr


amu is approximately equal to molar mass (g/mol)


87Rb atoms=109.7 μg×10-6 g1 μg×1 mol86.90919 g×6.022×1023 atoms1 mol


87Rb = 7.6012x1017 atoms


87Sr atoms=3.1 μg×10-6 g1 μg×1 mol86.90888 g×6.022×1023 atoms1 mol


87Sr = 2.148x1016 atoms


initial amount of 87Rb = 7.6012x1017 atoms + 7.6012x1017 atoms

initial amount of 87Rb = 7.816x1017 atoms



Calculate the age of a rock sample:


[N]0 =  87Rb initial = 7.816x1017 atoms                        k = 1.4748x10-11 yr–1 

[N]t = 87Rb final = 7.6012x1017 atoms                         t = ???


Solving for t:

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Problem Details

Rubidium-87 decays by β-particle production to strontium-87 with a half-life of 4.7 x 1010 years. What is the age of a rock sample that contains 109.7 μg of  87Rb and 3.1 μg of  87Sr? Assume that no 87Sr was present when the rock was formed. The atomic masses for   87Rb and 87Sr are 86.90919 u and 86.90888 u, respectively.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Chamberlain's class at UCD.

What textbook is this problem found in?

Our data indicates that this problem or a close variation was asked in Chemistry: An Atoms First Approach - Zumdahl 2nd Edition. You can also practice Chemistry: An Atoms First Approach - Zumdahl 2nd Edition practice problems.