# What is an example of an isotope abundance practice problem?

Nov 6, 2014

Problem:
Nitrogen has two naturally occurring isotopes, nitrogen-14 and nitrogen 15. What is the percent abundance of each isotope?

Explanation:
The sum of the percent abundance of both isotopes must equal 100%, or, in decimal form, 1. The atomic weight of each isotope must be known.

Known/Given:
atomic weight of nitrogen-14 is 14.003074008
atomic weight of nitrogen-15 is 15.0001088982.
standard atomic weight of nitrogen is 14.0067.

Values used are from the National Institute of Standards and Technology in the United States. http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl

SOLUTION:
Let x = the abundance of nitrogen-14 and (1-x) = the abundance of nitrogen-15. Set up the equation as follows:

(14.003074008)(x) + (15.0001088982)(1-x) = 14.0067

Complete multiplications.

14.003074008x + 15.0001088982 - 15.0001088982x = 14.0067

1. Combine x values.

-0.9970348902x + 15.0001088982 = 14.0067

2. Substract 15.0001088982 from both sides.

-0.99703489902x = -0.9964 (answer has four decimal places due to significant figure rules for addition and subtraction)

3. Divide both sides by -0.99703489902.

x = .9964 = abundance of nitrogen-14 (4 decimal places due to significant figure rules

1-x = 0.0036 = abundance of nitrogen-15

Multiply the values of x and (1-x) times 100 to get percent.

.9964 x 100 = 99.64%
0.0036 x 100 = 0.36%