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

##### 1 Answer

**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%

**Answer:**

Percent abundance of nitrogen-14 = 99.64%

Percent abundance of nitrogen-15 = 0.36%