# Nitrogen has two isotopes, N-14 and N-15, with atomic masses of 14.00031 amu and 15.001 amu, respectively. What is the percent abundance of N-15?

Sep 7, 2016

The percent abundance of N-15 is 0.6403%.

#### Explanation:

The atomic mass of an element is a weighted average of its isotopes in which the sum of the abundance of each isotope is equal to 1 or 100%.

Formula for Calculating Isotope Percent Abundance

(x)("mass") + (1-x)("mass")=100%

In order to determine the percent abundance of nitrogen-15:

$\text{Let}$

$x = \text{% of nitrogen-15}$

$\left(1 - x\right) = \text{% of nitrogen-14}$

100%=14.0067, the atomic mass of nitrogen

Set up the formula for nitrogen-15 and nitrogen-14.

$15.001 x + 14.00031 \left(1 - x\right) = 14.0067$

Simplify the left-hand side.

$15.001 x + 14.00031 - 14.00031 x = 14.0067$

Simplify.

$0.9979 x + 14.00031 = 14.0067$

Subtract $14.00031$ from both sides.

$0.9979 x = 14.0067 - 14.00031$

Simplify.

$0.9979 x = 0.00639$

Divide both sides by $0.9979$.

x=0.006403xx100=0.6403% "nitrogen-15"

In case you're interested, the percent abundance of nitrogen-14 is

$1 - x =$

$1 - 0.006403 = 0.993597$

0.993597xx100=99.3597% "nitrogen-14"

99.3597% + 0.6403%=100%