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?

1 Answer
Sep 7, 2016

Answer:

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:

#"Let"#

#x="% of nitrogen-15"#

#(1-x)="% of nitrogen-14"#

#100%=14.0067#, the atomic mass of nitrogen

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

#15.001x+14.00031(1-x)=14.0067#

Simplify the left-hand side.

#15.001x+14.00031-14.00031x=14.0067#

Simplify.

#0.9979x+14.00031=14.0067#

Subtract #14.00031# from both sides.

#0.9979x=14.0067-14.00031#

Simplify.

#0.9979x=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%#