Question

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?

Answer 1

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%`