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?

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Answer 1 · 2016-09-07T04:27:52

The percent abundance of N-15 is 0.6403%.

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

$1-x=$

$1-0.006403=0.993597$

$0.993597xx100=99.3597% "nitrogen-14"$

$99.3597% + 0.6403%=100%$