William W. answered • 11/14/19

BS in Mechanical Engineering with 35 years experience

There's a typo in your question, Oxygen has an Atomic Mass of 15.9994 not 15.9949.

Atomic mass of an element is calculated by taking the atomic mass of isotope #1 times the percentage of that isotope found in the world (called its "abundance") plus the atomic mass of isotope #2 times its abundance plus the atomic mass of isotope #3 times its abundance . . . until all naturally occurring isotopes are covered. So it's a weighted average. Consequently, the sum of all the "abundances" must add up to 100% or 1.00.

So, if we identify isotope #1 as the one with weight 15.9949 and say its abundance is a_{1} and if we say isotope #2 is the one with weight 16.9993 and say its abundance is a_{2} then we can say the following:

1) a_{1} + a_{2} + 0.00204 = 1.000000 (notice I converted percent to a decimal)

and

2) 15.9994 = (15.9949)(a_{1}) + (16.9993)(a_{2}) + (17.9992)(0.00204)

Solving equation 1) above for a_{2}, we get a_{2} = (0.99796)(a_{1})

Substituting "(0.99796)(a_{1})" for a_{2} in equation 2) above, we get:

15.9994 = (15.9949)(a_{1}) + (16.9993)(0.99796)(a_{1}) + (17.9992)(0.00204)

and then we can solve for a_{1} to get a_{1} = 0.99755 or 99.755%

Then plugging 0.99755 in for a_{1} into equation 1), we get a_{2} = 0.000409 or 0.0409%