The value percentages of O17 and O18 can be determined based on the known value of O16 and the average atomic mass of oxygen (16.008). Here's the math behind it:
Let's assume x represents the percentage of O17 and y represents the percentage of O18.
The average atomic mass of oxygen (16.008) is a weighted average of the isotopic masses of O16, O17, and O18, taking into account their respective abundance percentages. The equation can be set up as follows:
(99.76 * 16) + (x * 17) + (y * 18) = 16.008
Here, we multiply the abundance percentage (99.76) of O16 by its mass (16), and similarly, we multiply the percentage of O17 (x) by its mass (17) and the percentage of O18 (y) by its mass (18).
Now, to solve for x and y, we need to rearrange the equation. Subtracting (99.76 * 16) from both sides, we get:
(x * 17) + (y * 18) = 16.008 - (99.76 * 16)
Simplifying further:
17x + 18y = 16.008 - (99.76 * 16)
To find the exact values of x and y, we need additional information about the abundance percentages of O17 and O18. Without this information, it is not possible to calculate their precise value percentages. However, if we assume that the sum of the abundance percentages of O17 and O18 is equal to 100% (i.e., neglecting any other isotopes or trace elements), we can substitute (100 - 99.76) for y and solve for x:
17x + 18(100 - 99.76) = 16.008 - (99.76 * 16)
Solving this equation will give you the value percentage of O17 under the given assumption. Similarly, if you assume a different abundance percentage for O17 or O18, you can substitute it in the equation to find their respective value percentages.