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I just need help with this one question, and then once I know how to do the steps, I think can do the others.

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The average atomic mass of argon is 39.95 u. Natural argon contains three isotopes: Ar-36 (35.967 u), Ar-38 (37.962 u)& Ar-40 (39.962 u). If the isotopic abundance of Ar-36 is 0.006000%, find the isotopic abundances of the other two isotopes.

Thanks for your help.
~Lucy

average*100= sum of weights*abundance

= 35.967*.006 + 37.962*P + 39.962*(100-P-.006)

solve for the abundance for Ar38 (P), then the abundance of Ar39 (100-P-.006)

Thanks for your help, but I tried and I still couldn't get the right answer.

I need help solving for P. . .

To find the isotopic abundances of Ar-38 and Ar-40, we can use the fact that the sum of the abundances of all isotopes in a sample should equal 100%.

Let's denote the abundance of Ar-38 as x and the abundance of Ar-40 as y. Since we already know the abundance of Ar-36 (0.006000%), we can subtract this value from 100% to find the sum of the abundances of Ar-38 and Ar-40:

(0.006000% + x + y) = 100%

To solve for x and y, we can rearrange the equation:

x + y = 100% - 0.006000%
x + y = 99.994000%

Now, let's use another piece of information: the average atomic mass of argon is 39.95 u. The average atomic mass is a weighted average of the masses of each isotope, where each isotope's mass is multiplied by its abundance.

We can set up an equation using the atomic masses and abundances of the isotopes:

(0.00006000% × 35.967 u) + (x × 37.962 u) + (y × 39.962 u) = 39.95 u

Simplifying this equation, we get:

(0.00006000% × 35.967 u) + (x × 37.962 u) + (y × 39.962 u) = 39.95 u

(0.00006000/100 × 35.967) + (37.962x) + (39.962y) = 39.95

0.0215802 + 37.962x + 39.962y = 39.95

37.962x + 39.962y = 39.95 - 0.0215802

37.962x + 39.962y = 39.9284198

Now we have a system of two equations:

x + y = 99.994000%
37.962x + 39.962y = 39.9284198

You can now solve this system of equations using substitution, elimination, or any other method you prefer to find the values of x and y, which represent the abundances of Ar-38 and Ar-40, respectively.