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# Help with relative atomic mass of rubidium.

I was doing some summer work given by my chem teacher to help prepare us for chemistry class starting in september. I need help with this question:

"Rubidium has only two isotopes in nature: 85Rb and 87Rb. Calculate the percentage abundance of the isotopes of rubidium given that the relative atomic mass (weighted average) is 85.47."

How would you calculate this?

Thank you.

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Ok, so basically you use the formula:

85.47 = (isotope mass x %) + (isotope mass x %)  / 100

since we do not know the % value of the isotopes you sub x as the percentage for the first isotope (Rb-85), which means that the second isotope (Rb-87) would have a percentage of 100 - x

therefore: 85.47 = 85 (x) + 87 (100-x)  /100

multiple each side by 100 and simplify.

therefore:
8547 = 85x + 8700 - 87x

8547 = -2x + 8700

-153 = -2x

x = 76.5

Once you work out what x is equal to you, you've basically found the percentage of the first isotope (Rb-85), and because there are only 2 isotopes, to work out the percentage of Rb-87 you do 100 - x.

so Rb-85 = 76.5%
Rb-87 = 100-76.5  = 23.5%

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The above procedure is correct, but the percent abundance numbers are incorrect. I was about to post the solution I had written out but they beat me to it.

Instead of assuming 85 and 87 as the mass numbers, use the actual masses, which is 84.9117 for 85Rb and 86.9092 for 87Rb. You will get 72.06% for 85Rb and 27.94% for the other isotope, which is correct according to several internet sources.

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