For my chemistry homework, I have been given the isotopes Rubidium-87 (86.91u) and Rubidium-85 (84.91u). I am supposed to determine what the percent abundance of each isotope is in Rubidium, if Rubidium's average atomic mass is 85.47u. Unfortunately, I have no idea how to do that.
What I tried was using random percentages just to see what it gave me, but I realized that there could be hundreds of possible combinations if I do it that way. Does anyone know how I can figure this out?
What I tried was using random percentages just to see what it gave me, but I realized that there could be hundreds of possible combinations if I do it that way. Does anyone know how I can figure this out?
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The atomic mass is the weighted average mass of the isotopes. This is how you solve it:
Let x = the abundance of Rb-87 and 1-x = the abundance of Rb-85.
Then (86.91)(x) + (84.91)(1-x) = 85.47
Solve for x, that will be the abundance of Rb-87 written as a decimal fraction. If you want percent, multiply by 100. Subtract the decimal fraction of Rb-87 from 1 to get the abundance of Rb-85 written as a decimal fraction. Or, just subtract the percentage of Rb-87 from 100.
Let x = the abundance of Rb-87 and 1-x = the abundance of Rb-85.
Then (86.91)(x) + (84.91)(1-x) = 85.47
Solve for x, that will be the abundance of Rb-87 written as a decimal fraction. If you want percent, multiply by 100. Subtract the decimal fraction of Rb-87 from 1 to get the abundance of Rb-85 written as a decimal fraction. Or, just subtract the percentage of Rb-87 from 100.