# Abundance of Isotopes

1. ### FeDeX_LaTeX

434
1. The problem statement, all variables and given/known data
1) "The relative atomic mass of antimony is 121.8. Antimony exists as two isotopes; antimony-121 and antimony-123. Calculate the relative abundances of the two isotopes."
2) "The relative atomic mass of rubidium is 85.5. Rubidium consists of two isotopes, rubidium-85 and rubidium-87. Calculate the percentage of rubidium-87 in naturally occurring rubidium."

2. Relevant equations
N/A

3. The attempt at a solution
I thought these questions should be relatively easy but the solutions at the back of the book don't seem to agree with my answers.

For question 1, I did [121*x + 123*(100-x)]/100 = 121.8 and solved for x. Likewise for question 2. For question 1, I get that antimony-121 is 60% and antimony-123 is 40%, but the textbook says the answers should be 37.5% and 62.5% respectively. For question 2, I get Rb-85 occurring 75% and Rb-87 occurring 25%, yet the textbook says Rb-87 occurs 23.5%. However I checked my answers and I do get the average relative atomic masses that they state. Where have I gone wrong?

Thanks.

Last edited: Jul 23, 2011
2. ### Ray Vickson

6,320
According to your type of calculation the average of the numbers 5 and 5 should be [5*x + 5*(100-x)] = 500. Do you see anything wrong with this calculation?

RGV

3. ### SammyS

8,910
Staff Emeritus
You need to know the atomic mass of each of the isotopes: antimony-121, antimony-123, rubidium-85, and rubidium-87. You can't assume that they're 121, 123, 85, and 87.

Last edited: Jul 23, 2011
4. ### FeDeX_LaTeX

434
Hello,

I'm just a little confused and would appreciate if someone could explain to me why my method is incorrect though. For example, for chlorine, Cl-35 occurs 75% of the time and Cl-37 occurs 25% of the time. So the average, according to the textbook, is;

(35*0.75)+(37*0.25) = 35.5

Which is why 35.5 amu is the relative atomic mass of chlorine.

In the questions I did, I followed the same method, but since the percentages are unknown I let the percentage be x, and the other percentage be (100-x), since percentages must total to 100.

I don't understand why the atomic mass Ar of Rb-85 wouldn't just be 85?

All questions are supposed to be doable using only the textbook.

The question before this I got correct using this method, and the method working they've shown looks identical to mine...

Last edited: Jul 24, 2011
5. ### Ray Vickson

6,320
In my first reply I asked you a question---for a good reason. So far you have not answered it, but had you done so you would see right away where your problem lies.

RGV

6. ### FeDeX_LaTeX

434
Hello,

I saw your post but I still don't see the error, solving for x I get x = 50% (or 0.5) which is how often each of your numbers (5 and 5) occur... I don't understand. I'm not sure how your example is relevant because it doesn't involve weighted averages...

For chlorine, the approximate relative atomic mass is 35.5, because the textbook explains that Cl-35 occurs 75% of the time and Cl-37 25% of the time, so by weighted averages, 35*0.75 + 37*0.25 = 35.5

This is exactly what I have done for my questions, so why are they incorrect?

Last edited: Jul 24, 2011
7. ### ehild

12,387
Find and use more accurate data for the average atomic masses and isotope masses. The links SammyS gave you are excellent.

ehild

8. ### SammyS

8,910
Staff Emeritus
I believe that the 60% you calculated is the percent mass of Sb-121 in a sample of antimony. Since each atom of Sb-121 has less mass than each atom of Sb-123, the number of atoms of Sb-121 is more than 60% of the total number of antimony atoms in the sample.

9. ### Ray Vickson

6,320
I was responding to the unedited post and had not noticed that you had edited it. That said, you got good advice from Sammy S. The actual weight of Antimony 121 is not exactly 121 times the weight of one nucleon, because of binding energy, etc. Of course, there is the possibility that the book's answer is wrong; that happens frequently.

RGV

RGV

Last edited: Jul 24, 2011

12,387