Question

Naturally occurring cobalt consists of only one isotope, cobalt59, whose relative atomic mass is 58.9332. A synthetic radioactive isotope of cobalt60, relative atomic mass 59.9338, is used in radiation therapy for cancer. A 1.8155 sample of cobalt has an apparent "atomic mass" of 58.9901.

FIND THE MASS OF COBALT60 IN THIS SAMPLE.

I DON'T KNOW WHERE TO START, I TRIED DOING CONVERSION FACTORS BUT I CANT GET A REASONABLE MASS.

HELP?

Answer 1

Let x = fractional abundance Co60
1-x = fractional abundance Co59
(Note that as percentages that will be x% and 100%-x%). Then
x(atomic mass Co60) + (1-x)(atomic mass Co59) = 58.8901
Solve for x and 1-x will give you the fractinal abundances of Co59 and Co60. Then fraction * 1.8155g = grams Co60 or Co59 depending upon which fraction you use. Post your work if you get stuck.

Answer 2

I get....
(x)(59.9338) +(1-x)(58.9332) =(58.9901)
59.9338x+58.9332-58.9332x=58.9901
1.0006x=0.0560
x=0.0569

cobalt60 abundance=0.0569%
cobalt59 abundance=0.9431%

0.0569/0.9431 X 1.8155g = .10953grams
Is that right?? It looks like i did it wrong.

Answer 3

We get...
OH wait, do we do

0.0569 X 1.8155g = 0.103g ?

so cobalt60=0.103g

Answer 4

Thanks!

Answer 5

Everything looks ok except where you converted to percent (which the problem didn't ask for). x = 0.0560 = Co60 abundance which is 5.60% if yu want to convert to percent.