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?
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.
We get...
OH wait, do we do
0.0569 X 1.8155g = 0.103g ?
so cobalt60=0.103g
Thanks!
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.
To find the mass of cobalt-60 in the given sample, we need to use the information given about the isotopes and their relative atomic masses. Here's how you can approach it step-by-step:
1. Determine the mass of cobalt-59 in the sample:
- Given that the relative atomic mass of cobalt-59 is 58.9332, we can assume that the entire sample consists of cobalt-59 atoms.
- Multiply the relative atomic mass of cobalt-59 by the mass of the sample:
Mass of cobalt-59 = 58.9332 * 1.8155 g
2. Determine the mass of cobalt-60 in the sample:
- Given that the relative atomic mass of cobalt-60 is 59.9338, we can assume that the difference between the apparent "atomic mass" of the sample (58.9901 g) and the mass of cobalt-59 will give us the mass of cobalt-60.
- Subtract the mass of cobalt-59 from the apparent "atomic mass":
Mass of cobalt-60 = (Apparent "atomic mass" of the sample - Mass of cobalt-59)
Using these steps, you can now calculate the mass of cobalt-60:
Mass of cobalt-59 = 58.9332 * 1.8155 g
Mass of cobalt-60 = 58.9901 g - (58.9332 * 1.8155 g)
By performing these calculations, you should be able to determine the mass of cobalt-60 in the given sample.
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.