There are only two naturally occurring isotopes of copper, Cu-63 and Cu-65. How do we find the natural abundance of Cu-65 ?

Question

anonymous · Answer

is the answer 50 percent?

anonymous · Answer

my guess was to do (63Cu)+(65Cu)=63.546 and then solve for Cu

anonymous · Answer

im not sure if im right though

jfraser · Answer

that's half of what you need. Right now you have 1 equation, but 2 unknowns. You also need to realize that X + Y = 1, where X is the percentage of Cu63, and Y is the percentage of Cu65. Then you can rearrange and substitute to remove one of the unknowns

anonymous · Answer

thats what i did originally but got the percentage to be 72.7 which was not one of the multiple choices given

jfraser · Answer

since the average mass is close to 63, the most abundant isotope is most likely Cu63. The 72.7 you found is probably the percentage of Cu63, not Cu65. Without doing the math, I can't say for certain

anonymous · Answer

Perhaps you also need the fact that the atomic mass of Cu-63 is not exactly 63, nor that of CU-65 exactly 65.  Webelements.com tells us that the mass of Cu-63 is 62.9296 and Cu-65 is 64.9278.  Those are very close to 63 and 65, but not exactly,   Here's my math:

$$x(64.9278) + (1-x)(62.9296) = 63.546$$
$$(64.9278 - 62.9296) x = 63.546 - 62.9296$$
$$1.9982 x = 0.6164$$
$$x = 0.308...$$

(The sig dig in the answer are controlled by the 3 sig places used in the average atomic mass of copper, because that gives you 3 sig dig on the RHS of the next to last equation.)

That's correct, as WebElements lists the abundance of Cu-65 as 30.83%.

anonymous · Answer

If you'd done this calculation with 63 and 65 as the atomic masses, you'd end up with 27.3%, which is close but nontrivially off.  Does that explain the discrepancy?

anonymous · Answer

yes it does! thank you!