hard chem question!!?

Question

copper (atomic mass 63.5) occurs in nature in the form of two isotopes. Cu-63 and Cu-65 use this info to calculate the percent abundance of each copper isotope....show workkk

Answer 1

let x = fraction of abundance of Cu-63
then 1-x = fraction of abundance of Cu-65

Since the reported atomic mass of copper is the weighted average of isotope atomic mass (weighted by abundance), the reported atomic mass = sum of the abundance of each isotope x it's molecular weight. ie....

63.5 = x * 63 + (1-x) * 65 = 63x -65x +65

-1.5 = -2x
x = .75
1-x = .25

ie. 75% of Copper is Cu-63. 25% is Cu-65

Answer 2

Hm.. shouldn't be too difficult, yet I'm not 100% sure it is like that.
But let's say x is the percent of Cu-63 and y the percent of Cu-65.
Then it should work this way: x*63 + y*65 = 100*63.5
By calculating it you should get the ratio of x to y and from that ratio calculate the percent abundance. (e.g. x : y = 3 : 7 --> x = 30%; y = 70%)

Answer 3

I think it works this way:

the atomic mass is an average. Assume this was the average atomic mass of 100 copper atoms. Let X be the percentage of Copper 63 atoms and Y = the percentage of Copper 65 atoms. From this, two equations can be written:

X + Y = 100
((63X + 65Y)/100) = 63.5

Now, use substitution to find X and Y:

Y = 100 - X
63X +65(100-X) = 6350
-2X = 6350 - 6500
X = 75%
Y = 25%

Hope this helps

Answer 4

Let x be the fraction of Cu-63. Then (1.0 - x) is the fraction of Cu-65.

63x + (1.0-x)65 = 63.5

63x + 65 - 65x = 63.5

-2x = -1.5

x = 0.75 = 75% Cu-63

25% = Cu-65

That's not quite the actual 70/30 natural abundance, but the data are approximate.