ANSWER: 30.848 %= 65Cu
69.152% = 63Cu
explanation:
We know that, average atomic mass of an element can be calculated by taking the weighted average of the atomic masses of its naturally occurring isotopes.
Generally, an element's naturally occurring isotopes will contribute to the average atomic mass of the element directly proportional to their abundance. Or we can write,
avg. atomic mass=∑i(isotope i×abundance x)
During actual calculation, we often use decimal abundances, which are simply % abundance divided by 100
Therefore, as we know that copper has two naturally occurring isotopes, copper-63 and copper-65. I.e. their respective decimal abundance must add up to give 1.
If we are taking x to be the decimal abundance of copper-63, we can say that the decimal abundance of copper-65 will be equal to 1−x.
And therefore,
copper-63 x⋅62.9296u+copper -65(1−x)⋅64.9278u=63.546u
Solving this equation for x , we get
62.9296⋅x−64.9278⋅x=63.546−64.9278
1.9982⋅x=1.3818⇒x=1.38181.9982=0.69152
This means that the percent abundances of the two isotopes will be
30.848 % = 65Cu
69.152% = 63Cu
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