Question

The element copper exists in nature as two isotopes: 63 Cu has a mass of 62.9296 u and Cu has a mass of 64.9278 u. The average atomic mass of copper is 63.55 u. Calculate the relative abundance of the two copper isotopes. % 66 Cu

Answer 1

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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