Copper has only two naturally occurring isotopes, Cu-63 and Cu-65. The mass of Cu-63 is 62.9396 amu, and the mass of Cu-65 is 64.9278 amu. Use the atomic mass of copper to determine the relative abundance of each isotope in a naturally occurring sample. (Hint: The relative abundances of the two isotopes sum to 100%.)

The percentage relative abundance of Cu-63 is 69.5% and that of Cu-65 is 30.5%

Explanation:

The mass of Cu-63 is 62.9396 amu

The mass of Cu-65 is 64.9278 amu

Relative abundance of each isotope ?

The average atomic mass of Copper is; 63.546 u

The relationship between abundance, mass of isotopes and average atomic mass is;

(M1)(x) + (M2)(1-x) = M(E)

Where;

M1 = Mass of first isotope

x = Abundance of first isotope

M2 = Mass of second isotope

M(E) = Average atomic mass

Inserting the vaues, we have;

62.9396 (x) + 64.9278 (1-x) = 63.546

62.9396x - 64.9278x + 64.9278 = 63.546

- 1.9882x = 63.546 - 64.9278

- 1.9882x  = - 1,3818

x = 0.695 or 69.5%

The percentage relative abundance of Cu-63 is 69.5% and that of Cu-65 is 30.5%