Question

The average atomic weight of copper, which has two naturally occurring isotopes, is 63.5. One of the isotopes has an atomic weight of 62.9 amu and constitutes 69.1% of the copper isotopes. The other isotope has an abundance of 30.9%. The atomic weight (amu) of the second isotope is ________ amu.

Answer 1

Answer: The atomic weight of the second isotope is 64.81 amu.

Explanation:

Average atomic mass of an element is defined as the sum of atomic masses of each isotope each multiplied by their natural fractional abundance

Formula used to calculate average atomic mass follows:

$\text{Average atomic mass }=\sum_{i=1}^n\text{(Atomic mass of an isotopes)}_i\times \text{(Fractional abundance})_i$     .....(1)

We are given:

Let the mass of isotope 2 be 'x'

Mass of isotope 1 = 62.9 amu

Percentage abundance of isotope 1 = 69.1 %

Fractional abundance of isotope 1 = 0.691

Mass of isotope 2 = 'x'

Percentage abundance of isotope 2 = 30.9%

Fractional abundance of isotope 2 = 0.309

Average atomic mass of copper = 63.5 amu

Putting values in equation 1, we get:

$\text{Average atomic mass of copper}=[(62.9\times 0.691)+(x\times 0.309)]$

$x=64.81amu$

Hence, the atomic weight of second isotope will be 64.81 amu.