Question

Copper has two naturally occurring isotopes, 63Cu Gsotopic mass 629396 arnu) and 65Cu Osotopic mass 64.9278 amu). If copper has an atomic mass of 63.546 amu, what is the percent abundance of each isotope?

Answer 1

Answer: The percentage abundance of $_{29}^{63}\textrm{Cu}$ and $_{29}^{65}\textrm{Cu}$ isotopes are 75.77% and 24.23% respectively

Explanation:

Average atomic mass of an element is defined as the sum of 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)

Let the fractional abundance of $_{29}^{63}\textrm{Cu}$ isotope be 'x'. So, fractional abundance of $_{29}^{63}\textrm{Cu}$ isotope will be '1 - x'

• For $_{29}^{63}\textrm{Cu}$ isotope:

Mass of $_{29}^{63}\textrm{Cu}$ isotope = 62.9396 amu

Fractional abundance of $_{29}^{63}\textrm{Cu}$ isotope = x

• For $_{29}^{65}\textrm{Cu}$ isotope:

Mass of $_{29}^{65}\textrm{Cu}$ isotope = 64.9278 amu

Fractional abundance of $_{29}^{65}\textrm{Cu}$ isotope = 1 - x

• Average atomic mass of copper = 63.546 amu

Putting values in equation 1, we get:

$63.546=[(62.9396\times x)+(64.9278\times (1-x))]\\\\x=0.6950$

Percentage abundance of $_{29}^{63}\textrm{Cu}$ isotope = $0.6950\times 100=69.50\%$

Percentage abundance of $_{29}^{65}\textrm{Cu}$ isotope = $(1-0.6950)=0.305\times 100=30.50\%$

Hence, the percentage abundance of $_{29}^{63}\textrm{Cu}$ and $_{29}^{65}\textrm{Cu}$ isotopes are 69.50% and 30.50% respectively.