Question

C65uCopper has twoC65unaturallyoccurring isotopes,${}^{\mathbf{63}}\mathit{C}\mathit{u}$(isotopic mass 62.9396 amu) and ${}^{\mathbf{65}}\mathit{C}$(isotopic mass 64.9278 amu). If copper has an atomic mass of 63.546 amu, what is the percent abundance of each isotope.

Short answer

Percentage abundance of isotope ${}^{63}Cu$= 69.50 %

Percentage abundance of isotope role="math" localid="1663338028833" ${}^{65}Cu$= 34.50 %

Step-by-step solution

Step 1: Average atomic mass 

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

Formula:

Step 2: Calculation of fractional abundance of isotope C63u

Let the fractional abundance of isotope ${}^{63}Cu$be 'X'

So, fractional abundance of isotope ${}^{65}Cu$will be '1 – X'

For isotope ${}^{63}Cu$:

Mass of isotope ${}^{63}Cu$= 62.9396 amu

Fractional abundance of isotope ${}^{63}Cu$= X

For isotope ${}^{65}Cu$:

Mass of isotope ${}^{65}Cu$= 64.9278 amu

Fractional abundance of isotope ${}^{65}Cu$= 1 – X

To find X, put above values in formula of average atomic mass

Calculation of percentage abundance of isotopes

Percentage abundance of isotope ${}^{63}Cu$= 0.6950 x 100=69.50 %

Percentage abundance of isotope ${}^{65}Cu$= (1 - 0.6590) x 100 = 0.3450 x 100 = 34.50 %

Hence, the percentage abundance of isotope${}^{63}Cu$and${}^{65}Cu$are 69.50 % and 34.50 % ­­respectively.