Q50P - Chemistry: Molecular Nature Of Matter And Change

Question

C65uCopper has two C65unaturally occurring 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.

Step-by-Step Solution

Answer

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

Percentage abundance of isotope ${}^{65}Cu$ = 34.50 %

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 C 63 u

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 

Step 3: 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.