Question

The average atomic mass of copper is 63.546 amu. Natural copper consists of two isotopes: 63 Cu and 65 Cu. Their natural abundances are 69.09 % and 30.91 % respectively. If the mass of 63 Cu isotope is 62.9292 amu. What is the mass of 65 Cu isotope?
A. 64.9000
B. 65.1233
C. 64.9233
D. 65.1933

Answer 1

Hint: There is a formula to calculate the average mass of the isotope using mass and percentage of the isotopes. The formula to calculate the average mass of the isotope is as follows.
\[Average\text{ }mass=\dfrac{{{M}_{1}}{{x}_{1}}+{{M}_{2}}{{x}_{2}}}{{{x}_{1}}+{{x}_{2}}}\]
Here ${{M}_{1}}$ = Mass of the isotope one
${{M}_{2}}$ = mass of the isotope two
${{x}_{1}}$ = percentage of abundance of isotope one
${{x}_{2}}$ = percentage of abundance of isotope two

Complete Solution :
- In this it is given that the average atomic mass of the copper is 63.546 amu, and gave the percentage of abundance of $^{63}Cu$ and $^{65}Cu$ as 69.09 % and 30.91 % respectively.
- It has given the mass of the $^{63}Cu$ isotope is 62.9292 amu and asked to calculate the mass of the $^{65}Cu$ isotope.

- By using the following formula we can calculate the mass of the $^{65}Cu$ isotope.
\[Average\text{ }mass=\dfrac{{{M}_{1}}{{x}_{1}}+{{M}_{2}}{{x}_{2}}}{{{x}_{1}}+{{x}_{2}}}\]
Here ${{M}_{1}}$ = Mass of the $^{63}Cu$ isotope = 62.9292 amu
${{M}_{2}}$ = mass of the $^{65}Cu$ isotope
${{x}_{1}}$ = percentage of abundance of $^{63}Cu$ isotope = 69.09 %
${{x}_{2}}$ = percentage of abundance of $^{65}Cu$ isotope = 30.91 %
Average mass of the copper is 63.546 amu

- Substitute all the known values in the above formula to get the mass of the $^{65}Cu$ isotope.
\[\begin{align}
  & Average\text{ }mass=\frac{{{M}_{1}}{{x}_{1}}+{{M}_{2}}{{x}_{2}}}{{{x}_{1}}+{{x}_{2}}} \\
 & 63.546=\frac{(62.9292)(69.09)+({{M}_{2}})(30.91)}{69.09+30.91} \\
 & {{M}_{2}}=64.9233amu \\
\end{align}\]
- Therefore the mass of the $^{65}Cu$ isotope is 64.9233 amu.
So, the correct answer is “Option C”.

Note: In nature isotopes for the chemical elements are available. Various elements have isotopes in nature. Some elements have only one isotope and few elements have two or more than isotopes in nature. The percentage of abundance of all the isotopes will not be the same.