Question

Copper has two naturally occurring isotopes with atomic masses of 62.9296 u () and 64.9278 u (). The atomic mass of copper is 63.546 u. What is the percent distribution of the isotopes

Answer 1

Answer:

The abundance of first isotope is 69.15 %

The abundance of second isotope is 30.85 %

Explanation:

The formula for the calculation of the average atomic mass is:

$Average\ atomic\ mass=(\frac {\%\ of\ the\ first\ isotope}{100}\times {Mass\ of\ the\ first\ isotope})+(\frac {\%\ of\ the\ second\ isotope}{100}\times {Mass\ of\ the\ second\ isotope})$

Given that:

Since the element has only 2 isotopes, so the let the percentage of first be x and the second is 100 -x.

For first isotope:

% = x %

Mass = 62.9296 u

For second isotope:

% = 100  - x  

Mass = 64.9278 u

Given, Average Mass = 63.546 u

Thus,  

$63.546=\frac{x}{100}\times {62.9296}+\frac{100-x}{100}\times {64.9278}$

Solving for x, we get that:

x = 69.15 %

The abundance of first isotope is 69.15 %

The abundance of second isotope is 100 - 69.15 % = 30.85 %