Question

Copper has two naturally occurring isotopes, 63Cu (isotopic mass 62.9296 amu) and 65Cu (isotopic mass 64.9278 amu). If copper has an atomic mass of 63.546 amu, what is the percent abundance of each isotope? Report your answer to 5 significant figures.

Answer 1

Answer:

Percentage of first isotope = 69.152 %

Percentage of second isotope =  30.848 %

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:

For first isotope:

Let % = x %

Mass = 62.9296 amu

For second isotope:

% = 100 - x  %  (Since, there are only two isotopes)

Mass = 64.9278 amu

Average mass = 63.546 amu

Thus,  

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

Solving,

1.9982 x = 138.18

Thus,

Percentage of first isotope = x = 69.152 %

Percentage of second isotope = 100 - x % = 30.848 %