22. The two naturally occurring isotopes of copper 63Cu &64Cu have masses 62.2996amu
&64.9278 amu respectively. The atomic mass of copper is 63.546amu. Calculate the
percent abundance of each isotopes in a piece of copper
Let the percent abundance of 63Cu be x%, then the percent abundance of 64Cu would be 100 - x%.
For the average atomic mass to be 63.546 amu, the weighted sum of the isotopes' masses must equal their average atomic mass.
(62.2996 amu * x/100) + (64.9278 amu * (100 - x)/100) = 63.546 amu
Simplifying the equation, we have:
(62.2996x + 6492.78 - 64.9278x) / 100 = 63.546
Cross multiplying to eliminate fractions, we have:
62.2996x + 6492.78 - 64.9278x = 6354.6
Combining like terms:
-2.6282x + 6492.78 = 6354.6
Subtracting 6492.78 from both sides:
-2.6282x = -138.18
Dividing both sides by -2.6282:
x = 52.6
Therefore, the percent abundance of 63Cu is 52.6%, and the percent abundance of 64Cu is 100 - 52.6 = 47.4%.