Question

There are two naturally occurring isotopes of copper. 63cu has a mass of 62.9296 amu. 65cu has a mass of 64.9278 amu. determine the abundance of each isotope.

Answer 1

1) You need to use the atomic mass of copper.


You can find it in a periodic table. It is 63.546 amu.


2) The atomic mass is the weigthed mass of the different isotopes.


This is, the atomic mass of one element is the atomic mass of each isotope times its corresponding abundance:


=> atomic mass of the element = abundance isotope 1 * atomic mass isotope 1 + abundance isotope 2 *  atomic mass isotope 2 + ....+abundance isotope n * atomic mass isotope n.


3) The statement tells there are two isotopes so the abundance of one is x and the abundance of the other is 1 - x


=> 63.546 amu = x * 62.9296 amu + (1-x)*64.9278


=> 63.546 = 62.9296x + 64.9278 - 64.9278x


=> 64.9278x - 62.9296 = 64.9278 - 63.546


=> 1.9982x = 1.3818


=> x = 1.3818 / 1.9982 = 0.6915 = 69.15%


=> 1 - x = 1 - 0.6915 = 0.3085 = 30.85%


Answer:


Cu-63 69.15%;


Cu-65 : 30.85%