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's assume the percent abundance of copper-63 is x and the percent abundance of copper-64 is y.
We know that the atomic mass of copper is the weighted average of the masses of the two isotopes:
(0.01x)(62.2996 amu) + (0.01y)(64.9278 amu) = 63.546 amu
However, we also know that the percent abundances must add up to 100%:
x + y = 100
Now we can solve this system of equations.
Rearranging the second equation, we have:
y = 100 - x
Substituting this into the first equation, we have:
(0.01x)(62.2996 amu) + (0.01(100-x))(64.9278 amu) = 63.546 amu
Expanding and simplifying:
0.622996x + 6.49278 - 0.649278x = 63.546
Combine like terms:
-0.026282x + 6.49278 = 63.546
Subtracting 6.49278 from both sides:
-0.026282x = 57.05322
Dividing both sides by -0.026282:
x ≈ -57.05322 / -0.026282 ≈ 2172.07
Since the percent abundance cannot be negative, this value is not meaningful. Therefore, we made an assumption that is not valid.
It is not possible to determine the percent abundance of each isotope with the given information.