To determine the percentages of each isotope in the mixture, we can set up a system of equations based on the average atomic mass and the masses of the isotopes.
Let's assume that x represents the percentage of the isotope with a mass of 33.00 amu, and (100 - x) represents the percentage of the isotope with a mass of 34.00 amu.
The average atomic mass is given as 33.79 amu, so we can set up the following equation:
(33.00 * x/100) + (34.00 * (100 - x)/100) = 33.79
Simplifying the equation:
(33.00x + 34.00(100 - x))/100 = 33.79
Expanding and rearranging:
(33.00x + 3400 - 34.00x)/100 = 33.79
-1.00x + 3400 = 3379
-1.00x = 3379 - 3400
-1.00x = -21
x = -21 / -1.00
x = 21
So, the percentage of the isotope with a mass of 33.00 amu is 21%, and the percentage of the isotope with a mass of 34.00 amu is (100 - x) = 79%.
The reason for these percentages is that the average atomic mass is closer to the mass of the heavier isotope (34.00 amu) than the lighter isotope (33.00 amu). This means that the heavier isotope contributes more to the overall mass and therefore must be present in a higher percentage in the mixture to achieve the average atomic mass of 33.79 amu.