To calculate the atomic mass of zinc, we can use the relative peak intensities and the atomic masses of the three major isotopes of zinc.
First, let's convert the percentages of the peak intensities to ratios. We can do this by dividing each percentage by 100:
- Zn-64: 100/100 = 1
- Zn-66: 57.4/100 = 0.574
- Zn-68: 38.6/100 = 0.386
Next, we need to find the total sum of these ratios. Adding them together, we get:
1 + 0.574 + 0.386 = 1.96
This sum tells us that the total peak intensity corresponds to 1.96 units.
The next step is to normalize these ratios by dividing each one by the total sum:
- Zn-64: 1/1.96 ≈ 0.5102
- Zn-66: 0.574/1.96 ≈ 0.2939
- Zn-68: 0.386/1.96 ≈ 0.1970
These normalized ratios represent the relative abundance of each isotope in the sample.
Finally, to calculate the atomic mass of zinc, we can multiply each normalized ratio by the atomic mass of the corresponding isotope and sum them up:
(0.5102 x 63.9291) + (0.2939 x 65.9260) + (0.1970 x 67.9248)
= 32.6169 + 19.3796 + 13.4045
= 65.401 Da
Therefore, the atomic mass of zinc, based on the given peak intensities, is approximately 65.401 Da.