Final answer:
To calculate the relative abundances of the isotopic peaks at m/z = 74 and 75 in the mass spectrum of (CH3)4Si, we need to consider the isotopic composition of silicon. Silicon has three naturally occurring isotopes: Si-28, Si-29, and Si-30. Using the relative abundances of these isotopes, we can calculate the relative abundances of the isotopic peaks at m/z = 74 and 75. The relative abundances are approximately 73.95% and 17.22%, respectively.
Step-by-step explanation:
In order to calculate the relative abundances of the isotopic peaks at m/z = 74 and 75 in the mass spectrum of (CH3)4Si, we need to consider the isotopic composition of silicon.
Silicon has three naturally occurring isotopes: Si-28, Si-29, and Si-30. The relative abundances of these isotopes are approximately: Si-28 (mass = 27.9769 amu) - 92.23%, Si-29 (mass = 28.9765 amu) - 4.67%, and Si-30 (mass = 29.9738 amu) - 3.10%.
Since (CH3)4Si contains four silicon atoms, we can consider the combination of the three isotopes to determine the relative abundances of the isotopic peaks at m/z = 74 and 75.
Let's first calculate the m/z values for each isotopic peak:
m/z = (74 * 4) / 4 = 74, and m/z = (75 * 4) / 4 = 75.
Now, we can calculate the relative abundances using the percentages of the isotopes:
For m/z = 74, the relative abundance is (92.23%)4 = 73.95%
For m/z = 75, the relative abundance is 4 * 92.23% * 4.67% = 17.22%
Therefore, the relative abundances of the isotopic peaks at m/z = 74 and 75 are approximately 73.95% and 17.22%, respectively.