Final answer:
The number of carbon atoms in the compound is determined by using the relative abundances of m to M+1, corresponding to 12C to 13C isotopes, and is found to be approximately 3 carbon atoms after calculation.
Step-by-step explanation:
The mass spectrum of an organic compound can reveal the number of carbon atoms based on the relative intensities of the M (due to 12C) and M+1 (due to 13C) peaks. To find the number of carbon atoms, we set up the following equation, where n is the number of carbon atoms, I(M) is the intensity of the M peak, and I(M+1) is the intensity of the M+1 peak:
I(M+1)/I(M) = (n * natural abundance of 13C) / (natural abundance of 12C)
Inserting the given values into the equation:
0.1607 / 0.6189 = (n * 0.0107) / 0.9893
Solving for n yields the number of carbon atoms in the compound:
n = (0.1607 / 0.6189) * (0.9893 / 0.0107)
Calculate n to find the number of carbon atoms.
With given percentages, we calculate:
n = (0.1607 / 0.6189) * (0.9893 / 0.0107)
≈ 2.52
Since the number of carbon atoms cannot be a fraction, we round to the nearest whole number. Therefore, the number of carbon atoms in the compound is approximately 3.