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Answer :
According to the given data, there are approximately 6.6 carbon atoms present in the molecule.
The peaks at 162 and 163 likely correspond to different isotopes of carbon, specifically carbon-12 and carbon-13. The ratio of the relative intensities of these peaks can be used to determine the number of carbon atoms present in the molecule.
The ratio of the intensities of the two peaks is:
162:163 = 46.59% : 5.17%
To simplify the calculation, we can convert the percentages to fractions:
46.59% = 0.4659
5.17% = 0.0517
The ratio can now be expressed as:
0.4659 : 0.0517
To find the number of carbon atoms, we can use the formula:
N = (I1 / I2) / (R1 / R2)
where N is the number of carbon atoms, I1 and I2 are the intensities of the two peaks, and R1 and R2 are the natural abundances of the two isotopes (i.e., the percentage of carbon-12 and carbon-13 in nature, respectively). The values for R1 and R2 are approximately 98.93% and 1.07%, respectively.
Substituting the values, we get:
N = (0.4659 / 0.0517) / (98.93% / 1.07%)
N ≈ 6.6
Therefore, according to the given data, there are approximately 6.6 carbon atoms present in the molecule.
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