By knowing the natural abundance of minor isotopes, it's possible to calculate the relative heights of M+ and M+1 peaks. If natural abundances are 12C - 98.9% and 13C - 1.10%, what are the relative heights, to the nearest 0.1%, of the M+ and M+1 peaks in the mass spectrum of cholesterol, C27H48O? Ignore the contributions of isotopes like 2H (deuterium; 0.015% natural abundance) and 17O (0.04% natural abundance) that are small. The relative heights are, in order of increasing mass: 100 to

the relative height of M⁺ : M+1 is; 0.7418 : 0.2228

The relative heights are; In order of increasing mass 100 : 30

Explanation:

Given the data in the question;

The M⁺ peak comes from all ¹²₆C atoms

so, the probability in cholesterol, C₂₇H₄₈O is ( 98.9% )²⁷ = ( 0.989 )²⁷ = 0.7418

The M+1 peak comes from the isotopic carbon ¹³₆C.

so, the probability in cholesterol is ⇒ 1.10% × ( 98.9% )²⁶ = 0.011 × ( 0.989)²⁶

The probability for 27 carbons is ⇒  27 × 0.011 × ( 0.989)²⁶ = 0.2228

Therefore, the relative height of M⁺ : M+1 is; 0.7418 : 0.2228

The relative heights are; In order of increasing mass 100 : 30  

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