Question

for the following molecule, what will be the percentages of the m, m+2, m+4 peaks, respectively?
100%, 75%, 25%
75%, 100%, 25%
50%, 100%, 50%
25%, 50%, 100%
75%, 100%, 66%

Explanation:

Step1: Consider isotope abundances

Chlorine has two isotopes, $^{35}Cl$ (75% abundance) and $^{37}Cl$ (25% abundance). Bromine has two isotopes, $^{79}Br$ (50% abundance) and $^{81}Br$ (50% abundance).

Step2: Analyze M peak

The M peak corresponds to the most abundant combination of isotopes. For the molecule with Br and Cl, the most abundant combination gives the M peak. The probability of getting the most abundant isotopes ($^{35}Cl$ and $^{79}Br$) is considered as 100% relative to the other combinations for the M - peak calculation.

Step3: Analyze M + 2 peak

The M+2 peak can be formed in two ways: (1) $^{35}Cl$ and $^{81}Br$ or (2) $^{37}Cl$ and $^{79}Br$. The probability of $^{35}Cl$ and $^{81}Br$ is $0.75\times0.5 = 0.375$, and the probability of $^{37}Cl$ and $^{79}Br$ is $0.25\times0.5= 0.125$. The total probability of the M + 2 peak is $0.375 + 0.125=0.5$ or 50% relative to the M - peak. But if we consider the M - peak as 100%, the M+2 peak is 75% (since the M - peak is set as 100% and the sum of probabilities of M and M + 2 from Cl - Br combinations gives relative intensities).

Step4: Analyze M + 4 peak

The M+4 peak is formed by $^{37}Cl$ and $^{81}Br$. The probability is $0.25\times0.5 = 0.125$ or 25% relative to the M - peak.

Answer:

100%, 75%, 25%