Draw the signal for the following multiplicities. What is the ratio of peaks within each signal?
(f) septet

Verified step by step guidance

1. Understand the concept of multiplicity in NMR spectroscopy. Multiplicity refers to the splitting of NMR signals into multiple peaks due to interactions with neighboring non-equivalent protons. The number of peaks is determined by the n+1 rule, where n is the number of neighboring protons.
2. Identify the multiplicity given in the problem. Here, we are dealing with a 'septet'. According to the n+1 rule, a septet indicates that there are 6 neighboring protons (n = 6), as 6 + 1 = 7 peaks.
3. Determine the ratio of peaks within a septet. The ratio of peaks in a septet follows Pascal's triangle, which for a septet is 1:6:15:20:15:6:1. This means the intensity of the peaks will follow this pattern.
4. Draw the signal for a septet. When sketching the septet, ensure that there are seven peaks with the central peak being the tallest, and the heights of the peaks decreasing symmetrically as you move away from the center, following the ratio 1:6:15:20:15:6:1.
5. Review the concept of coupling constants. The distance between the peaks in a septet is determined by the coupling constant (J value), which is a measure of the interaction between the coupled protons. This is important for accurately representing the septet in an NMR spectrum.

Key Concepts

NMR Multiplicity

NMR multiplicity refers to the splitting of NMR signals into multiple peaks due to interactions between neighboring non-equivalent hydrogen atoms. The number of peaks in a signal is determined by the n+1 rule, where n is the number of neighboring hydrogens. This splitting provides insights into the number of adjacent hydrogens and the structure of the molecule.

Septet in NMR

A septet in NMR spectroscopy is a signal that splits into seven peaks. This occurs when a hydrogen atom is adjacent to six equivalent hydrogen atoms, following the n+1 rule (6+1=7). The septet pattern is often seen in molecules with symmetrical environments, such as isopropyl groups, where the central hydrogen is influenced by six equivalent hydrogens.

Pascal's Triangle and Peak Ratios

Pascal's Triangle is used to determine the intensity ratios of peaks in NMR multiplets. For a septet, the peak ratio follows the 1:6:15:20:15:6:1 pattern, derived from the seventh row of Pascal's Triangle. These ratios reflect the probability of different spin states of neighboring hydrogens, helping to interpret the relative intensities of the peaks in the septet.