(a) Draw all of the possible spin states to explain why a hydrogen with four neighbors appears as a quintet (quint, five peaks).

Verified step by step guidance

1. Identify the hydrogen atom in question and its neighboring hydrogen atoms. In this case, the hydrogen has four neighboring hydrogens.
2. Recall the n+1 rule for splitting patterns in NMR spectroscopy, where 'n' is the number of neighboring hydrogens. For four neighbors, the splitting pattern will be a quintet (4+1=5).
3. Consider the possible spin states of the neighboring hydrogens. Each hydrogen can have a spin of +1/2 or -1/2.
4. Calculate the different combinations of spin states for the four neighboring hydrogens. These combinations will determine the number of peaks in the quintet.
5. Visualize or draw the energy levels corresponding to each combination of spin states, showing how they result in five distinct peaks in the NMR spectrum.

Key Concepts

Spin States

Spin states refer to the intrinsic angular momentum of particles, such as electrons, which can exist in different orientations. For a hydrogen atom, the spin can be either 'up' or 'down', leading to various combinations when considering neighboring atoms. The total number of spin states is crucial for understanding the resulting magnetic interactions in NMR spectroscopy.

Nuclear Magnetic Resonance (NMR) Spectroscopy

NMR spectroscopy is a technique used to observe the magnetic properties of atomic nuclei. In the context of hydrogen atoms, the presence of neighboring hydrogen atoms influences the splitting of NMR signals, known as spin-spin coupling. The number of neighboring hydrogen atoms determines the multiplicity of the signal, which is observed as peaks in the spectrum.

Multiplicity and Coupling

Multiplicity refers to the number of peaks in an NMR signal, which is determined by the number of neighboring hydrogen atoms plus one (n+1 rule). When a hydrogen atom has four neighboring hydrogens, it results in a quintet, indicating five distinct peaks. This phenomenon occurs due to the coupling interactions between the spins of the hydrogen atoms, leading to a specific pattern in the NMR spectrum.