Draw the expected signal for a hydrogen with the following coupling constants.
(a) Hₐ : δ 5.34 (Jₐ꜀ = 12 , Jₐ₆ = 2)

Verified step by step guidance

1. Identify the type of hydrogen environment: The hydrogen Hₐ is located at δ 5.34 ppm, which suggests it is in an alkene or aromatic environment.
2. Understand the coupling constants: Jₐ꜀ = 12 Hz indicates a trans coupling, typical for alkenes, while Jₐ₆ = 2 Hz suggests a long-range or allylic coupling.
3. Determine the splitting pattern: The hydrogen Hₐ will be split into a doublet of doublets due to the two different coupling constants.
4. Draw the signal: Start by drawing a doublet with a splitting of 12 Hz, then split each of these peaks further into doublets with a splitting of 2 Hz.
5. Label the peaks: Ensure that the peaks are labeled with the correct coupling constants, showing the larger splitting (12 Hz) and the smaller splitting (2 Hz).

Key Concepts

Chemical Shift (δ)

Chemical shift (δ) is a measure of the resonance frequency of a nucleus relative to a standard in a magnetic field. It is expressed in parts per million (ppm) and provides information about the electronic environment surrounding the nucleus. In this question, δ 5.34 indicates the position of the hydrogen signal on the NMR spectrum.

Coupling Constant (J)

The coupling constant (J) is a parameter that quantifies the interaction between nuclear spins in NMR spectroscopy, resulting in signal splitting. It is measured in Hertz (Hz) and reflects the strength of spin-spin coupling. Jₐ꜀ = 12 Hz and Jₐ₆ = 2 Hz indicate the splitting pattern of the hydrogen signal due to interactions with neighboring nuclei.

Signal Multiplicity

Signal multiplicity refers to the number of peaks observed in an NMR signal due to spin-spin coupling. It is determined by the number of neighboring hydrogen atoms and their coupling constants. In this question, the hydrogen signal will be split into a pattern based on the given coupling constants, indicating the presence of adjacent hydrogen atoms.