Question

Calculate the \( \lambda_{\text{max}} \) of the following molecule:

• A. 283 nm
• B. 273 nm
• C. 234 nm
• D. 244 nm

Hint:

- Conjugated systems generally result in longer wavelength absorption maxima (higher \(\lambda _\text{max}\) values). - The larger the conjugation, the lower the energy required for electron transitions, resulting in higher \( \lambda_{\text{max}} \) values.

Answer 1

The Correct Option is B

The \( \lambda_{\text{max}} \), or the maximum absorption wavelength, is an important characteristic of a molecule and is typically determined by its conjugated system, i.e., the extent of \(\pi-electron \) delocalization. The molecule shown in the question contains a benzene ring fused with another six-membered ring, forming a bicyclic structure. In general, the \(\lambda _\text{max}\) of such molecules can be predicted based on their conjugation. The molecule in question has an extended conjugated system, and based on similar structures and their known absorption maxima, we expect the \(\lambda _\text{max}\) for this molecule to be around 273 nm. The given options indicate that 273 nm is the correct maximum absorption wavelength. 

Why Other Options Are Incorrect: - (A) 283 nm: This value is higher than the expected absorption wavelength for this molecule with the given conjugation. 
- (C) 234 nm: This is a typical absorption wavelength for smaller, less conjugated molecules but not appropriate for the given molecule. 
- (D) 244 nm: This is also too low given the structure and expected conjugation. 
Thus, the correct value for \( \lambda_{\text{max}} \) is 273 nm, corresponding to option (B).

Answer 2

The question asks us to calculate the \( \lambda_{\text{max}} \) of the given conjugated diene using the Woodward-Fieser rules. These rules build the predicted wavelength from a base chromophore value plus fixed increments for each additional feature attached to it, so let's check what each answer choice would imply.

1. 283 nm: Reaching 283 nm from a homoannular diene base of \( 253 \) nm needs an extra \( 30 \) nm of substituent contribution, which would mean six ring-residue or alkyl substituents at \( 5 \) nm each. That is more substituents than the structure actually carries, so this value overshoots.
2. 273 nm: Starting from the homoannular diene base value of \( 253 \) nm and adding \( 5 \) nm for each of the four ring-residue substituents attached to the diene system gives \( 253 + (4 \times 5) = 253 + 20 = 273 \) nm, which matches the number of substituents actually present on this molecule.
3. 234 nm: This figure sits below even the plain base value most quoted for a simple heteroannular diene ( \( 214 \) nm) once one or two increments are added, and it does not correspond to a consistent increment count for this structure; it undershoots what the substitution pattern here would give.
4. 244 nm: Building up to \( 244 \) nm from the homoannular base of \( 253 \) nm is not possible since increments are always added, never subtracted, so this number cannot be produced by the Woodward-Fieser addition scheme for this chromophore at all.

Only adding four ring-residue increments of \( 5 \) nm to the \( 253 \) nm homoannular diene base reproduces a value consistent with the substitution seen on the molecule, giving \( 273 \) nm.

Therefore, the correct answer is 273 nm.