Question

Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then:

• A. \(λ_3 > λ_2, λ_1 = 2λ_2 \)
• B. \(λ_3 > λ_2, λ_1 = 4λ_2 \)
• C. \(λ_1 > λ_2, λ_2 = 2λ_3\)
• D. \(λ_2 > λ_1, λ_2 = 2λ_3\)

Answer 1

The Correct Option is D

The energy \(E\) of a photon is related to its wavelength \(\lambda\) by the equation \(E = \frac{hc}{\lambda}\). This implies an inverse proportionality between wavelength and energy: \(\lambda \propto \frac{1}{E}\).

Based on the diagram:

Wavelength \(\lambda_1\) is associated with an energy difference of \(E\).

Wavelength \(\lambda_2\) is associated with an energy difference of \(\frac{E}{2}\).

Wavelength \(\lambda_3\) is associated with an energy difference of \(\frac{E}{2}\).

Consequently, \(\lambda_2 = 2\lambda_3\) and \(\lambda_2 > \lambda_1\).