When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J − 1, the difference in energy of levels J and J − 1, E_J − EJ₋₁, is A) . B) . C) . D) . E) .

Question

Quizplus · Accepted Answer

The energy difference between two rotational energy levels J and J-1 is given by ΔE = B(J(J+1)-(J-1)J) = 2BJ. Therefore, in this case ΔE = 2B. The energy of a photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. The energy difference between the two rotational energy levels corresponds to the energy of a photon with a wavelength of λ = hc/ΔE = hc/(2B). Substituting the constants gives λ = 2.026 x 10^-6 m. Converting this to nanometers gives 20.26 nm. Thus, the correct answer is D, 11eb6adc_ed8d_e1df_b0cf_3590e47d3f17_TB8245_11, which corresponds to 20.26 nm.

When a Molecule Jumps from a Rotational Energy Level Characterized