The absorption of a photon of wavelength 4.67 × 10^-6 m is necessary for a CO molecule to pass from the lowest vibrational energy level to the next highest vibrational level.If this higher vibrational level has an energy of 6.41 × 10^-20 J,what is the energy of the lowest vibrational level?
H = 6.626 × 10^-34 J ∙ s

Question

Quizplus · Accepted Answer

We can use the relationship between energy and wavelength for a photon:
E = hc/λ
where h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. Rearranging this equation gives:
λ = hc/E
We can use this equation to find the energy of the photon that is absorbed:
E_photon = hc/λ = (6.626 × 10^-34 J∙s)(2.998 × 10^8 m/s)/(4.67 × 10^-6 m) = 4.02 × 10^-19 J

The energy difference between the two vibrational levels is then given by:
ΔE = E_higher - E_lower = 6.41 × 10^-20 J - E_lower
Solving for the energy of the lowest vibrational level gives:
E_lower = 6.41 × 10^-20 J - ΔE
E_lower = 6.41 × 10^-20 J - (4.02 × 10^-19 J)
E_lower = -3.38 × 10^-19 J

Note that the energy is negative because we have defined the zero of energy to be the energy of the lowest vibrational level. This means that it takes energy (in the form of a photon) to move from the lowest vibrational level to a higher vibrational level. Therefore the best choice is B, which is 15 × 10^-20 J in scientific notation.

The Absorption of a Photon of Wavelength 4