The absorption of a photon of wavelength 4.67 Ã 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 Ã 10-20 J, what is the energy of the lowest vibrational level? (h = 6.626 Ã 10-34 J â s; c = 3.00 x 108 m/s) SHOW WORK.
A. 2.15 x 10-20 J
B. 3.20 x 10-20 J
C. 4.26 x 10-20 J
D. 1.60 x 10-20 J

The energy of a photon is the Planck constant (h) multiplied by the velocity of the light (c = 3.00x10⁸ m/s) and divided by the wavelength (4.67x10⁻⁶ m), so:

E = (6.626x10⁻³⁴x3.00x10⁸)/(4.67x10⁻⁶)

E = 4.26x10⁻²⁰ J

This is the initial energy. The energy of the higher vibration level less the energy of the lowest vibration level must be equal to the initial energy of the photon so:

6.41x10⁻²⁰ - El = 4.26x10⁻²⁰

El = 6.41x10⁻²⁰ - 4.26x10⁻²⁰

El = 2.15x10⁻²⁰ J