Question

Chemists use infrared absorption spectra to identify chemicals in a sample. In one sample, a chemist finds that light of wavelength 5.9 μm is absorbed when a molecule makes a transition from its ground harmonic oscillator level to its first excited level. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Vibration in a crystal. Find the energy of this transition. Express your answer in electron volts.

Answer 1

The energy of the transition can be found using the equation:

E = hc/λ

where:

h = Planck's constant = 6.626 x 10^-34 J s

c = speed of light = 2.998 x 10^8 m/s

λ = wavelength of light absorbed = 5.9 μm = 5.9 x 10^-6 m

First, we need to convert the wavelength from meters to centimeters:

λ = 5.9 x 10^-6 m = 5.9 x 10^-4 cm

Now we can substitute into the equation:

E = (6.626 x 10^-34 J s) x (2.998 x 10^8 m/s) / (5.9 x 10^-4 cm)

E = 3.37 x 10^-20 J

To convert from joules to electron volts (eV), we divide by the elementary charge (e):

1 eV = 1.602 x 10^-19 J/e

E = (3.37 x 10^-20 J) / (1.602 x 10^-19 J/eV)

E = 0.21 eV

Therefore, the energy of the transition is 0.21 eV.