Covalent bonds in a molecule absorb radiation in the IR region and vibrate at characteristic frequencies.

(a) The C-O bond absorbs radiation of wavelength 9.6 μm. What frequency (in s⁻¹) corresponds to that wavelength?

(b) The H-Cl bond has a frequency of vibration of 8.652 x 10¹³ Hz. What wavelength (in μm) corresponds to that frequency?

(a) ν = 3.1 * 10¹³ s⁻¹

(b) λ = 3.467 μm

Explanation:

We can solve both problems using the following expression.

c = λ * ν

where,

c: speed of light

λ: wavelength

ν: frequency

(a)

c = λ * ν

ν = c / λ

ν = (3.000 * 10⁸ m/s) / (9.6 * 10⁻⁶ m)

ν = 3.1 * 10¹³ s⁻¹

(b)

c = λ * ν

λ = c / ν

λ = (3.000 * 10⁸ m/s) / (8.652 * 10¹³ s⁻¹)

λ = 3.467 * 10⁻⁶ m

λ = 3.467 * 10⁻⁶ m (10⁶ μm / 1 m)

λ = 3.467 μm