Infrared spectra are used by chemists to help identify an unknown substance. Ato
ID: 2075433 • Letter: I
Question
Infrared spectra are used by chemists to help identify an unknown substance. Atoms in a molecule that are bound together by a particular bond vibrate at a predictable frequency, and light at that frequency is absorbed strongly by the atom. In the case of the C=O double bond, for example, the oxygen atom is bound to the carbon by a bond that has an effective spring constant of 2700 N/m. If we assume the carbon atom remains stationary (it is attached to other atoms in the molecule), (a) determine the resonant frequency of this bond. (The mass of an oxygen atom is 2.66x1026 kg.)
(b) the wavelength of light that matches that frequency.
In what region of the electromagnetic wave spectrum does this emission fall?
Explanation / Answer
a) f = 1/ 2 pi * sqrt [ k / m ]
= 1 / 2 pi * sqrt [2700 / 2.66 * 10-26]
resonant frequency = 5.07 * 1013 Hz
b) lambda = c / f
= (3 * 108) / ( 5.07 * 1013)
lambda = 5.92 * 10-6 m = 5.92 mum