Infrared spectra are used by chemists to help identify an unknown substance. Ato
ID: 1356164 • 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 2800 N/m. If we assume that the carbon atom remains stationary (it is attached to other atoms in the molecule), determine the resonant frequency of this bond and the wavelength of light that matches that frequency. (The mass of an oxygen atom is 2.66 10-26 kg.)
f = ________ Hz
= ________ µm
Explanation / Answer
The period T of the vibration is given by the standard equation
T = 2 * (m / k)
Substituting m and k
T = 2 * (2.66 10-26 / 2800)
T = 1.9366 * 10-14 seconds
Now, for frequency we can use f = 1 / T
=> f = 1 / (1.9366 * 10-14 ) = 5.16367 * 1013 Hz
Therefore, f = 5.16367 * 1013 Hz
Now, we can use c = f * to find (where c is the speed of light)
= c / f = 3.00×108 / 5.16367 * 1013 = 5.8098 * 10-6 meters
Therefore, = 5.8098 * 10-6 meters or 5.8098 micro meters