Infrared spectra are used by chemists to help identify an unknown substance. Ato

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.)

Does this wavelength lie in the infrared region of the spectrum?

Yes No

Explanation / Answer

Hi,

In this case we should use the following equation:

f = (1/2) (k/u) 1/2 ; where k is the effective spring constant, f is the resonant frequency and u is the reduced mass.

As we are considering that the carbon atom is static, then the reduced mass is equal to the mass of the other atom that forms the molecular bond (the oxygen, in this case)

So:

f = (1/2) (2800 N/m / 2.66*10-26 kg)1/2 = 5.16*1013 Hz

Besides, we know that the relation between the wavelength and the frequency for an eletromagnetic wave is:

c = f* ; where c is the light speed (c = 3*108 m/s)

So, the wavelenght that matches the resonant frequency is:

= (3*108 m/s) / (5.16*1013 Hz) = 5.81*10-6 m = 5.81 µm

The infrared spectrum goes from 800 nm to 1000 µm, therefore, this wavelength lies in the infrared region.

I hope it helps.

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