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.)

f =
Your response differs from the correct answer by more than 100%. Hz ? = 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?3

Explanation / Answer

we have f=?/2?=1/2?*?(k/m)=5.16*1013 Hz wavelength: ?=c/f=5.8 ?m YES this wavelength lie in the infrared region ofthe spectrum    we have f=?/2?=1/2?*?(k/m)=5.16*1013 Hz wavelength: ?=c/f=5.8 ?m YES this wavelength lie in the infrared region ofthe spectrum    YES this wavelength lie in the infrared region ofthe spectrum   

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