Final answer:
To calculate the frequencies and wavelengths of infrared light given wavenumbers, use the formulas: frequency (s^(-1)) = wavenumber (cm^(-1)) * speed of light and wavelength (micrometers) = speed of light / frequency. For (a) 2200 cm^(-1), the frequency is 6.6 x 10^(13) s^(-1) and the wavelength is 4.5 x 10^(-4) micrometers. For (b) 3000 cm^(-1), the frequency is 9 x 10^(13) s^(-1) and the wavelength is 3.3 x 10^(-4) micrometers.
Step-by-step explanation:
Wavenumbers are used in spectroscopy to describe the frequency and wavelength of electromagnetic waves. Infrared light falls within the range of 200 - 5,000 cm^(-1). To convert a wavenumber to frequency, use the formula: frequency (s^(-1)) = wavenumber (cm^(-1)) * speed of light (3 x 10^(10) cm/s). To convert frequency to wavelength, use the formula: wavelength (micrometers) = speed of light (3 x 10^(10) cm/s) / frequency (s^(-1)).
By applying these formulas to the given wavenumbers:
(a) 2200 cm^(-1):
Frequency = 2200 cm^(-1) * 3 x 10^(10) cm/s = 6.6 x 10^(13) s^(-1)
Wavelength = 3 x 10^(10) cm/s / 6.6 x 10^(13) s^(-1) = 4.5 x 10^(-4) micrometers
(b) 3000 cm^(-1):
Frequency = 3000 cm^(-1) * 3 x 10^(10) cm/s = 9 x 10^(13) s^(-1)
Wavelength = 3 x 10^(10) cm/s / 9 x 10^(13) s^(-1) = 3.3 x 10^(-4) micrometers