Question: Convert the following infrared wavenumbers into wavelengths.

(a) 1600 cm^-1, typical for an aromatic

(b) 3000 cm^-1 , typical for a saturated C-H bond

(c) 1715 cm^-1 , typical for a ketone carbonyl

(d) 1750cm^-1 , typical for an ester carbonyl

(e)2200cm^-1 , typical for a nitrile

(f) 3300cm^-1 , typical for an alcohol O-H.

The number of waves that are present in the unit distance is termed a wave number. The wave number and wavelength are related as:

The given wave number of a radiation is .

The wavelength of the radiation can be determined by using the following formula:

$$\begin{gathered} wave length=\frac{1}{wave number} \\ =\frac{1}{1600 c{m}^{-1}} \\ =6.25\times {10}^{-4} cm \\ =62500 A° \end{gathered}$$

Hence, the wavelength of the given radiation is$62500 A°$ .

The given wave number of a radiation is 3000 cm^-1 .

The wavelength of the radiation can be determined by using the following formula:

$$\begin{gathered} wave length=\frac{1}{wave number} \\ =\frac{1}{3000 c{m}^{-1}} \\ =3.33\times {10}^{-4} cm \\ =33300 A° \end{gathered}$$

Hence, the wavelength of the given radiation is$33300 A°$.

The given wave number of a radiation is $1715 c{m}^{-1}$.

ng formula:

$$\begin{gathered} wave length=\frac{1}{wave number} \\ =\frac{1}{1715 c{m}^{-1}} \\ =5.83\times {10}^{-4} cm \\ =58300 A° \end{gathered}$$

Hence, the wavelength of the given radiation is$58300 A°$ .

The given wave number of a radiation is$1750 c{m}^{-1}$ .

The wavelength of the radiation can be determined by using the following formula:

$$\begin{gathered} wave length=\frac{1}{wave number} \\ =\frac{1}{1750 c{m}^{-1}} \\ =5.71\times {10}^{-4} cm \\ =57100 A° \end{gathered}$$

Hence, the wavelength of the given radiation is$57100 A°$ .

The given wave number of a radiation is .

The wavelength of the radiation can be determined by using the following formula:

$$\begin{gathered} wave length=\frac{1}{wave number} \\ =\frac{1}{2200 c{m}^{-1}} \\ =4.54\times {10}^{-4} cm \\ =45400 A° \end{gathered}$$

Hence, the wavelength of the given radiation is $45400 A°$.

The given wave number of a radiation is .

The wavelength of the radiation can be determined by using the following formula:

$$\begin{gathered} wave length=\frac{1}{wave number} \\ =\frac{1}{3300 c{m}^{-1}} \\ =3.03\times {10}^{-4} cm \\ =30300 A° \end{gathered}$$

Hence, the wavelength of the given radiation is$30300 A°$ .