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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.

Short Answer

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Answer

Step by step solution

01

Wave number

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

wave number=1wave length
02

Subpart (a)

The given wave number of a radiation is .

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

wave length=1wave number=11600 cm-1=6.25×10-4 cm=62500 A°

Hence, the wavelength of the given radiation is62500 A° .

03

Subpart (b)

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

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

wave length=1wave number=13000 cm-1=3.33×10-4 cm=33300 A°

Hence, the wavelength of the given radiation is33300 A°.

04

Subpart (c)

The given wave number of a radiation is 1715 cm-1.

58300 A°

ng formula:

wave length=1wave number=11715 cm-1=5.83×10-4 cm=58300 A°

Hence, the wavelength of the given radiation is58300 A° .

05

 Step 5: Subpart (d)

The given wave number of a radiation is1750 cm-1 .

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

wave length=1wave number=11750 cm-1=5.71×10-4 cm=57100 A°

Hence, the wavelength of the given radiation is57100 A° .

06

Subpart (e)

The given wave number of a radiation is .

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

wave length=1wave number=12200 cm-1=4.54×10-4 cm=45400 A°

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

07

Subpart (f)

The given wave number of a radiation is .

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

wave length=1wave number=13300 cm-1=3.03×10-4 cm=30300 A°

Hence, the wavelength of the given radiation is30300 A° .

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