Introduction to High Resolution Spectroscopy

 Introduction Rotational Vibrational Miscellaneous

Units Commonly Used In Spectroscopy

Spectroscopy is concerned with the measurement of the energy difference between the energy levels of a molecule. A molecule can increase its rotational, vibrational or electronic energy by absorbing light or emitting light.

Microwaves excite molecular rotations, infrared light excites molecular vibrations and visible/ultraviolet light excites electrons. Microwaves, infrared, visible and ultraviolet light all form part of the electromagnetic spectrum:
• they act like waves and all travel at the speed of light, c = 2.99 x 108 m s-1,
• the number of waves arriving each second is the frequency, ν (Greek letter 'nu') measured in Hertz (s-1)
• they have wavelength λ (Greek letter 'landa'), measured in metres or, more conveniently nanometres (1 nm = 1 x 109 m)

The speed, wavelength and frequency of light are linked:

 (1) or (2)

The light absorbed or emitted by a molecule is often reported either in Hertz (frequency) or in nanometres (wavelength).

Planck's equation relates the frequency of light to its energy (in Joules):

 (3)

where h = 6.634 x10-34 Js.

The frequency is proportional to the energy difference between the energy levels of the molecule. The energy difference is just the frequency multiplied by Planck's constant h. For this reason, spectroscopists often refer to the frequency as a unit of energy.

Combining equations (3) and (2) gives the energy in terms of the wavelength:

 (4)

The wavelength is inversely proportional to the energy difference. Alternatively, the energy difference is proportional to 1/λ. An alternative unit to the frequency is the 'wavenumber', 1/λ. It is usually more convenient to use cm-1 instead of m-1.

Converting between different spectroscopic units

The calculator below converts between the common (and some of the less commonly) used units in spectroscopy. Enter a value to be converted and choose its units from the list. Press 'convert' to convert the number into the available units.

To enter a large or small number using scientific notation - for example, enter 1.9e2-27 for 1.9x10-27 and 6.03e23 for 6.03x1023.

# Convert from Wavelength (nm) Wavenumber (1/cm) Frequency (Hz) Electronvolt Per Molecule Atomic Unit Per Molecule Joules Per Mole with significant figures

As spectroscopic frequencies, wavelengths and energies are often very large or small, it is common to employ prefixes to make the numbers more manageable. The table below lists the most commonly used prefixes in spectroscopy.

For example,
• 0.0000000512 m = 5 x 10-9 m = 5.12 nm
• 299792458 m s -1 = 2.99792458 x 108 m s-1 = 0.299792458 Gm s-1

# Prefixes

fraction prefixsymbol   fraction prefixsymbol
10-1 decid  10deca da
10-2 centic  102 hectoh
10-3 millim  103 kilok
10-6 microm   106 megaM
10-9 nanon  109 gigaG
10-12 picop   1012 teraT
10-15 femtof   1015 petaP
10-18 attoa   1018 exaE
10-21 zeptoz   1021 zettaZ
10-24 yoctoy   1024 yottaY

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