How to convert
cm^{1} to microns or nanometers
Basics
Spectroscopists of the chemistry
variety have found that inverse cm is a wonderful way to measure light. It is
proportional to the wavenumber and the frequency (and therefore energy), but it
makes those of us that are trained in rational units pull our hair out. And
then if you get into a discussion with semiconductor experts, they want you to
talk in electronvolts (eV).
IF you are
talking about ABSOLUTE wavelength (i.e. the wavelength of CO_{2} laser
is 10.6 microns) then the conversion goes as follows:
Wavelength in µm = 10,000/cm^{1} So
the wavelength of light having a wavenumber 300 cm^{1} => 33
microns
10,000/300 = 33 µm
Wavelength in nm =
10,000,000/cm^{1}
so the
wavelength of light having a wavenumber of 4000
cm^{1} => 2500
nm 10,000,000/4000 = 2500 nm
How to convert microns
or nm to cm^{1}(inverse cm)
Wavenumbers in
cm^{1}=
10,000/µm So the wavelength of CO_{2} lasers of 10.6
microns => 943 cm^{1}
10,000/10.6 = 943 cm^{1}
Wavenumbers in
cm^{1}=
10,000,000/nm So 632.8 nm => 15800
cm^{1}
How to convert
absolute cm^{1} to electron volts or eV We
mentioned before that inverse cm are proportional to the photon energy. The
energy of a photon is hc/lambda , so if you are working in eV and nm
eV = 1.23984 x 10^{3}/nm
So the photon energy in eV =
1.23984 x 10^{4}* cm^{1} So 632.8 nm HeNe laser photons
have an energy of 15800 wavenumbers or 1.96 eV 1.2394 x 10^{3}/
632.8 = 1.96 eV
In other words, the proportionality constant is Plank's
constant times the speed of lighthc in units of eV/cm
How to convert
absolute cm^{1} to Joules Since one eV is 1.602 x
10^{19} Joules, use the above formula and multiply by that
factor
Joules = 1.986 x 10^{23}/nm You may recognize the
number 1.602 x 10^{19} as the charge of an electron in Coulombs.
How to convert delta
microns or nanometers to delta cm^{1}(inverse cm)
Of course
this is where it gets tricky, because the result depends on the absolute
wavenumber, in other words a bandwidth of 10 cm^{1} is 1000 microns at
one wavelength, but 0.1 microns at another. If you have a peak width of inverse
centimeters converting to a peak width of microns could be painful. But taking
the derivative of the above equations you can get the formula
d( Wavelength in µm) = (10,000 *
d(cm^{1})/(cm^{1})^{2})
The notation is a little awkward, sorry. What this means
is that you take the peak width [d(cm^{1})], divide it by the square
of the absolute wavenumber of the center of the peak [(cm^{1})] and
multiply it by 10,000 to get the peak width in µm. So a peak that
is centered at 943 cm^{1} and is 12 cm^{1} wide would be also
a peak centered at 10.6 microns and 0.13 microns wide.
d( Wavelength in nm) = (10,000,000 *
d(cm^{1})/(cm^{1})^{2}) So
a peak that is centered at 20492 cm1 with a line width of 10 cm1 would also
be a peak centered at 488 nm with a linewidth of 2.4 · 10^{8}
nm.
How to convert delta
cm^{1} to delta micrometers or delta nanometers
d (Wavenumber in cm^{1}) =
(10,000 * d(µm)/(µm)^{2}) Or
a peak that has wavelength of 33 microns and is 0.2 microns wide would be
centered at 303 cm^{1} and be 1.84 cm^{1} wide
d( Wavenumber in cm^{1}) =
(10,000,000 * d(nm)/(nm)^{2})
or a peak that has a wavelength of 1.06 nm
and a linewidth of .01 nm would be centered at 9433962 cm^{1} with a
line width of 89000 cm^{1}
How to convert delta
cm^{1} to delta electronvolts or eV Since eV is
proportional to cm^{1} this is easy
d(eV) = d(cm^{1})
* 1.23984 x 10^{4}
So a bandwidth of 10 cm^{1} would
be a bandwidth of 1.24 meV
