Convert cm^-1 to eV: Solve with Solution

[Fowler_NottinghamUni]

Apparently In optical spectroscopy it is common to use the unit cm^-1 tro define the energy (or frequency of a photon that is emitted or absorbed in a transition between electronic states of an atom. This is derived from the reciprocal of the wavelength of the photon (wavelength in cm). Determine the conversion factor that converts cm^-1 to eV. I have no idea how to do this in the problem sheet that he gave us the solution to this particular problem means that we can use the result to complete the rest of the problem.

 

[inha]

E=hc/lambda. plug in the constants and see what's the energy of a 1cm wavelength photon. I don't think there's really anything more to it.

 

[R0man]

The conversion factor to convert cm^-1 to eV is 1 cm^-1 = 0.00012398 eV. This can be derived from the relationship between energy and wavelength, where energy is equal to Planck's constant (h) times the speed of light (c) divided by the wavelength. In this case, we can use the fact that the wavelength is in cm and the energy is in eV to determine the conversion factor.

First, we need to convert the wavelength from cm to meters, as the speed of light is typically given in meters per second. This can be done by multiplying the wavelength in cm by 0.01 (since there are 100 cm in 1 meter).

Next, we can rearrange the equation to solve for energy, which gives us energy = (h*c)/wavelength. Plugging in the values for Planck's constant (6.626 x 10^-34 J*s) and the speed of light (3.00 x 10^8 m/s), we get energy = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s)/wavelength.

Since we want the energy in eV, we can divide the energy by the conversion factor for Joules to eV, which is 6.24 x 10^18. This gives us energy = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s)/wavelength * (1 eV/6.24 x 10^18 J). Simplifying this, we get energy = 1.06 x 10^-5/wavelength eV.

Finally, to convert from cm^-1 to eV, we need to take the reciprocal of the wavelength (since cm^-1 is the reciprocal of wavelength in cm). This gives us the conversion factor of 1 cm^-1 = 1/wavelength eV. Plugging in the value for wavelength (in meters), we get 1 cm^-1 = 1/(wavelength in cm * 0.01) eV. Simplifying this, we get 1 cm^-1 = 0.00012398 eV.

Therefore, to convert from cm^-1 to eV, we simply need to multiply the value in cm^-1 by 0.00012398. For example, if we have a value of 500 cm