How Do You Calculate Spectral Line Width?

[r-dizzel]

anyone know how to find the spectral line width given the wavelength of the ejected photon, the energy values for the atom (usual hydrogen e values) and the lifetime in the excited state.

any help much appriciated!#


cheers all

rob

 

[lalbatros]

see Heisenberg for that

 

[denian]

The spectral line width is a measure of the range of frequencies present in a spectral line. It is affected by a number of factors, including the energy levels of the atom, the lifetime of the excited state, and the Doppler effect due to the motion of the atom.

To find the spectral line width, you can use the formula:

Δν = (1/λ) * (ΔE/h)

where Δν is the spectral line width, λ is the wavelength of the ejected photon, ΔE is the difference in energy levels of the atom, and h is Planck's constant.

You can obtain the ΔE value from the energy levels of the atom, which can be found in tables for different elements. For hydrogen, you can use the Rydberg formula to calculate the energy levels.

The lifetime of the excited state can also be found in tables or can be measured experimentally. It is important to note that the shorter the lifetime, the broader the spectral line width will be.

In addition, the Doppler effect can also contribute to the spectral line width. This is due to the motion of the atom, which can cause a shift in the frequency of the emitted photon. This can be taken into account by adding the Doppler broadening term to the formula:

Δν = (1/λ) * (ΔE/h) + (ν/c) * (v/c)

where ν is the frequency of the emitted photon, c is the speed of light, and v is the velocity of the atom.

I hope this helps in your calculations. It is always important to consider all the factors that can contribute to the spectral line width in order to accurately measure it.