Intrinsic spectral line widths and the uncertainty principle
Here's a question for you. According to the bohr model of the atom, the energy difference between two levels is quantized i.e it is an integer. Therefore, an absorption or emission quanta related to these two levels should have a unique energy/frequency value i.e in an intensity vs frequency profile, the emission or absorption line should be a perfect dirac delta function. But it is a known fact that spectral lines, em/abs, have a finite width. The profile is not a delta function but a lorentzian. How come?
The answer lies in the uncertainty principle. The uncertainty people, as most know it, is a relation between the uncertainty in position against the uncertainty in momentum of a species. It can also be written as the uncertainty in energy against the uncertainty in time of the species. As defined on Wiki, natural broadening occurs from the fact that excited species have a specific lifetime and the larger the uncertainty in this lifetime is, the smaller the uncertainty in energy of the transition and vice versa.
Someone had asked me this question a long time back. There are a couple of other reasons for why spectral lines are broadened such as collisional or pressure broadening and Doppler broadening. I got to know of this intrinsic line width roughly an year ago and am still amazed at the concept! I thought I'd share it with you because it has been recurring in my courses over the last couple of days...
The answer lies in the uncertainty principle. The uncertainty people, as most know it, is a relation between the uncertainty in position against the uncertainty in momentum of a species. It can also be written as the uncertainty in energy against the uncertainty in time of the species. As defined on Wiki, natural broadening occurs from the fact that excited species have a specific lifetime and the larger the uncertainty in this lifetime is, the smaller the uncertainty in energy of the transition and vice versa.
Someone had asked me this question a long time back. There are a couple of other reasons for why spectral lines are broadened such as collisional or pressure broadening and Doppler broadening. I got to know of this intrinsic line width roughly an year ago and am still amazed at the concept! I thought I'd share it with you because it has been recurring in my courses over the last couple of days...