- #1
gboff21
- 50
- 0
Homework Statement
In the 2p state of lithium, two fine structure components are formed due to spin-orbit interaction. They produce wavelengths of 670.960nm and 670.975nm. Compare Doppler and natural broadening at 700K. The lifetime of the 2p state is 27ns and [itex]\frac{\Delta \lambda}{\lambda} ~= \frac{\Delta \nu}{\nu} [/itex] at [itex]\frac{\Delta \nu}{\nu} << 1[/itex]
Homework Equations
Given Doppler broadening: [itex]\Delta \nu = \frac{2 \nu_{0}}{c}\sqrt{\frac{2KT}{M}*ln(2)}[/itex]
The Attempt at a Solution
My Natural broadening derivation:
uncertainty principle: [itex]\Delta E \tau = \hbar[/itex] (tau is lifetime)
so [itex]\Delta \lambda = 2 \pi c \tau[/itex] (which comes out as ~50m)
This is clearly wrong since the doppler broadening comes out as in the order of 10^-12.
Any clues?