Spectral Transitions

The width of spectral lines is a function of:

1. Collision Broadening: Atoms are in continual motion and frequent collisions perturb the energies of outer electrons, resulting in broadening of width of UV and visible spectral lines.
2. Doppler Broadening: Motion of particles causes Doppler shift; motion is random ==> shift in both high and low frequencies.
3. Heisenberg's Uncertainty Principle: absolutely unavoidable! If a state has lifetime $\delta t$ then its energy is uncertain to an extent $\delta E$ given by
(1)
\begin{align} \delta E \times \delta t \geq \hbar \end{align}

The intensity of spectral lines is a function of:

1. Transition Probability (gives rise to selection rules)

2. Population of States: Boltzmann distribution ==> at thermal equilibirum,

(2)
\begin{align} \frac{N_{2}}{N_{1}} = \frac{g_{2}}{g_{1}}\frac{e^{-E_{2}/kT}}{e^{-E_{1}/kT}} \end{align}

Here, $g_{i}$ is the degeneracy of state $E_{i}$.

3. Path Length of sample: The Beer Lambert law relates the intensities of incident and transmitted radiation by

(3)
\begin{align} \frac{I}{I_{0}} = e^{-\kappa c l} \end{align}

where $\kappa$ is a constant for the transition being studied. This is consistent with the exponential drop in intensity as successive samples of the substance are placed in the path of the radiation.

page revision: 0, last edited: 16 Oct 2007 08:35