Chapter 7 Line Width Line Width (natural) Oscillator strength
Broadening Some atomic emission lines are narrow and some are broad. Why? 1: Natural Line Width Conclusions The energy levels shown are infinitely sharp.
In reality, however, the energy levels will have finite width. Even with optical instruments (spectrograph/ grating monochromator) of very high resolving power, the observed line radiation is not strictly monochromatic. 4)Exhibit a variationof intensity with frequency over a relatively narrow frequency interval. 5) Intensity of radiation variation with frequency (or line shape) is discussed in the context of emission. Example: Intensity frequency Note: Assumed that the lower state is a stable state and has infinite lifetime. Case 1: Lower state is not Stable 2: Broadening of Natural Linewidth Oscillator Strength Selection Rules 1. Parity Rule 2. Orbital Angular Momentum- Selection Rule 4. Total Angular Momentum Selection Rule
3. Spin Selection Rule Transitions between two states j and i are allowed with no change in spin i.e. S = 0. 4. Total Angular Momentum Selection Rule The change in total angular momentum can be J = 0, 1 for Allowed Transitions. But Jj of j = 0 Ji = 0 of i transitions are not allowed. Hydrogen atom emission spectrum 2. Broadening of Emission Lines For example: In Gases: uradiation = 3.32 x 107 s-1 for He i.e. = 30.1 ns (life time) No. of collisions per second (which depends on the gas pressure) = 7.5 x 106 s-1 for 1 Torr u = urad + ucollision = 3.32 x x 106 s-1 for 1 Torr In solution: Thermal velocities = ( 102 103) m/s
Distance between excited molecule and the solvent molecule ~ m So collision time = (10-10 m) / (102 103 m/s) s In solids: The collision are with phonons.
Decay rate depends on how well the excited Electrons are protected from the solvent. For example d and f electrons are located inside and protected by s and p electrons. For Ti-sapphire crystal : urad ~3.7 x 10-6 s at T = 20 150 K , urad ~ 3.0 x 10-6 s at T = 273 K Decreasing then rapidly for higher temperature. Types of collisional effects:
Collisons that knock the electron down from excited state. This shortens the actual dwell time in the excited state (excited state life time is reduced). Processes that broadens the spectrum but do not shorten the lifetime. Broadening of Emission line
Dephasing collisions Amorphous crystal broadening Doppler broadening Isotope broadening. is a homogeneous broadening, and (b) (d) are inhomogeneous broadening. Homogeneous broadening is Lorentzian (shape of emission line). Inhomogeneous broadening is Gaussian (shape of emission line). Nonradiative Collision Decay:
This is called T1 Broadening. (a) Dephasing Collisions
A coherence is the sum over all the atoms in the medium. The collisions "dephase" the emission, causing cancellation of the total emitted light, typically exponentially. Why do coherences decay? Amplitude of individual dipoles unaffected by dephasing collisions, amplitude of total emitted light decreases. Consider three oscillators in phase at time t0. This is called T2 broadening. (b) Amorphous Crystal Broadening (c ) Doppler Broadening
Doppler broadening is due to the distribution of atomic velocities (speed and direction), which each have a Doppler shift with respect to an observer. Top: Narrow emissions lines for a gas at "rest" (low temperature means low particle speeds)
Bottom: Emissions lines become broader as gas temperature rises and motions increase.