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.
