Interaction of Light with Matter: Fluorescence, Phosphorescence, and Molecule Dynamics

Physics 203/204 10 Interaction of Light with Matter • Fluorescence and Phosphorescence • Lasers • Diatomic Molecules • Rotational and Vibrational Motion of a Molecule • Molecular Spectra

Fluorescence and Phosphorescence • Fluorescence • Light emission ends instantly incident radiation does • Phosphorescence • Light emission continues after incident radiation is shut off • LIFETIME of excited state short • FLUORESCENCE • LIFETIME of excited state long • PHOSPHORESCENCE

h  Spontaneous Emission

Emitted frequency does not have to equal incident frequency • Must be less than or equal to incident frequency • Incidentbluelight can produceredlight • Incidentredlight CANNOT producebluelight

h

h  h  h  h  STIMULATED EMISSION

Emitted light is • In phase • Going in same direction • More intense • same frequency • with incident light • Thus we get intense MONOCHROMATIC • light emitted

Need long lived excited state • in order to have high probability • of Stimulated emission • META STABLE STATE • If all light produced by stimulated emission • is made to travel in same direction • and not diverge (Attenuate) • We would have a strong beam of parallel intense monochromatic light

L ight • A mplified by • S timulated • E mission of • R adiation

Metastable State E2 He-Ne collisions h  E2-E1 E1 Laser light 632.8 nm Pumping Electric discharge rapid decay ground state E0 Neon States Helium States

Diatomic Molecules ( ) Y r , r , r K 1 2 n l m m n l m m N L 1 1 l s N N l s 1 1 N N = Antisymmetric combination of the products ( ) ( ) ( ) F r F r F r L 1 2 n l m m n l m m n l m m N 1 1 l s 2 2 l s N N l s 1 1 2 2 N N

Motion of an object can be analyzed into three types • translation of the center of mass • rotation (rigid) about the center of mass • vibration (elastic) about center of mass

The rotational energy of a molecule is given by 1 1 1 2 ( ) 2 2 E = I w = I w = L rot cm cm cm 2 2 I 2 I cm cm æ m m ö ç 1 2 ÷ 2 2 I = r = m r cm è m + m ø 1 2 m º reduced mass , r = inter atomic distance The angular momentum of the molecule is quantized L = J ( J + 1 ) ; J = 0 , 1 , 2 , 3 , h K cm 2 h Þ E = J ( J + 1 ) ; J = 0 , 1 , 2 , 3 , K rot 2 I cm The frequency differences between these levels lie in the microwave frequency range

Near the equilibrium bond length, the bonding force between the nuclei can be approximated by a spring force and a diatomic molecule simulates a simple harmonic oscillator of frequency 1 k f = ; k º spring constant 2 p m motion of reduced mass about spring whose é ù ê ú equilibrium length is the equilibrium bond ê ú length ë û 1 æ ö E Þ v + h n ; v = 0 , 1 , 2 , K è ø vib 2 The frequency differences between these levels lie in the infrared range

Molecular spectra will have both vibrational and rotational levels . The spacing between rotational levels is much smaller. Hence for each electronic level there will be a set of vibrational levels superimposed and for vibrational levels there will be a set of rotational levels superimposed . The total energy for a fixed electronic standing wave pattern labeled by " n " is the sum of the energies due to vibrational and rotational modes 2 æ 1 h ö [ ] ( ) E = E + 2 J J + 1 + v + h n ; J = 0 , 1 , 2 , ; v = 0 , 1 , 2 , K K è ø nvJ n 2 I 2

E020 E010 E001 E120 E110 E101 Molecules will absorb or emit photons that have frequencies equal to the DIFFERENCE of natural frequencies E100 E000

Interaction of Light with Matter: Fluorescence, Phosphorescence, and Molecule Dynamics