# Absorption and Emission of Light

Stimulated Absorption & Emission, Spontaneous Emission

E2

Incident radiation hν hν Emitted & transmitted radiation

E1

Resonance condition E2-E1=hν

• Rate of stimulated emission is: −dN1/dt = N1B1->2 ρ(ν) • Rate of absorption is the sum of the rated due to stimulated emission and spontaneous emission: −dN2/dt = N2B2->1 ρ(ν) + N2A2->1 where B1->2 is the Einstein transition probability for induced absorption, B2->1 is the Einstein transition probability for induced emission, A2->1 is the Einstein transition probability for spontaneous emission ρ(ν) is the radiation density at frequency ν, N1 and N2 are the populations in states 1 & 2.

• At equilibrium (steady state), we have: N2{A2->1 + B2->1 ρ(ν)} = N1B1->2 ρ(ν)

Maxwell-Boltzmann distribution, Population Inversion & Saturation E2

Incident radiation hν hν Emitted & transmitted radiation

E1

• If subjected to very intense radiation for a long time, the populations of the lower and upper states equalize. • This is called saturation; there is no more net absorption of radiation. • Saturation corresponds to “infinite temperature” since

N2/N1 = e-(E2-E1)/kT

• A short pulse of very intense radiation can even produce a population inversion, where N2>N1

Fluorescence & Phosphorescence

: a “forbidden” slow process (possible only because of spin-orbit coupling)

: milliseconds to hours : picoseconds to milliseconds

Molecular Orbital Diagrams for CO

Particle-in-a-box model for conjugated molecules

Ethylene

Butadiene

Octatetraene

• Energy levels for a particle in a (1-D) box: En α n2/mL2 – where n is the quantum number, – m is the mass of the particle, – and L is the length of the box.

• The energy spacings between levels (and thus absorption frequencies) are also inversely proportional to L2: hν = En-En’ α (n2-n’2)/mL2

n→π* and π→π* transitions

• Ultraviolet and visible radiation interacts with matter which causes electronic...

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