Optical Spectroscopy

What does sign nu (ν) represent?

Frequency

What does sign nu tilde (ṽ) represent?

Wavenumber

An ideal emitter

At all freq.s emits the same amount of or more radiation than any other body at the same temperature.

A diffuse emitter

Emits the same amount of radiation in all directions.

A blackbody emitter is

Ideal and diffuse

Stopping voltage is

a property of the metal

Planck-Einstein Relation

E=hv(nu)

de Broglie wavelength equation

λ = h/mv(nu)

de Broglie wavelength represents

the length scale at which its wave-like properties are important

Microwave radiation causes

rotational spectroscopy

Infra-red radiation causes

vibrational spectroscopy

Spectroscopy definition

the study of the interaction of EM radiation with matter

Peak intensity is determined by

Population, transition probability, state degeneracy, path length of sample

Heisenberg uncertainty equation

ΔEΔt >=h/2π, t is time spent in excited state

Natural linewidth is

the limit to how narrow spectral lines can be.

In order for an atom or molecule to absorb/emit a photon at a specific frequency,

it must possess a dipole oscillating at that frequency.

Beer-Lambert Law

A = εLc

A =

log(I0/I), I=intensity

ln(I0/I) =

σLc = αL, σ=absorption cross-section, α=absorption coefficient

T (transmittance)=

I/I0

z (collisional frequency) =

σv(rel)p/kT

v(rel) =

(8kT/πμ)^0.5

collisional/pressure broadening

z/2π

Lifetime of the excited state

τ_sp

A_1←0 =

1/τ_sp

lifetime broadening

broadening (Δṽ) = A_1←0/2πc

doppler broadening

Δṽ = 2ṽ/c * (2kbTln2/m)^0.5

For rotational spectroscopy to be possible,

energy level of electrons must change by 1

B (rotational constant (cm^-1)) =

ћ/4πcI

ћ =

h/2π

I (inertia)=

μr², r=bond length

F_J (energy of state J) =

BJ(J+1)

transition between energy levels (ṽ(J+1←J)) =

2B(J+1)

The bit we observe is

the transition between energy levels

J’’ is the

initial energy level

J’ is the

final energy level

How does population affect line intensity?

If there is no population in a state, no transitions from that state will be seen

Boltzmann expression:

N_J/N = g_Je^(-E_J/kT)

g_J (degeneracy of level J) =

2J + 1

E_J (energy level in joules)=

hc * BJ(J+1) (hc to convert cm^-1 to J)

J_max (J value with highest intensity peak) =

(kT/2hcB)^0.5 - 0.5

correctional factor for centrifugal distortion:

D_JJ²(J+1)²

D_J =

4B³/ṽ² (this means higher bond strength = lower centrifugal distortion)

ΔF_J(J+1←J) =

2B(J+1) - 4D_J(J+1)³

difference between requirement for rotational and vibrational spectroscopy

Rotational requires permanent dipole moment, vibrational can have permanent or induced dipole moment.