Physical 5

for each electronic transition, the probability is determined by..

the selection rules

what is photochemistry

chem initiated by light

what does photon absorption create

an excited electronic state

when does an electronic transition occur

when a photon is absorbed

what typically induces an electronic transition

UV-Visible light

what range of WLs does UV-vis light cover

200-800 nm

energy of one photon, E =

hν = hc/λ

energy of one mole of photons, E =

Nₐhν

wavenumber =

1/ (λ x 100) converts m to cm

Beer lambert law

A = εcl

excited states are usually created by…

the absorption of light but sometimes by chem rxn

in its ground state, e-s usually occupy..

bonding or non-bonding (lps) MOs

what does photon absorption induce

an electronic transition

what are e- spin props of a state described by

the multiplicity

multiplicity =

2S + 1

S is total spin

born-oppenheimer approx

electronic, vib and rot props are considered to be independent of each other

ψ(total) =

ψ(e) + ψ(v) + ψ(r)

E(total) =

E(e) + E(v) + E(r) - v diff ens so can be considered to be independent

aprox wavenumber of electronic energies

10^4 cm^-1

aprox wavenumber of vib energies

10^3 cm^-1

aprox wavenumber of rotational energies

10^1 cm^-1

rot fine structure can be seen from

gases

vib structure is seen from

gases

liquids and solids

for each electronic transition, the energy of the photon required is determined by…

the energy gap btwn ground and excited states

for an electronic transition, to excite an e- from one orbital to another…

the electric field of light must cause a displacement of charge, giving a transition dipole moment

transition moment =

***∫***Ψ’\* μ(hat) Ψ’’ d**τ**

what can the electronic wavefunction be split into

electron spin, S, and orbital, φ, wavefunctions

what is the spin selection rule

e- has 2 poss spin states: α and β

for the TM (transition moment) to be non-zero, the e- must retain its spin

the orbital part of the transition moment can be sep into components…

along the x, y, z axis

\
TM(orbital) = TM(x) + TM(y) + TM(z)

\
all 3 components must be 0 to be symmetry forbidden

when is the state totally symmetric

if the orbitals contain spin-paired e-s

if some orbitals contain single e-s, what is the symmetry of the state given by

the direct product of the symmetries of these singly occupied orbitals

if the initial and final orbitals of a transition occupy a region of space that is similar, the spatial overlap integral is

large thus spatially allowed → if overlap is better → more likely to move

if the initial and final orbitals of a transition occupy a region of space that is different, the spatial overlap integral is

small thus spatially forbidden

vibrational transitions occur mainly from.. to..

v” = 0 in the S0 state to v’ lvls that give large vib overlap integrals

Frank Condon Principle

e-s move faster than nuclei bc of their relative masses

the probability of the transition is given by the…

oscillator strength, f

the probability of the transition relates to

* the transition dipole moment as f ∝ TM**²**
* to experimental absorption coefficient as f ∝ *∫*εᵥ dv where the integral is the area under the band and ε values are given by Beer-Lambert Law

what does allowed mean

high probability (high ε value)

what does disallowed mean

low probability (low ε value)

when is a spin-flip transition weakly allowed

in the presence of heavy atoms:

* within the molecule (internal)
* within other molecules, e.g. solvent (external)

what is photophysics

the non-reactive decay of excited states

en and longevity of excited states

large excess en and short-lived → lose excess en and return to ground state

what are 2 ways excited states lose excess en

radiative (emission of light in form of a photon)

non-radiative

how does vibrational relaxation work

excess vib en is given to surrounding molecules (e.g. solvent) by collisions (collides & loses en) i.e. vr is a non-radiative process

rate constant for vib relaxation in liquids…

is v high

time scale =

\~ 1/rate constant (k)

what is luminescence

general name for a radiative transition

what is fluorescence

a radiative transition btwn states of the same multiplicity

rate constant for fluorescence

typically high

the spacing between the ndividual peaks (vib fine structure) gives…

the spacing of the vib en lvls in the final state of the transition

the spacings in absorption and emission spectra are slightly diff bc

the vib ens are diff in the S1 and S0 states

phosphoresence from T1 gives

S0

hexagonal close packed structure

layer 3 balls directly on top of layer 1 (a, b, a, b, a, b)

cubic close packed structure

layer 3 balls on top of spaces of layer 1 and 2

band theory: conductors vs insulators

conductors: band gap separates valence band and conduction band

insulators: fermi lvl: no band gap

dipole moment, μ =

magnitude of charges x dist btwn dipoles

% ionic character =

ac dipole moment/max theoretical dipole moment

relationship btwn polarisability and bp

increase polarisability, increase bp

dipole strength is important in influencing bp as long as theres not a massive change in size of molecules (and thus polarisability)

The term polarizability refers to

the tendency of molecules to generate induced electric dipole moments when subjected to an electric field.

why would a molecule be above troutons line

more structure in (l) e.g. H bonds

why would a molecule be below troutons line

more structure in (g) e.g. ethanoic acid exists as dimeric pairs in g phase

mixing and deltaG

deltaG > 0 then no spontaneous mixing

what happens if waves pass through 1 slit? 2 slits?

1: difracts

2: get interference

aufbau principle

orbs filled in order of en, lowest first

when are diffraction effects greatest

when slit encountered is approx same size as WL of wave

wjhy are e—s only specific ens in a particle

bc e- in an atom must be a standing wave (no discontinuities) → must fit circumference of orbital exactly → only certain ens

heisenbergs uncertainty

∆p∆x ≥ h/4π

(or 0.5hbar)

p = momentum

x = position

orbitals for H are

en degenerate (i.e. no diff in en of s and p orbs)→ only works for single e- atoms

orbital aapproximation

wf for N e- atom is equal to product of N single e- wfs

perfect gas eq of st

pV=nRT

SATP

T = 298K

p = 1 × 10⁵ Pa

STP

T = 0 degC

p = 1 atm

partial pressure is

the pressure gas would exert if it occupied the container on its own

mole. fraction is

the amount (in moles) of A as a fraction of the total amount

what is effusion

gas escapes through a hole

at a fixed T and p, rate of effusion of a gas is..

inversely proportional to sq rt of its molar mass

below criticzl temp, gases can be liquified by

compression

K_c is an equilib contant expressed in terms of

molar concs

K_c for:

N₂ + 3H₂ ←→ 2NH₃

[NH₃]² / [N₂][H₂]³

K_p is an equilib contant expressed in terms of

partial pressures e.g. p(NH₃)

zeroth law

if 2 systems are each in thermal equilib with a 3rd, theyre in thermal equilib w each other

open system exchanges

en and matter w surroundings

closed system exchanges

en but not matter w surroundings

what is work

a transfer of en that causes motion against an opposing force

equation for work. work =

force x distance

intensive props are

values that dont depend on quantity of a sub e.g. density, SHC

extensive props are

values that depend on quantity of a sub e.g. mass, length, vol

how to find stationary points of a function

values of x for which f’(x) = 0

how to know if a stationary point is a minimum point

f’(x) = 0 and f’’(x) >0

how to know if a stationary point is a maximum point

f’(x) = 0 and f’’(x) <0

how to know if a stationary point is a point of inflection

f’(x) = 0 and f’’(x) = 0

i =

√-1

√-8 =

√8√-1 = √8i

accuracy is

the degree to which the measurement conforms to the correct value

precision is

how consistent the data are

systematic error…

• affects accuracy

• oft from instrument used

random error….

• affects precision

• oft reduced by collecting more data

10.0 is how many sf

3 bc trailing zeros become signif if theres a dp

10. is how many sf

2