lecture 7 Flashcards
atomic spec can also be called ,,, and what is seen
electronic spec
u can only see changes to do with electrons
when we change the state of an atom what do we also change
when we change the state of an atom,, we change its wavefunction!!!
think about all the steps we did : splitting it into radial and angular wave functions: if we change the first bit,, the wavefunction will also change.
if wavefunction changes when u change the position of an e-. ,, and in electronic//atomic spec we interact an atom with a photon of light to change its position,, what different wavefunctions will we have
we will have an initial wavefunction: before the e- moving // transitioning due to absorbtion of a photon.
Y.i
and we will also have a final wavefunction,, this is the wavefunction after the atom has interacted with the photon of light. and has moved from its original place. Y.f
gross selection rule for atomic // electronic spec
there must be a change in the dipole moment between the initial and final states.
what can symmetry do
symmetry can predict if the whether the transition dipole is non zero
initial and final wavefunctions of H
1s
2s
2p
initial wavefunction is all about
n, l , ml
aka if we have a 1s 2s 2p etc orbital
specific selection rule of atomic//electronic spec
describes the allowed transitions between states
shows what changes are allowed when things abs//emit photons of light
more focused on graphs whereas the gross selection rule is more focussed on the atom itself
emission
lose photon
lose energy via a photon
absorption
gain energy by absorbing a photon of light
describe a photon and what quantum numbers it has
photon = one bit of light
it has a mass of 0
it has a spin of 0
it has an angular momentum of 1
l = 1
what is conservation of angular momentum
when the angular momentum of the atom and light (photon) interact + act together
they conserve momentum between the initial and final wavefunctions.
what transitions can and cant occur
only transitions that conserve angular momentum between initial and final are allowed!!
for Hydrogen: write down the transition rules
change in l = +- l
change in ml = 0, +-1
change in n doesnt matter as long as l and ml dont change!!!
what does the selection rule: change in l = +- 1 mean
that u can have transitions between
s -> p
p -> d
but u cant have an s -> s transition!!
think of the energy level diagram with energy on the y axid and l values on the x axis.
on the energy level diagram of energy on the y and l value on the x,, what are the ml’s seen as
okay so for 2p
u have 3 different lines
theyre ml: -1 0 +1
those are whwat we mean by ml
so if ur allowed a change of l +- 1,, what does this mean
where the line is of the initial e- position,, u can either move to the right or to the left but only by 1.
and same with ml values,, for s the ml = 0
so make sure u label ur graph fully so yk whats going on 💗 and remember that change in the n value doesnt matter if l = +-1 and ml = 0, +-1
the labelled energy diagram with all the lines of the allowed transitions is called a
gotrian diagram
the thicker the lines: the more of that transition there issssss.
okay so the H electron is special bc we only ever need to think of 1 e-,, and this can be described using what quantum numbers
n , l , ml
dont even need ms bc its 1/2
okay but for He and for other atoms,, there are more than 1e- so what quantum numbers are used to describe them
we need the L, S, and J quantum numbers
bc these describe the whole atom,, not just 1e-,, they include all the e-!!!
so the grotrian diagram for multielectron systems will include what difference to the normal H one.
the normal H one doesnt have J values and so theyre energy diagram isnt split into low and high energy.
bu for other atoms,, there is a J value,, and we need to show the higher and lower energy line splits!!! also label these bc it makes life sm easier once we think about the allowed transitions and selectrion rules!!
okay so for a multielectron system :what rules are there and explain themmmm
change in J: 0, +-1
change in L: 0, +-1
change in S: 0!!
J when energy levels are split make sure u labels them using the 3/2 1/2 and 5/2 3/2 bc it makes this sm easier to do!!
for L = 0, +-1
remmeber that small l values can change,, but it may leave the L unaffected. L means u can move right / left
also its kinda easier if u draw the orbitals on top of eachother: so like the 4d ones directly above the 3p ones and draw arrows coming down that way: its easier to see the different j level changes
if theres 3 different possible transitions,, what is there in emission spec
3 transition that lead to emissions gives u 3 lines in emission speccccc
what is the multiplicity equation again
2S+1
u get a singlet,, doublet,, triplet etcccccc
u still need to respect pauli aswell tho
so for He,, what is the multiplicity
1s2 ground state
and they cancel out bc theyre antiparallel
to give s=0
so then 2 x 0 + 1 = 1 so its a singlet
He excited state multiplicity
1s1 2s1 same spin
add them = 1
2 x 1 + 1 = 3 triplet state
lower energy arrangement due to spin pair energy!!!!
1s1 2s1 but opp spins = cacel to give s = 0
and then 2 x 0 + 1 to give 1 so another singlet!!! but this is the higher energy arrangement
why is a He triplet state lower energy than the He single stage
it’s lower in energy bc it’s spin pairing energy!!
bc they have the same spin (both going anti clock // clockwise)
can u go from a singlet to a triplet state
nope
bc change in S = 0
and S in singlet is 0
and S in triplet is 1
so this would give a change in 1
if change in S can’t change and has to be 0,, what happens when an atom,, like He,, has a singlet (s=0) and a triplet (s=1) state
u would see 2 different spectra
one for each spin state.
and each spin state will contain its transitions in its own spin state part
fine structure due to spin orbit coupling: what do we see
we see how the orbitals in different shells are split into low and higher energy
what differences in spectra does fine structure give
it gives 2 lines!!!
and the cm-1 between the lines is based on the atoms Z (nuc charge)
larger Z = larger angular momentum!!
so larger atoms will have a larger cm-1 value!!!
for change in J being restricted to 0 or +-1 what’s an easier was to check this and see how many peaks are in emission spec
u draw the 4d split orbitals and the 3p split orbitals directly above one another and label the splits with their number (5/2 3/2) (3/2 1/2) then draw a line to where the e- is allowed to transition to based on J values.
the amount of lines u have is the amount of peaks ur emission spec will have.
wavefunction strategy in atomic spec
okay so atomic spec causes a change in electrons : from where it initially is to where it finally will end up.
so a change in the atom = change in Y = Yi + Yf
