lecture 6!!!

Question 1

what quantum numbers from last year do we need to think about when we think of the H atom

Answer 1

n
l
ml

we dont need to think of ms bc H only has 1e- and it doesnt rlly matter if its spin up or spin down

Question 2

what is spin orbit coupling all about

Answer 2

a moving charge can and does generate a magnetic field

Question 3

the solution to the angular schrodinger equation gives what

Answer 3

l

the angular momentum
it gave us orbitals

and told us that l can have values of 0 –> n-1

but they need to be integers, ,they cant be a decimal plave

Question 4

what does l and ml tell us about

Answer 4

tells us about the motion of an e-

Question 5

what is l

Answer 5

the orbitals angular momentum

Question 6

how does spin affect angular momentum

Answer 6

the more spin,, the more angular momentum

think of it like:
hands stuck out spinning > hands tucked in spinning.

Question 7

what is angular momentum tho

Answer 7

the amount by which an e- is spinning arounda fixed proton in the middle

Question 8

what is S

Answer 8

spin angular momentum

Question 9

what is the value of S and what is s

Answer 9

s is the spin angular momentum

s value = 1/2

it can either spin clockwise or anticlockwise

Question 10

how many magnetic fields are there inside an atom

Answer 10

theres the orbital movement and the electron spin movement

SO THERES THE SPIN MAGNETIC FIELD AND THE ORBITAL MAGNETIC FIELD

Question 11

whats cool about the e- spin and orbital magnetic field

Answer 11

they interact with eachother

Question 12

which magenetic field in an atom is larger

Answer 12

the orbtial magnetic field is larger than the e- spin magnetic field.

Question 13

how would the 2 magnetic fields like to interact with eachother

Answer 13

they would like to be opposites of one another : low energy arrangement, one spinning one way and the other spinning the other way.

the other arrangement is where theyre both spinning the same way,, this is a high energy arrangement and isnt favoured.

Question 14

the size of the coupling depends on what

Answer 14

the magnetic field

Question 15

everything is still only applicable tooo

Answer 15

the H atom

the whole interaction and ml and l is only for H..

Question 16

so what is spin orbital coupling

Answer 16

the 2 magnetic fields in a atom// H atom: the orbital magnetic field and the e- magnetic field interact with eachother

Question 17

what is j

Answer 17

the total angular momentum quantim numberrrr

from the orbital(l) and the e- spin (s=1/2)

describes how the l and s magnetic fields interact with eachother

DESCRIBES SPIN - ORBITAL COUPLING

Question 18

how do we find the j value + describe how and conditions that need to be met

Answer 18

j is the total angular quantum number : so smt to so with the s and l magnetic fields

j = |l+-s|

the lines show that its an absolute value: it means that if the answer comes back negative,, we do the other sign,,, j must be positive

Question 19

wait so if the j value = | l +- s| when do we add s and when do we subtract s

Answer 19

we add the s to the l value if the orbital and e- spin magnetic fields have a high energy arrangement: aka if theyre both spinning up in terms of the arrows.

we take the s away from the l value if theres a low energy arrangement: aka when the things are spinning in the opposite direction: when one arrow is pointing up and the other arrow is pointing down.

Question 20

what does j primarily depend on

Answer 20

j depends primarily on the l value

bc the l value can be 0–> ‘n-1’ whereas ‘s’ will always be = 1/2 bc its the electron spin

Question 21

what is the ground state of a H atom:
- its e- configuration
- its l value
- its s value
- possible j values

Answer 21

1e- only
so 1s^1 is the ground state e- configuration

l = o (bc its 1s)
s = 1/2 bc obvsss its an e-

j = 0 + (1/2)
j = 0 - (1/2)

but the j value is an absolute value,, meaning it has to be positive,, so the only optioon we really have for the total angular momentum quantum number issssss

j = 0 +1/2 = 1/2 or 0.5 if u will 💗 so easy girl u can do this!!!!

Question 22

if l = 0 ,,, what does this tell ussssssssss

Answer 22

s is the only other magnet

s= 1/2 which is an actual value

l = 0 ,, this isnt an actual value

so if l = 0 this means that there is only the s magnet.

so no 2 magnets = no interaction between the 2 = no spin orbital couplinggg 🤭

the only motion + magnetic field we have is due to the e- spinning ,, not the orbital spinning bc its l = 0. a cirlce which is the same all round.

Question 23

1st interesting excited state of H

Answer 23

2p1

bc 2s1 is still l=0 and s=1/2

Question 24

do the whole breakdown of a 2p1 excited state

Answer 24

n = 2 but we can ignore this bc this doesnt twll us about motion 💸

l = 1 = p
s = 1/2 bc its an e- duh

j = |l+- s |
j = 1 + 1/2
j = 1 - 1/2

as they both give positive values j = 1/2 and 3/2

SO THERE ARE 2 MAGNETIC FIELDS BC NOTHING IS EQUAL TO 0,, MEANING THEY INTERACT,, MEANING THERE IS SPIN ORBITAL COUPLING

Question 25

do the whole breakdown for the 3d1 electron config

Answer 25

n = 3 but it doesnt tll us about motion so we ignore.

l = 2 = d
s = 1/2 bc its an e- duhhh

j = | l +- 1/2 |
j = 2 + 1/2 = 2.5
j = 2 - 1/2 = 1.5

both work as theyre both positive

meaning theres 2 magnetic fields bc theres e- spin motion and orbital motion,, which can interact with eachother to giveeeee SPIN ORBITAL COUPLINGGGGGG

Question 26

what is meant by fine structure

Answer 26

fine structure describes what a ‘single energy level’ actually is.

Question 27

describe the fine structure energy graph

Answer 27

y axis = energy

x axis = increasing l value.

increase in ‘n’ as u go up the y axis obvs

s -> p -> d going to the right

the s shells dont split up into high/ low energy bc theres no spin orbital coupling

the p shells split into high and low energy bc p = l = 1 so u can get 1.5 or 0.5 (different energy)

Question 28

the gaps within the shell in the fine structure energy diagram can be seen,, what does the energy gap depend on thooooo

Answer 28

depends on the j , l and s quantum numbersssss!!!!

Question 29

the larger j value hasssss what energy

Answer 29

high energy (more unstable)
higher j value bc u added the different magnetic fields meaning they were in the high energy arrangement… both spinning the same way.

Question 30

how do we get a larger magnetic field

Answer 30

by having a larger atomic number

larger atomic number =
larger nuc charge =
e- is closer to nuc =
e- is going to spin around it faster =
higher magnetic field bc more faster motion!!!!

Question 31

okay so will H or Cs have a larger magnetic field

Answer 31

the Cs!!!

bc it has a larger atomic mass = larger Z = e- is pulled in more = spins faster around the nuc = more motion = larger magnetic field
= larger gap between the different energy j values. = LARGER SPIN ORBITAL COUPLING VALUE.

allso kinda think of the radius and think that a larger radius will give u a larger magnetttttt. so the j value separation will be largerrr.

Question 32

higher j value can be written assss

Answer 32

1/2 hcA

A is large for heavy atoms.

Question 33

lower j value can be written asssss

Answer 33

• hcA

A is smaller for smaller// lighter atoms.

Question 34

what unit does A have

Answer 34

cm-1

wavenumber vibessssss

Question 35

how does the value of A change down the group

Answer 35

down a group = heavier the atom = larger the A value.

so u get a larger energy split between the different j values of the same shell.

Question 36

okay so so far all this is only applicable tooooo

Answer 36

only applicable to the H atommmmm!!

the magnetic fields interacting and the different j values and all this is.

Question 37

okay so for multielectron atoms what is Y

Answer 37

Y(1,2)
= Y(1) Y(2)

u multiply them together

Question 38

helium ground state config ,, it has 2e-

Answer 38

1s2

Question 39

helium excited states

Answer 39

1s1 2s1
1s1 2p1

Question 40

whats so different between the e- in hydrogen and any other atoms e-

Answer 40

in hydrogen that e- cannot interact with any other e- as there is no other e-.

in multielectron atoms,, the electrons will interactttttttt.

Question 41

how do we evaluate the total angular momentum when we have a multielectron atom

Answer 41

we use russel saunders coupling !!

the ‘complex’ thing but we’ve got this 🤭

Question 42

what are the steps involved in russel saunders’ evaluation of j for multielectron atoms

Answer 42

• start with configuration
• l (orbital momentum) = strongest interaction
• s (e- spin momentum)

then the j value + their interactions!!

Question 43

for a multi electron atom there are many e-, meaning each has its own set of quantum numbers that describe it,, meaning what

Answer 43

each e- in an atom will have its own l value

these group together to give the atoms L value.

Question 44

okay girl 👩‍🏫 how what is L again and how do we find it

Answer 44

• for multi electron atoms there are many e- and each will have its own l value (aka angular momentum aka orbital shape)
• so we need to combine these to give ‘L’ which is the l of the whole atom. big L bc lots of little l’s.

to find L:
l1+l2-0,, l1+l2-1,, l1+l2-2,, l1+l2-3,,,,,,,,, until |l1-l2|

,,,, = in steps of 1

Question 45

L for He ground state

Answer 45

He ground state = 1s2
1s1 and 1s1

gives l1 = 0
gives l1 = 0
bc theyre both in the s shell = l = 0

L = 0+0,,,, |0+0| = 0

if theres no angular momentum in both e- u can make it out of thin air,, so its obs gonna be 0.

so L for He g.s = 0 = S big S bc for the whole atom

Question 46

if L = 0 what is it called

Answer 46

S big S

bc L = 0 = s orbital

but bc its for the whole atom its capital : S

S state

Question 47

ground state for the whole He atom is what

Answer 47

its an S state

found using russel saunders

Question 48

okay how do we find the acc value of S aka the spin of the whole atom

Answer 48

same way as we find the L

but usig 1/2 bc e- can only have spin = 1/2

so [(1/2+1/2)-0], [(1/2+1/2)-1], [(1/2+1/2)-2] ,,,,, |1/2-1/2|

it should acc be s1 + s2 but s will always be 1/2 so do ur thing girl!!

1,0

Question 49

multiplicity equation

Answer 49

2S + 1

u use the whole atoms spin : S which u find using the ‘in steps of 1’ thing.

if S = 1, 0

2x1+1 = 3 so u have a triplet
2x0+1 = 1 so u have a singlet

Question 50

singlet S value

Answer 50

s = 0

bc 2S+1

Question 51

finding J for the whole atom,, notive how we use small j for the e- and big J for the atom : okay so how do we find J for the atom

and what should we not include for He ground state

Answer 51

we use every combo of L and S resultsssss

J = L+S-0 ,, L+S-1,,,,,, |L-S|

L=0,, S=1 is one combo : J=0+1 tilllll |0-1| so 1,,,1 = 1

L=0,, S=0 is another combo
J=0+0 –> |0-0|= 0

do every combooooo of L and S. takes time so dont worry girl .

so possible J values = 1 and 0

He:gs: 1s2: 2 e- in the 1s: u cant use the S=1 bc that means youve added the spins of both e-: u did 1/2 + 1/2 meaning they have the same spin,, which goes against the pauli exclusion principle: so u acc shouldnt invlove S=1 for the combo!! so the J value is only 0 (the J where L=0 and S=0)

Question 52

aka to find J what equation do we use + when should we not bother with the equation

Answer 52

J = L+S-0, L+S-1, L+S-2,,,,,, |L-S|
u use the values of S and L

u do this whole thing for every possible combination of S and L values!!

we shouldn’t bother when we’re doing the S=1 for He. bc this means the e- go against the pauli exclusion principle!! bc it means they have the same spin.