5b

Question 1

before,, when we were looking at the distance between the nuc and the e- in that graph,, we were looking at how many e-

Answer 1

we were looking at the distance between the nuc and 1e-.

there were no interactions with other e-.

the axis were z up,, x going right and y going towards us.

Question 2

from now,, when we draw the graph xyz graph away from the nuc,, we think of how many e-

Answer 2

we think of 2 e-

we therefore need to think of the effects they will have on eachother!! and how the movement of one affects the movement of the other.

Question 3

for H-,, what is Z

Answer 3

1

Question 4

for He,, what is Z

Answer 4

2

Question 5

what do we need to solve majority of the time

Answer 5

HY=EY

where Y is the wavefunction
E is energy

Question 6

xyz nuc graph,, what is r1, r2, and r12

Answer 6

r1 = distance between nuc and e1-

r2 = distance between nuc and e2-

r12 = distance between both e-. between e1- and e2-!!!

Question 7

what does H equal for complex atoms,, atoms with more than 1e-!! and what does each thing mean + what do we forget about bc its constant

Answer 7

H = T.nuc + SUM.T.el + SUM.V.nuc-el + V.el-el

Tnuc= change in nuc’s kinetic energy : nuc is so heavy we can ignore this bc the e- just follow it around anyways.

Tel = kinetic energy of moving e-.
Vel-el = potential of the electrons = r12

Question 8

what does Tel equal to

Answer 8

kinetic energy of electron.

(-h2 / 2me) x (1/V2)

Question 9

what does V.nuc-el mean

Answer 9

potential between the nuc and the e-! negative number bc as they get closer the energy decreases bc opposites attract and its more stable.

-Ze^2 / 4nEr1

n = pi
E = Eo = vacuum permeability
e = charge on an e-.
r1 = e1- –> nuc distance.
Z = nuclear charge

Question 10

what does V.el-el

Answer 10

potential between the 2e-‘s.
+ number bc the closer the 2 e-‘s get to eachother,, the more unstable things are bc theyre the same charges: theres repulsion etc.

+e^2 / 4nEr12

e = e- charge
n = pi
E = vacuum permeability
r12 = distance between e1 and e2

Question 11

Y in HY=EY when theres 2 e-

Answer 11

Y(x1,y1,z1, x2, y2, z2)
Y(r, sigma. gama, r2, sigma2, gama2)

the gama is like a circle with a line running up to down.

Question 12

what is Y + how many dimensions is it when theres 2 e- and why.

Answer 12

wavefunction
the probability of what both e-s are doing

it has 6 dimensions when there are 2e-.

bc each e- can move in 3 dimensions: x y z

Question 13

approx waefunction gives us

Answer 13

the approx energy

Question 14

approx schrodinger equation

Answer 14

HYapprox = E.approx x Y.approx

Question 15

what does Y.approx give us + what do we do with it

Answer 15

gives us an approximation for an orbital.
an orbital approx.

we break down the 6D –> 2x(3D)

so Yapprox = (Y=Y1 x Y2)
gives Y1(x,y,z)

Question 16

what is an orbital in terms of wavefunctions

Answer 16

an orbital is a 1e- wavefunction

Question 17

ground state of He configuration + its wavefunction

Answer 17

1s2

Y(1,2) = Y(1s) x Y(1s)

Question 18

what spin do e- have + how do we know they have spins

Answer 18

they have intrinsic spins

+-1/2

we know this from the stern experiment when an e- was either curved up or down due to their spin.

Question 19

quantum number for e- spins

Answer 19

ms

+-1/2

Question 20

so for He,, the wavefunction will be

Answer 20

Y(1,2) = Y(1s1 1/2) x Y(1s2 -1/2)

or

Y(1,2) = Y(1s1 -1/2) x Y( 1s2 1/2)

bc we have included their different spins

Question 21

S = 1/2 which means e- spins areeeee

Answer 21

fermions

this is bc they are half integer spins

Question 22

due to their different spins,, the nuc xyz graph can be drawn in 2 ways which are

Answer 22

different e- having different spins

aka e1 = 1/2
and e2 = -1/2

and then e1 = -1/2 and e2 = 1/2

spins can stay in the same place but the e- will change place

Question 23

why does the Y sign have to change

Answer 23

bc electron spins are fermions + have half integer spins

this means the wavefunction sign must change.

so Y(1,2) = -Y(2,1)
but we normally do Y^2,, which gives a positive number anywayssss. so we cant rlly see the diff between

[Y(1,2)]^2 and [-Y(2,1)]^2

Question 24

what do we use to make sure we have a combo of each spin

Answer 24

we use determinants

|a b| = ad - bc
|c d|

and the negative of the original

|c d| = cb - da
|a b|

but instead we would have
| Y1 1/2 Y2 1/2 |
| Y1 1/2 Y2 -1/2|

Question 25

ground state of H2 Y,, integration limits and equation

Answer 25

limits = infinity and -infinity

Y^2 dx dy dz = 2

Question 26

what do determinants do

Answer 26

they make sure Y(1,1) = 0

bc the only way to make Y(1,1) = -Y(1,1) is to have it equal 0.

Question 27

pauli exclusion principle in terms of wavefunction

Answer 27

if 2e- occupy the same orbital with the same spin,, the wavefunction and probability is 0

they must have different spins!!

no 2 electrons can have the same n,l, ml, and ms quantum numbers in the same orbital.

ms must be different as this is the e- spin!!

Question 28

for Li the Z =

Answer 28

3 nuc charge

Question 29

how many ground states are possible for Li

Answer 29

2!!

1s2 2s1
or
1s2 2p1

Question 30

why are the s and p orbitals not degenerate for multi electron systems

Answer 30

due to screening + due to there not being only one e-.

they interact with eachother

Zeff and all those effects

Question 31

in multi electron ysstem,, do both e- ever feel the nuc charge

Answer 31

yes!!

think of an equilateral triangle!! with 2e- and nuc as the corners

Question 32

at some points in multi electron systems,, what does repulstion between e- do

Answer 32

reduces the attraction an e- feels to the nuc

reduces the Zeff flet byt the other e-.

think of like a weird slanted triangle with 2e- and nuc as the corners.

Question 33

little screening has what wavefunction graph

Answer 33

2s

large amplitude close to nuc: e- spends lots of time near nuc

graph starts high,, and drops down below axis then rises just before axis

Question 34

large sccreening has what effect on the wavefunction graph

Answer 34

2p
more screening

larger amplitude awsy from the nuc

starts at 0,, rises then falls like a hill. no node.

Question 35

orbitas with least to most energy

Answer 35

s
p
d
f

Question 36

are Hudrogen orbitals degen and why if so

Answer 36

they are degenerate!!

bc theres no screening as theres only one e-. the Zeff effects are not shielded by other e- as there are no other electrons.

Question 37

do other atoms have degenerate orbitals

Answer 37

nope

other atoms are multielectron systems meaning e- will shield outermost electrons from the Z,, reducing the amount of Zeff they feel.

due to having more e-.

there are screening effects.

Question 38

Be has 4 e-,, what is its config

Answer 38

1s2 2s2

Question 39

B has 5 e-,, whats its e- config

Answer 39

1s2 2s2 2p1

Question 40

1st excited state of Li : 3e- total

Answer 40

1s2 2s1

or 1s2 2p1

Question 41

C has 6e-,, whats its configuration + what p orbital can we use

Answer 41

its config is 1s2 2s2 2p2

we can use px pz py bc theyre degenerate but we use hunds rule meaning the e- need to be unpaired and have the same spins in the p orbitals.

this means C is a triplet state as theres 3 different ways of filling the p orbitals : pxpy pypz pzpx!!

Question 42

what does ‘full shell mean’

Answer 42

full shell means that the s or p or d or f orbitals are completely full.

Question 43

schrodinger equation for approx values

Answer 43

H Y.approx = E.approx Y.approx

Question 44

V.nuc-el meaning + equation + why it cant be used for nucs with a higher charge than 1

Answer 44

potential energy between nucleus and electron!!

= -Ze^2 / 4n Eo r1

Z = nuc charge
e = charge on nuc
n = pi
E = vacuum permeability
r1 = distance from bnuc to electron 1

cant be use for nucs with a higher charge than 1 bc the outer e- doesnt feel the whole nuclear charge due to screening effects due to there being more e- that prevent it from feeling the whole nuclear charge.

Question 45

what do we plot when we see the H Y.approx = E.approx Y.approx

Answer 45

we plot the E.approx against Z effective

this gives a parabola that looks like a smiley face.

the lowest bit of this is the Zeff, its normally a decomal number as it doesnt equal the full nuc charge due to screening.

this helps us by mapping the eigen values // helps us map out the eigen values // we map out the eigen values.

Question 46

the orbitals being degenerate in the same shell aka the px py and pz and the approx values work until what atom,, and why doesnt it work past this

Answer 46

they work until Ca.

after Ca the 3d and 4s orbitals are too close in energy + as u keep going down relativity becomes important!!

relativity = difference from theoretical and experimental as u go down the groups due to atoms acting differently due having more e-,, more shells and the e- move faster.