5b Flashcards
before,, when we were looking at the distance between the nuc and the e- in that graph,, we were looking at how many e-
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.
from now,, when we draw the graph xyz graph away from the nuc,, we think of how many e-
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.
for H-,, what is Z
1
for He,, what is Z
2
what do we need to solve majority of the time
HY=EY
where Y is the wavefunction
E is energy
xyz nuc graph,, what is r1, r2, and r12
r1 = distance between nuc and e1-
r2 = distance between nuc and e2-
r12 = distance between both e-. between e1- and e2-!!!
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
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
what does Tel equal to
kinetic energy of electron.
(-h2 / 2me) x (1/V2)
what does V.nuc-el mean
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
what does V.el-el
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
Y in HY=EY when theres 2 e-
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.
what is Y + how many dimensions is it when theres 2 e- and why.
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
approx waefunction gives us
the approx energy
approx schrodinger equation
HYapprox = E.approx x Y.approx
what does Y.approx give us + what do we do with it
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)
what is an orbital in terms of wavefunctions
an orbital is a 1e- wavefunction
ground state of He configuration + its wavefunction
1s2
Y(1,2) = Y(1s) x Y(1s)
what spin do e- have + how do we know they have spins
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.
quantum number for e- spins
ms
+-1/2
so for He,, the wavefunction will be
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
S = 1/2 which means e- spins areeeee
fermions
this is bc they are half integer spins
due to their different spins,, the nuc xyz graph can be drawn in 2 ways which are
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
why does the Y sign have to change
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
what do we use to make sure we have a combo of each spin
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|
ground state of H2 Y,, integration limits and equation
limits = infinity and -infinity
Y^2 dx dy dz = 2
what do determinants do
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.
pauli exclusion principle in terms of wavefunction
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!!
for Li the Z =
3 nuc charge
how many ground states are possible for Li
2!!
1s2 2s1
or
1s2 2p1
why are the s and p orbitals not degenerate for multi electron systems
due to screening + due to there not being only one e-.
they interact with eachother
Zeff and all those effects
in multi electron ysstem,, do both e- ever feel the nuc charge
yes!!
think of an equilateral triangle!! with 2e- and nuc as the corners
at some points in multi electron systems,, what does repulstion between e- do
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.
little screening has what wavefunction graph
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
large sccreening has what effect on the wavefunction graph
2p
more screening
larger amplitude awsy from the nuc
starts at 0,, rises then falls like a hill. no node.
orbitas with least to most energy
s
p
d
f
are Hudrogen orbitals degen and why if so
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.
do other atoms have degenerate orbitals
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.
Be has 4 e-,, what is its config
1s2 2s2
B has 5 e-,, whats its e- config
1s2 2s2 2p1
1st excited state of Li : 3e- total
1s2 2s1
or 1s2 2p1
C has 6e-,, whats its configuration + what p orbital can we use
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!!
what does ‘full shell mean’
full shell means that the s or p or d or f orbitals are completely full.
schrodinger equation for approx values
H Y.approx = E.approx Y.approx
V.nuc-el meaning + equation + why it cant be used for nucs with a higher charge than 1
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.
what do we plot when we see the H Y.approx = E.approx Y.approx
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.
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
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.
