Chapter 5!!!! Electronic Structure of Atoms and Ions

Question 1

• Atomic Orbital - explain

Question 2

• Quantum Numbers and their allowed values

Question 3

• Define Orbital Radial Probability Distribution

Question 4

• What does angular node mean? Where would it be located?

Question 5

• What does radial node mean? Where would it be located?

Question 6

• How do you determine the quantum number/name of an orbital, how would you draw it on a cartesian coordinate system + phases and nodes

Question 7

• in your head, what do orbital 3D diagrams/cross sectional/radial probability distributions look like?

Question 8

• how do you calculate energy/draw energy level diagrams for one electron atoms and ions??

Question 9

What does coulomb’s law describe??

Answer 9

PE of attraction between two charges

Question 10

coulomb’s law

Answer 10

V(r) [proportionate to squiggly unfinished infinity] (q1*q2)/r

where V(r) = potential energy
q1 = charge of particle one
q2 = charge of particle 2
r = distance between two particles

in atomic units (ex -1 for electron)

Question 11

lowest PE similarly charged particles??

Answer 11

lowest pe long distances large r, forces are repulsive

Question 12

lowest pe oppositely charged particles??

Answer 12

short distances (small r)

Question 13

what terms does the schrodinger equation include???

Answer 13

term rep KE, PE, and depends on 3 coordinates, as the electron is moving in 3D space

Question 14

Spherical polar coordinates??

Answer 14

(r, 0 with line through horizontally, o with line through vertically)

image a coordinate plane with x,y flat on the ground @ 90 degrees between, z goes straight up 90 to x and y

r is the distance between point (electron etc) and the origin

0 with horizontal is the angle between r and z

o line verticle angle between projection of r onto the xy plane, and x

Question 15

How do you write the wave-function for one electron species???

Answer 15

using spherical polar, and as a product of two parts;
R(r) and Y(0,o)

R(r) depends only on r and describes the size of the orbital, imagining origin is the nucleus

Y(0,o) depends on angles 0 and o and describes shape and orientation of the orbital

Question 16

n principle quantum number

Answer 16

describes the size of the orbital - gives how many subshells in an atom

can only be whole numbers above 0; 1,2,3,4 etc.

can only be 1 value of n for each system

Question 17

swirly l quantum number

Answer 17

indicates s, p, or d subshell;

l=0=s, l=1=p, l=2=d etc

can be any integer value between 0 and n - 1, ex if n = 4, l = 0,1,2,3

number of l values indicates how many subshells there will be, n values of l, so n also indicates how many subshells

also called the angular momentum quantum number

Question 18

m swirly l quantum number

Answer 18

magnetic quantum number

takes on all integer (whole) values between and including -l and l

ex if l = 2, ml can be -2,-1,0,1,2

indicates number of orbitals and orientation within a subshell, ex if there are 2 m values there will be 2 orbitals from 1s to 2p

Question 19

l values and their associated subshells

Answer 19

0 - subshell s
1 - subshell p
2- subshell d
3 - subshell f

Question 20

n = 2, what are l and ml and what do they mean??

Answer 20

n = 2,
l =0, 1

if l = 1, ml can equal -1, 0, or 1
l = 1 indicates subshell p, and 3 ml values so 2px, 2py, 2pz - 3 orbitals

if l = 0, ml can only be 0
l = 0 indicates subshell s, so just 2s

4 total orbitals in n = 2

Question 21

radial nodes!!

Answer 21

at radial coordinates, on r, like layers of the onion

number of radial coordinates = (n-1) - l

Question 22

what gives total nodes

Answer 22

n - 1

Question 23

angular nodes! <3

Answer 23

in the angular coordinates, like slices of the onion

total number is given by l

Question 24

little summary of what n l and ml mean

Answer 24

n gives number of subshells, also refers to size of electron shell, 1 the smallest and so on
l determines which subshell; 0 means s, 1 means p, 2 means d, 3 means f
ml gives number of orbitals within a subshell specified by l

Question 25

how many orbitals in the n shell?

Answer 25

n^2 orbitals total in n shell

Question 26

how many orbitals for each value of l?

Answer 26

2l + 1 orbitals, each orbital has a unique ml value

Question 27

what is the probability of finding an orbital at particular location?

Answer 27

proportional to psi (wavefunction)^2 and zero at a node

Question 28

where does phase of the wave function change??
what does that mean??

Answer 28

over every node, switches sign

Question 29

what equation gives radial probability distribution for s shell?

what is that equation based on??

Answer 29

4(pi)r^2*R^2

only based on r (RADIAL) r^2 would give max probability at the nucleus which isnt possible, so you need to multiply r by the total sa of a sphere

Question 30

what do you multiply to find full probability of 3D atoms?

Answer 30

radial probability distribution x angular probability distribution

Question 31

s orbitals!!!!

Answer 31

l = 0 therefore no angular notes

probability distribution varies with r only, spherical!!!

STILL RADIAL NODES you can have l = 0 with n = 4 and more, in that case there would be 3 radial nodes

remember n determines number of shells, if I have 1s only 1 shell, no radial nodes; 2s 2 shells so 1 radial node between shells; 3s, 3 shells, 2 radial nodes (1 between each shell)

Question 32

1s vs 3s how does where you’re most likely to find an electron change???

Answer 32

3s more likely to find the electron further from the nucleus compared to 1s BUT you could still find it close, even closer than 1s electron just not super probable

Question 33

does probability ever reach 0 to the right of the graph??

Answer 33

technically no, it extends to infinity but the it would be considered to be removed from the nucleus

Question 34

how do trends in probability decay relate to different species, increase in Z

Answer 34

as the nucleus grows more positively charged ex H vs Li^2+, for comprehension only considering s subshell, probability is more noticibly greater closer to the nucleus (higher peak and closer to nucleus) and the probability decays faster because electrons are more attracted to the positively charged nucleus

Question 35

how do you figure out what dimensions etc to draw your 3D model to???/ what do scientists do

s orbital

Answer 35

find the value of r for which 90% of the area of the radial prob distribution lies under, s orbital can be drawn to that r value

Question 36

how would you draw a cross sectional diagram of an s orbital??

Answer 36

1 plane, either z x or zy or yx, nice little circle with nodes represented by dotted lines, arrow pointing to outside of circle with [r subscript 90%], LABEL PHASES, switch positive to minus or minus to positive every node

Question 37

p orbitals!!!

Answer 37

there are 3 p orbitals , px, py, and pz

l = 1, therefore ml can be -1, 0, 1

ALSO l = 1 so 1 angular node
- number of radial nodes determined by (n - 1) - 1

^^ that means for each value of p, 2p, 3p 3 orbitals of each

they look like peanuts!!!

Question 38

what equations represent p orbitals?

Answer 38

psi(px) ~ xR(r)
psi(py) ~ yR(r)
psi(pz) ~ zR(r)

R(r) = an exponentially decreasing function of r
x, y, and z represent distances along corresponding cartesian coordinates of the atom

Question 39

where does the angular node occur for p orbitals???

Answer 39

there are 3 p orbitals, px py and pz.

px, for example, lies right across the x axis (kebabed by x). py kebabed by y, pz kebabed by z

the nodes occur for each when _ letter = 0, therefore at the plane of the other two (like the kebab was sliced in half at _ = 0

Question 40

radial probability/radial nodes for p orbitals???

Answer 40

same as s, greater n value more likely electrons will be further but they can still be close!!

Question 41

where would radial nodes be for p orbitals, how do you draw that?

Answer 41

imagine a cross section of a peanut, looks like an hour glass, each radial node would be like you cut the peanut with a circular cookie cutter nicely centered, remember to write phase changes too!!!

Question 42

d orbitals!!!

Answer 42

d orbital when l = 2

2 angular nodes

therefrom ml can be -2, -1, 0, 1, 2

5 different d orbitals!!! these can be dxy, yz, xz, x^2y-y^2, z^2

for xy, yz, xz, the two angular nodes are coming up from the axis in the description, so it looks like theyre 4 ballons all tied together and each balloon condined to in a quarter of the _ _ axis in the discription - xy is zero where y equals 0 which is xz plane, and where x = 0 so yz plane

for x^2 - y^2 looks kinda that same, like 4 ballons, except angular nodes occur where the 45 degree mark would sort of be, extending up from the xy plane (where x^2 =. y^2)

the z^2 one is WIERD doesn’t look like 4 balloons, but rather like one big donut laying flat along xy plane but skewered by axis there is a donut hole. on either side of this donut, skewered only by z axis.

Question 43

how to draw d orbitals

Answer 43

dxy show x and y axis with the 4 dew drops settled nicely each quarter
dxz show x z axis, dewdrops nicely nestled
dyz same, nestley dewdrops with z and y axis
x^2 y^2 - xy axis and 4 dewdrops but theyre skewered by the axis
dz^2 - z axis and either x or y, along z axis just two dew drops skewered by axis, +
on x or y axis on either side of the dew drops two circles (this is the cross section of the donuts

Question 44

shell structure of an atom, explained!

Answer 44

all orbitals w same n value have maximum probability distributions about the same distance from the atom, leading to believe layered structures like onions!, greatest n in the valence shell, and define how an element/atom reacts with it’s environment

Question 45

what describes the energy of an electron??

Answer 45

the function En = -2.18 x 10^-18 J x (Z^2/n^2)

energy depends on n only!! so electron in 2s 2p 2d all have the same energy

Question 46

degeneracy

Answer 46

multiple states with the same energy

Question 47

what does E = 0 correspond to

Answer 47

electron seperated at infinite distance from the nucleus, so ionized from an atom!!!

Question 48

what makes the energy of the state increase

Answer 48

Z decreases (which is atomic charge) or n increases

Question 49

what would an energy level diagram look like for an atom??

Answer 49

ground state energy, 1s, low down then biiiiig jump between that and n = 2, then littler jumps between all the others until almost immeasurable!

Question 50

is the energy in an electron positive or negative??

Answer 50

negative due to coiulombic attraction, values depend on n and Z