week 2

Question 1

what did de broglie propose?

Answer 1

all moving objects have a wavelength
all matter has wave-like properties

electrons are both waves and particles

Question 2

give the wave-particle duality equation

Answer 2

λ=h/mv

λ is wavelength
h is planks constant
m is mass
v is velocity

Question 3

how is the wave-particle duality equation derived?

Answer 3

know that E=h𝝂
know that 𝝂λ=c
sub in v into E=h𝝂=hc/λ

combine with E=mc^2
λ=h/mc –> λ=h/mv
(v velocity)
only works for when h is tiny so good for electrons

Question 4

what is the phase of a wave

Answer 4

sign of the amplitude

can be positive, negative or zero

Question 5

what does an area of zero amplitude mean

Answer 5

0 amplitude = node

eg where sinx wave intersects x-axis

Question 6

as frequency increases…

• wavelength…
• energy…
• number of nodes…

Answer 6

• wavelength gets shorter
• energy increases
• number of nodes increases

Question 7

what effects do electrons experience and what does this lead to? what does this suggest?

Answer 7

electrons experience interference and diffraction effects which lead to areas of higher and lower intensities = suggests electrons behave as waves

Question 8

give the equation for quantisation of angular momentum

Answer 8

mvr = nh/2𝛑
m is mass
v is velocity 
r is radius
n is number of wavelengths 
h is planck's constant

Question 9

what is a wave function?

what symbol is used for wave functions?

Answer 9

a mathematical way of describing the wave-like nature of an electron in three dimensions

symbol 𝛙 psi greek letter

Question 10

in terms of the schrodinger equation for the hydrogen atom:

what is a Hamiltonian operator?
what is an eigenvalue?
what is an eigenfunction?

Answer 10

hamiltonian operator = describes a physical property of a wave

• energy, angular momentum… etc
• each property has a specific operator

eigenvalue = possible values of the property defined by the operator

eigenfunction = describes the associated energy levels

Question 11

what three numbers define each solution of a wave function?

Answer 11

n = describes energy/size
l = describes shape
mL = describes orientation

Question 12

what is meant by the heissenberg uncertainty principle? use waves to describe this

Answer 12

cannot know for sure the position and momentum of an electron
cannot have classical (“solar system”) electron orbits where momentum and position are known
we need to talk in terms of probability, which is known from the wave functions

eg in a localised wave

• continuous waves, fixed wavelength
• well defined wavelength hence well defined momentum
• frequency identified with high precision
• BUT cannot define position because its spread out

eg in a delocalised wave

• wave is localised by having lots of waves of different wavelengths
• no longer well defined momentum frequency

Question 13

what is an atomic orbital and what does it describe?

Answer 13

atomic orbital = quantum state of an individual electron in the electron cloud around a single atom

describes the probability distribution of the electron’s position

Question 14

squaring the wave function gives ?

Answer 14

the probability of finding an electron in any region of space

Question 15

what does the radial distribution function describe?

Answer 15

probability of finding an electron at a certain distance from the nucleus

describes how electron density varies as a function of the radius from the nucleus

Question 16

how is the RDF derived?

Answer 16

R(r) = radial component depends on n (principal quantum number)
R(r)^2 = probability of finding electron at fixed distance r from nucleus
electron could be found anywhere of sphere so take surface area 4𝛑r^2

multiplying probability and surface area = 4𝛑r^2•R(r)^2 = RDF

Question 17

on an RDF where is there 0 probability of finding an electron?

Answer 17

at a radial node = radial because in all directions there is 0 probability of finding an electron

Question 18

what do the peaks on an RDF graph represent?

Answer 18

maximum points represent the most probable distance of finding an electron from the nucleus

Question 19

as the principal quantum number (n) increases what happens to the number of radial nodes on an RDF?

Answer 19

number of radial nodes increases

Question 20

what is an angular node?

which quantum number determines number of nodes?

Answer 20

a plane that goes thru an orbital where there is 0 electron probability

defined by quantum number L

Question 21

describe the shape and number of nodal planes in an s-orbital

Answer 21

circular shape
one phase throughout
0 nodal planes

Question 22

describe the shape and number of nodal planes in an p-orbital

Answer 22

dumbbell shape, two lobes of opposite phase

1 nodal plane

Question 23

describe the shape and number of nodal planes in an d-orbital

Answer 23

4 lobes of interchanging phase

two nodal planes because two changes in phase, passes thru a node twice

Question 24

how many mL values for an s-orbital?

Answer 24

only 1, mL=0 because its circular, only one orientation

Question 25

how many mL values for an p-orbital?

Answer 25

3 for three different orientations px, py, pz lobes of electron density lie along corresponding axis eg pz orbital has electron density along z-axis

Question 26

how many mL values for an d-orbital?

Answer 26

5 for 5 different orientation - dxy, dxz, dyz - electron density lies between corresponding axes - dx^2-z^2 - electron density lies along x and y axes, lobes sits on x and y axes - dz^2 - electron density lies along z-axis, two lobes and a donut in the middle , nodal cones around larger lobes

Question 27

number of radial nodes on and orbital =

Answer 27

n-1-L eg in 2p orbital n = 2 L = 1 radial nodes = 0 as seen on RDF

Question 28

``` which type of orbital corresponds to each l value? l = 0 l = 1 l = 2 l = 3 ```

Answer 28

s p d f

Question 29

what is the fourth quantum number? what does it represent? what values can it take?

Answer 29

magnetic spin quantum number - ms represents the spin of electrons can be +1/2 or -1/2 --> in an orbital with two electron, one electron is ms = +1/2 and the other ms = -1/2 in said orbital, total ms is 0, halves cancel out

Question 30

give the Pauli principle

Answer 30

no two electrons in an atom can have the same set of four quantum numbers each electron has a unique set

Question 31

give the Aufbau principle

Answer 31

the ground state/lowest energy electron configuration arises when the orbitals are filled in order of increasing energy electrons fill from lowest energy orbitals first

Question 32

give Hund's rule

Answer 32

when filling degenerate orbitals, electrons of same ms value (same spin) fill in different orbitals, unpaired, keeping repelling electrons as far apart as possible

Question 33

excited state configuration follow which rules?

Answer 33

excited state configurations only follow Pauli's principle not hund's or aufbau's

Question 34

define paramagnetic

Answer 34

species with unpaired electrons

Question 35

define diamagnetic

Answer 35

species with no unpaired electrons

Question 36

define and give the symbol for the total spin quantum number | when is this number at a maximum?

Answer 36

S, sum of ms values in a given energy level | at a maximum at the ground state

Question 37

define and give the symbol for total orbital angular momentum quantum number

Answer 37

L, number of ways electrons can be arranged in the given energy level without the use of energy electrons can be rearranged in the degenerate orbitals

Question 38

give the formula for finding the term symbol

Answer 38

superscript: 2S+1 normal script: L S = sum of ms values L = sum of mL values of the filled orbitals

Question 39

total orbital angular momentum quantum number give the orbital names for the number of possible electron combinations give the L value and the corresponding symbol 1? 3? 5? 7?

Answer 39

1 - orbital singlet - L = 0 - S 3 - triplet - L = 1 - P 5 - pentet - L = 2 - D 7 - septet - L = 3 - F

Question 40

define symmetry operation | name the three symmetry operations

Answer 40

an action performed on an object by which the object looks the same before and after rotational axis mirror plane centre of inversion

Question 41

describe the rotational axis symmetry operation how is it labelled what is the principle axis

Answer 41

a line about which a molecule is rotated so it looks the same before and after axes are labelled with C then a subscript number 'n' where n = the degrees as a fraction of 360 (360/degrees = n) of which the molecule has been rotated eg. H2O can be rotated 180° about the O atom and look the same --> 360/180 = 2 so C2 rotational axis principle axis = the axis of a molecule of the highest order and is by convention the z-axis

Question 42

describe the mirror plane symmetry operation how is it labelled what are the two types of mirror plane? how are they labelled and assigned?

Answer 42

a plane that passes thru the molecule in which the molecule is reflected and looks the same before and after labelled with sigma σ vertical mirror plane - σv - vertical wrt principle axis horizontal mirror plane - σh - horizontal wrt principle axis planes are assigned by first determining the principal axis/z-axis)

Question 43

describe the centre of inversion symmetry operation how is it labelled how many per molecule

Answer 43

based on a point on the molecule thru which any part of the molecule can pass and come out the other side at the same distance and become an equivalent point, leaving the molecule unchanged labelled i only one per molecule

Question 44

2pz orbital rotational axis? mirror planes?

Answer 44

C∞ | infinite mirror planes

Question 45

3dx^2-y^2 orbital rotational axis? mirror planes?

Answer 45

C2 rotational axis can be rotated 180° at a time and look the same 2 vertical mirror planes wrt principal axis

Question 46

define gerade in terms of orbitals

Answer 46

aka symmetric when the same phases are swapped around wrt the centre of inversion eg 3dx^2-y^2

Question 47

define ungerade in terms of orbitals

Answer 47

aka unsymmetric when opposite phases are swapped wrt the centre of inversion eg 2pz

Question 48

what is a symmetric operation what is an anti-symmetric operation

Answer 48

symmetric = something maps onto itself before and after anti-symmetric = outcome of the operation is the opposite of the original

Question 49

is the 2s orbital symmetric or anti-symmetric wrt rotational axis and mirror plane?

Answer 49

it is symmetric because it maps onto itself when symmetry operation are carried out