week 2 Flashcards
what did de broglie propose?
all moving objects have a wavelength
all matter has wave-like properties
electrons are both waves and particles
give the wave-particle duality equation
λ=h/mv
λ is wavelength
h is planks constant
m is mass
v is velocity
how is the wave-particle duality equation derived?
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
what is the phase of a wave
sign of the amplitude
can be positive, negative or zero
what does an area of zero amplitude mean
0 amplitude = node
eg where sinx wave intersects x-axis
as frequency increases…
- wavelength…
- energy…
- number of nodes…
- wavelength gets shorter
- energy increases
- number of nodes increases
what effects do electrons experience and what does this lead to? what does this suggest?
electrons experience interference and diffraction effects which lead to areas of higher and lower intensities = suggests electrons behave as waves
give the equation for quantisation of angular momentum
mvr = nh/2𝛑 m is mass v is velocity r is radius n is number of wavelengths h is planck's constant
what is a wave function?
what symbol is used for wave functions?
a mathematical way of describing the wave-like nature of an electron in three dimensions
symbol 𝛙 psi greek letter
in terms of the schrodinger equation for the hydrogen atom:
what is a Hamiltonian operator?
what is an eigenvalue?
what is an eigenfunction?
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
what three numbers define each solution of a wave function?
n = describes energy/size l = describes shape mL = describes orientation
what is meant by the heissenberg uncertainty principle? use waves to describe this
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
what is an atomic orbital and what does it describe?
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
squaring the wave function gives ?
the probability of finding an electron in any region of space
what does the radial distribution function describe?
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
how is the RDF derived?
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
on an RDF where is there 0 probability of finding an electron?
at a radial node = radial because in all directions there is 0 probability of finding an electron
what do the peaks on an RDF graph represent?
maximum points represent the most probable distance of finding an electron from the nucleus
as the principal quantum number (n) increases what happens to the number of radial nodes on an RDF?
number of radial nodes increases
what is an angular node?
which quantum number determines number of nodes?
a plane that goes thru an orbital where there is 0 electron probability
defined by quantum number L
describe the shape and number of nodal planes in an s-orbital
circular shape
one phase throughout
0 nodal planes
describe the shape and number of nodal planes in an p-orbital
dumbbell shape, two lobes of opposite phase
1 nodal plane
describe the shape and number of nodal planes in an d-orbital
4 lobes of interchanging phase
two nodal planes because two changes in phase, passes thru a node twice
how many mL values for an s-orbital?
only 1, mL=0 because its circular, only one orientation
how many mL values for an p-orbital?
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
how many mL values for an d-orbital?
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
number of radial nodes on and orbital =
n-1-L
eg in 2p orbital
n = 2
L = 1
radial nodes = 0 as seen on RDF
which type of orbital corresponds to each l value? l = 0 l = 1 l = 2 l = 3
s
p
d
f
what is the fourth quantum number?
what does it represent?
what values can it take?
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
give the Pauli principle
no two electrons in an atom can have the same set of four quantum numbers
each electron has a unique set
give the Aufbau principle
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
give Hund’s rule
when filling degenerate orbitals, electrons of same ms value (same spin) fill in different orbitals, unpaired, keeping repelling electrons as far apart as possible
excited state configuration follow which rules?
excited state configurations only follow Pauli’s principle
not hund’s or aufbau’s
define paramagnetic
species with unpaired electrons
define diamagnetic
species with no unpaired electrons
define and give the symbol for the total spin quantum number
when is this number at a maximum?
S, sum of ms values in a given energy level
at a maximum at the ground state
define and give the symbol for total orbital angular momentum quantum number
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
give the formula for finding the term symbol
superscript: 2S+1 normal script: L
S = sum of ms values
L = sum of mL values of the filled orbitals
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?
1 - orbital singlet - L = 0 - S
3 - triplet - L = 1 - P
5 - pentet - L = 2 - D
7 - septet - L = 3 - F
define symmetry operation
name the three symmetry operations
an action performed on an object by which the object looks the same before and after
rotational axis
mirror plane
centre of inversion
describe the rotational axis symmetry operation
how is it labelled
what is the principle axis
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
describe the mirror plane symmetry operation
how is it labelled
what are the two types of mirror plane? how are they labelled and assigned?
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)
describe the centre of inversion symmetry operation
how is it labelled
how many per molecule
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
2pz orbital
rotational axis?
mirror planes?
C∞
infinite mirror planes
3dx^2-y^2 orbital
rotational axis?
mirror planes?
C2 rotational axis
can be rotated 180° at a time and look the same
2 vertical mirror planes wrt principal axis
define gerade in terms of orbitals
aka symmetric
when the same phases are swapped around wrt the centre of inversion
eg 3dx^2-y^2
define ungerade in terms of orbitals
aka unsymmetric
when opposite phases are swapped wrt the centre of inversion
eg 2pz
what is a symmetric operation
what is an anti-symmetric operation
symmetric = something maps onto itself before and after
anti-symmetric = outcome of the operation is the opposite of the original
is the 2s orbital symmetric or anti-symmetric wrt rotational axis and mirror plane?
it is symmetric because it maps onto itself when symmetry operation are carried out
