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Quantum Phenomena 2 Flashcards

1
Q

problems with Rutherford’s model

A

if electrons orbited around the nucleus, they should have lost energy doing so and circle down into the nucleus.

As electrons orbited down, their angular speeds would change continuously so energy emitted would constantly change frequency but spectra has distinct lines?

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2
Q

Bohr’s solution

A

electrons orbit nucleus at fixed distance and do not radiate energy.

definite energy associated with each available stable orbit and electron only emits energy when it moves from one orbit to another.

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3
Q

energy emitted in an electron transition is in the form of

A

a photon

Ephton=hf=Einitial-Efinal

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4
Q

angular momentum of the electron

A

an integer multiple of h/2pi ie quantised

L=mvr=nh/2pi (n=1,2,3…)

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5
Q

principle quantum number

A

the value of n for each orbit

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6
Q

for the radius to remain constant in the Bohr model

A

electrostatic force must provide exactly the radial motion force

ie Fc=Fe

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7
Q

equations for kinetic energy for an electron in a given orbit

A

Fc=Fe

rearrange for v and plug into 1/2mv^2

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8
Q

taking the Bohr model further

A

applying Schrodinger equation to find the wave functions for states with definite energy values for the hydrogen atom.

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9
Q

issue with mass, strictly speaking

A

the electrons do not orbit the proton, they both orbit their common centre of mass.

use reduced mass.

mr=m1m2/m1+m2

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10
Q

spherical coordinates to solve Schrodinger equation

A

r, θ, Φ

r- distance of orbiting electron from nucleus
θ - angle the line 0-r makes with z-axis
Φ - angle the same line makes with the y-axis

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11
Q

why is spherical coordinate system useful?

A

potential energy only depends on r

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12
Q

solutions of Schrodinger equation

A

obtained by separating variables involved

wave function expressed as a product of three functions
(R depends only on r etc)

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13
Q

how are physically acceptable solutions to Schrodinger obtained?

A

applying boundary conditions

R(r) tends to 0 as r increases
phi(phi) must be periodic

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14
Q

solving with boundary conditions

A

produces relation for energy levels, identical to those predicted to the Bohr model

En=-13.60eV/n^2

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15
Q

orbital angular momentum

A

vector quantity, denoted by L

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16
Q

magnitude of orbital angular momentum

A

magnitude can take values determined by theta being finite

possible values L=root l(l+1) h bar

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17
Q

orbital angular momentum quantum number

A

l
an integer, l=0,1,2,..,n-1

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18
Q

permitted values that a component of the vector L can take are determined by

A

the requirement that phi is periodic.

eg: z component, Lz=mlhbar

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19
Q

orbital magnetic quantum number

A

ml

also called orbital angular momentum projection quantum number

takes values m=-l,…,0,…,l

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20
Q

comparing Lz with L itself

A

the component Lz can never be quite as big as L itself (unless both zero)

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21
Q

minimum angle between the overall angular momentum vector and the z-axis

A

theta l = arccosLz/L (draw out to show)

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22
Q

if we knew the direction of the orbital angular momentum, then we could

A

define that direction to be the z-axis i.e. Lz=L

only in the x-y plane

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23
Q

if all motion of the particle is in the x-y plane

A

z component of linear momentum would be zero and carry no uncertainty.

therefore, from the uncertainty principle, uncertainty in Z would be infinite

this is impossible so conclude that we never know precise direction

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24
Q

wave functions for the hydrogen atom are determined by

A

the values of the three quantum numbers: n,l,ml

n determines energy values En
l sets magnitude of the orbital angular momentum
ml fixes the value of the z-component of angular momentum

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25
degeneracy
the existence of more than one distinct state with the same energy
26
letters used to label states with various values of l
l=0 s state l=1 p state l=2 d state l=3 f state l=4 g state l=5 h state and so on, alphabetically
27
spectroscopic notation
eg: if n=2 and l=1 this is 2p state n=4,l=0 this is 4s state
28
n=1
k shell
29
n=2
L shell
30
n=3
M shell
31
n=4
N shell
32
for each n, different values of l correspond to
different subshells eg n=2 contains 2s and 2p subshells
33
to find total number of distinct states in atom
eg: n=4 list all possible l values and then ml values count the number of possible ml states for each l and add up
34
total angular momentum
vector sum of the two components of angular momentum (orbital and spin)
35
electron carries a charge so its spin creates
current loops and a magnetic moment
36
spin angular momentum
possible values sz=+/-h bar/2
37
magnitude of the spin angular momentum
expression equivalent to orbital angular momentum s=root 1/2 (1/2+1) h bar = root3/4 h bar
38
ms
quantum number to specify electron spin orientation takes value 1/2 or -1/2 sz=ms h bar
39
spin up
z component is + h bar/2
40
spin down
z component is -h bar/2
41
in quantum mechanics, the specific Bohr orbits are replaced by
probability distributions electron is point-like, spin is an intrinsic property of particles that mathematically behaves like angular momentum.
42
total angular momentum
defined by J J=L+S
43
possible values of the magnitude of the total angular momentum J
given in terms of another quantum number j J=root j(j+1) h bar j=|l+/-1/2|
44
l + 1/2 state
case which vectors L and S have parallel z components
45
l-1/2 state
L and S have anti-parallel z components
46
spectroscopic notation using j quantum number
superscript is the number of possible spin orientations capital P indicates state with l=1 (or S, D etc) subscript is the value of j eg: 2P1/2
47
issues with applying Schrodinger equation to the general atom
complexity is so extreme that it has not been solved for even Helium. number of variables of interaction is too large (electrons with each other and electrons with every proton)
48
simplest approximation for Schrodinger to the general atom
assume that when an electron moves, it ignores the effects of all other electrons and only feels the influence of the nucleus, which is taken as a point charge. now have nuclear charge of Ze so every factor of e^2 in wave function is replaced by Ze^2
49
central field approximation
better option] think of all the electrons together as making up a charge cloud that is on average spherically symmetric take each electron to be moving in field due to nucleus and averaged out cloud
50
difference in Schrodinger equation to equation for hydrogen
1/r potential energy function is replaced by different function U(r) (only a function of r so phi and theta are exactly as before) all quantum numbers and z-components same as before
51
radial wave functions and probabilities are different than for hydrogen because of
change in U(r) so the energy levels are no longer given by previous equation in general, energy of a state now depends on both n and l rather than just n
52
why is uncertainty principle needed?
would expect gradual changes as more electrons in each atom but properties of elements vary widely in order of atomic number eg: halogens form compounds by acquiring additional electron, alkali metals lose electrons and noble gases do not form compounds at all
53
since we do not get gradual changes in properties, in the ground state of a complex atom
all the electrons cannot be in the ground state
54
Pauli exclusion principle
no two electrons can occupy the same quantum-mechanical state in a given system i.e. no two electrons in an atom can have the same values of all four quantum numbers n,l,ml,ml
55
chemical properties of an atom are determined principally by
interactions involving the outermost (valence) electrons
56
chemical behaviour due to electronic configuration
just the same as higher/advanced higher chem eg: noble gas filled shell, alkali metals 'noble gas plus one', halogens 'noble gas minus one'
57
3d and 4s
3d and 4s have similar energies in potassium, additional electron goes to 4s state as energy lower than 3d (transition metals) (same again starting Z=57 and Z=89)
58
in classical physics we describe the interaction of charged particles in terms of
coulomb's law forces
59
in quantum mechanics, we describe interaction in terms of
emission and absorption of photons eg: two electrons repelling each other. Think of it as one throwing out a photon and other catches
60
uncertainty principle in terms of t and E`
ΔEΔt>/= h bar/2
61
virtual photon
uncertainty allows the creation of a photon with energy ΔE provided it lives no longer than Δt. (like borrowing energy from a bank, you can have it as long as you pay back within time frame)
62
nuclear potential energy between two nucleons
in this equation, f represents strength of the interaction and r0 is the range r is the distance at which the potential is measured
63
comparing coulomb potential energy with Yukawa potential energy (e^-r/r0 / r)
two functions are similar for small values of r but Yukawa potential energy drops off much more quickly for larger values of r
64
how to predict the approximate lifetime of a particle
must live long enough, Δt to travel distance comparable to range of nuclear force. This range is of the order 1.5fm. Assuming speed is comparable to c, its lifetime must be of the order 5*10^24s
65
alternative mass unit
MeV/c^2 (using E=mc^2)
66
all particles are created through
the interactions between other particles and involve the exchange of virtual particles that exist due to borrowed energy allowed by the uncertainty principle.
67
In decreasing order of strength, four interactions are
1. strong interaction 2. electromagnetic interaction 3. weak interaction 4. gravitational interaction
68
spin of photon
1
69
spin of graviton
2
70
strong interaction
responsible for nuclear force and production of pions (and other particles)
71
units of constant f^2
energy times distance
72
basis for comparison with other forces
dimensionless ratio f^2/h barc called the coupling constant for the interaction
73
weak interaction
responsible for beta decay (eg neutron into proton, electron and anti-neutrino) W+,W- and Z0 are short lived, have spin 1, have mass
74
result of mediating particles for weak force having mass
range much shorter than string force so weaker by a factor of 10^9
75
hadrons
includes mesons and baryons
76
femions
half integer spins obey exclusion principle
77
bosons
zero or integer spins do not obey the exclusion principle
78
the 6 leptons
electron, muon and tau and their associated neutrinos (all has a distinct anti-particle)
79
spin of leptons
all have spin 1/2 so are fermions
80
lepton conservation principle
3 lepton numbers Le,Lµ and L𝜏 electron and electron neutrino have Le=1 and antiparticles have Le=-1 same idea for muon and tau *in all interactions, each lepton number is separately conserved**
81
quarks
spin half fermions that make up protons and neutrons (and other baryons/mesons) each baryon consists of three quarks and anti baryon consists of three anti quarks
82
meson
quark,anti-quark pair
83
quark charge
have magnitude of 1/3e or 2/3e
84
principle of conservation of baryon number
analogous to conservation of lepton number each quark has a value 1/3 for its baryon number and each anti quark has -1/3 **conserved in all interactions**
85
spin angular momentum in meson
components parallel to form a spin-1 meson or antiparallel to form a spin-0 meson
86
spin of baryon
form spin-half or spin-3/2 baryon
87
quark number conservation
conserved in strong interactions but not in weak interactions
88
Q/e for quarks
u,c,t = 2/3 d,s,b =-1/3
89
proton
uud
90
neutron
udd
91
pi+
u antidown
92
quark colour
come in three colours - red, green and blue baryon contains one of each gluon contains colour-anticolour pair
93
emission and absorption of a gluon by a quark
colour conserved
94
gluon exchange process
changes the colours of the quarks so that there is always one quark of each colour in every baryon
95
colour of an individual quark
changes continually as gluons are exchanged
96
mesons
spin 0 or 1 are bosons there are no stable mesons - they all decay
97
only stable baryon
proton
98
criteria for a particle to be its own antiparticle
quark content the same eg: c cbar = c bar c
99
conservation of strangeness
conserved in production processes but not usually when strange particles decay individually general rule is conserved in strong interactions
100
bottomness
similar rule to strangeness (conserved in strong)
101
3 families of particles in the standard model
1. 6 leptons 2. 6 quarks 3. mediating particles
102
what does the standard model not include
gravity
103
why is Higgs boson needed
for non-zero masses
104
electroweak theory
at low energies, electromagnetic and weak interactions behave differently due to the mass difference between the photons and the bosons this disappears at high energy and merges into single interaction
105
grand unified theories
assumes that at very high energies, strong interaction will merge with electroweak interaction some theories predict protons are not stable which violates conservation of baryon number
106
supersymmetric theories and theory of everything
ultimate goal to combine all four under one theory. Need a space-time continuum with more than 4 dimensions with extra dimensions rolled up into tiny structure we do not notice
107
redshift
receding sources shifted to longer wavelengths
108
speed of recession
found by rearranging equation for wavelength v=(λ0/λs)^2 -1 /(λ0/λs)^2+1 c
109
parsec
1/3600 degree = 1 arcsecond
110
estimation of age of universe from hubble's law
14 billion years assumes all speeds constant after Big Bang, ignores change in expansion rate caused by gravitational interactions
111
inflating balloon Universe
as balloon gets bigger, radius gets bigger but the specific coordinates of a point on the surface do not change distance between points increases, as does the rate of change of distance
112
taking inflating balloon idea into 3D space
need the curvature of space scale factor R describes size of the universe, R0 denotes scale factor today (without subscript is any value past, present or future)
113
further an object is
the longer it takes light to get to us and the greater the change in R and λ
114
whether universe continues to expand indefinitely depend on
average density of the matter in the Universe denser=lot of gravitational attraction to slow and eventually stop expansion and contract again
115
critical density
needed to just stop the expansion continuing indefinitely
116
ways of working out density of universe
1. counting number of galaxies in patch of sky, average mass of star and average number of stars in average galaxy 2. study motion of galaxies within galaxy clusters by monitoring redshift to get an idea of speeds. Speeds related to gravitational force exerted on each galaxy by other cluster members which is related to mass.
117
dark matter
average density of all matter in the universe is around 26% of critical density. Average density of luminous matter is only 4% majority of the Universe does not emit electromagnetic radiation - i.e. dark matter
118
candidates for dark matter
1. WIMPs - subatomic particles heavier than others 2. MACHOs - black holes that might form halos around galaxies
119
proof that universe is continuing to expand
if expansion was slowing, must have been faster in past so would expect very distant galaxies to have greater redshifts than predicted by Hubble law
120
dark energy
explains why rate of expansion is increasing despite gravitational attractions energy density of dark energy is nearly 3 times greater than that of matter so expansion will never stop and universe will never contract
121
planck length
assumed that at high energies and short distances, gravitation unites with the others. Plancks length is the length as which this happens.
122
planck time
time required for light to travel planck length
123
exoergic reactions
release energy, heating up the star

Physics 1 (10 decks)

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