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Physics 1 > Quantum Phenomena 2 > Flashcards

Quantum Phenomena 2 Flashcards

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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
Q

degeneracy

A

the existence of more than one distinct state with the same energy

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26
Q

letters used to label states with various values of l

A

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

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27
Q

spectroscopic notation

A

eg: if n=2 and l=1 this is 2p state

n=4,l=0 this is 4s state

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28
Q

n=1

A

k shell

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29
Q

n=2

A

L shell

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30
Q

n=3

A

M shell

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31
Q

n=4

A

N shell

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32
Q

for each n, different values of l correspond to

A

different subshells eg n=2 contains 2s and 2p subshells

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33
Q

to find total number of distinct states in atom

A

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

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34
Q

total angular momentum

A

vector sum of the two components of angular momentum (orbital and spin)

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35
Q

electron carries a charge so its spin creates

A

current loops and a magnetic moment

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36
Q

spin angular momentum

A

possible values sz=+/-h bar/2

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37
Q

magnitude of the spin angular momentum

A

expression equivalent to orbital angular momentum

s=root 1/2 (1/2+1) h bar = root3/4 h bar

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38
Q

ms

A

quantum number to specify electron spin orientation

takes value 1/2 or -1/2

sz=ms h bar

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39
Q

spin up

A

z component is + h bar/2

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40
Q

spin down

A

z component is -h bar/2

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41
Q

in quantum mechanics, the specific Bohr orbits are replaced by

A

probability distributions

electron is point-like, spin is an intrinsic property of particles that mathematically behaves like angular momentum.

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42
Q

total angular momentum

A

defined by J

J=L+S

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43
Q

possible values of the magnitude of the total angular momentum J

A

given in terms of another quantum number j

J=root j(j+1) h bar

j=|l+/-1/2|

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44
Q

l + 1/2 state

A

case which vectors L and S have parallel z components

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45
Q

l-1/2 state

A

L and S have anti-parallel z components

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46
Q

spectroscopic notation using j quantum number

A

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

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47
Q

issues with applying Schrodinger equation to the general atom

A

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)

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48
Q

simplest approximation for Schrodinger to the general atom

A

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

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49
Q

central field approximation

A

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

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50
Q

difference in Schrodinger equation to equation for hydrogen

A

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
Q

radial wave functions and probabilities are different than for hydrogen because of

A

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
Q

why is uncertainty principle needed?

A

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
Q

since we do not get gradual changes in properties, in the ground state of a complex atom

A

all the electrons cannot be in the ground state

54
Q

Pauli exclusion principle

A

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
Q

chemical properties of an atom are determined principally by

A

interactions involving the outermost (valence) electrons

56
Q

chemical behaviour due to electronic configuration

A

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
Q

3d and 4s

A

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
Q

in classical physics we describe the interaction of charged particles in terms of

A

coulomb’s law forces

59
Q

in quantum mechanics, we describe interaction in terms of

A

emission and absorption of photons

eg: two electrons repelling each other. Think of it as one throwing out a photon and other catches

60
Q

uncertainty principle in terms of t and E`

A

ΔEΔt>/= h bar/2

61
Q

virtual photon

A

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
Q

nuclear potential energy between two nucleons

A

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
Q

comparing coulomb potential energy with Yukawa potential energy (e^-r/r0 / r)

A

two functions are similar for small values of r but Yukawa potential energy drops off much more quickly for larger values of r

64
Q

how to predict the approximate lifetime of a particle

A

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
Q

alternative mass unit

A

MeV/c^2 (using E=mc^2)

66
Q

all particles are created through

A

the interactions between other particles and involve the exchange of virtual particles that exist due to borrowed energy allowed by the uncertainty principle.

67
Q

In decreasing order of strength, four interactions are

A
  1. strong interaction
  2. electromagnetic interaction
  3. weak interaction
  4. gravitational interaction
68
Q

spin of photon

A

1

69
Q

spin of graviton

A

2

70
Q

strong interaction

A

responsible for nuclear force and production of pions (and other particles)

71
Q

units of constant f^2

A

energy times distance

72
Q

basis for comparison with other forces

A

dimensionless ratio f^2/h barc

called the coupling constant for the interaction

73
Q

weak interaction

A

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
Q

result of mediating particles for weak force having mass

A

range much shorter than string force so weaker by a factor of 10^9

75
Q

hadrons

A

includes mesons and baryons

76
Q

femions

A

half integer spins

obey exclusion principle

77
Q

bosons

A

zero or integer spins

do not obey the exclusion principle

78
Q

the 6 leptons

A

electron, muon and tau and their associated neutrinos (all has a distinct anti-particle)

79
Q

spin of leptons

A

all have spin 1/2 so are fermions

80
Q

lepton conservation principle

A

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
Q

quarks

A

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
Q

meson

A

quark,anti-quark pair

83
Q

quark charge

A

have magnitude of 1/3e or 2/3e

84
Q

principle of conservation of baryon number

A

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
Q

spin angular momentum in meson

A

components parallel to form a spin-1 meson or antiparallel to form a spin-0 meson

86
Q

spin of baryon

A

form spin-half or spin-3/2 baryon

87
Q

quark number conservation

A

conserved in strong interactions but not in weak interactions

88
Q

Q/e for quarks

A

u,c,t = 2/3
d,s,b =-1/3

89
Q

proton

A

uud

90
Q

neutron

A

udd

91
Q

pi+

A

u antidown

92
Q

quark colour

A

come in three colours - red, green and blue

baryon contains one of each
gluon contains colour-anticolour pair

93
Q

emission and absorption of a gluon by a quark

A

colour conserved

94
Q

gluon exchange process

A

changes the colours of the quarks so that there is always one quark of each colour in every baryon

95
Q

colour of an individual quark

A

changes continually as gluons are exchanged

96
Q

mesons

A

spin 0 or 1
are bosons
there are no stable mesons - they all decay

97
Q

only stable baryon

A

proton

98
Q

criteria for a particle to be its own antiparticle

A

quark content the same

eg: c cbar = c bar c

99
Q

conservation of strangeness

A

conserved in production processes but not usually when strange particles decay individually

general rule is conserved in strong interactions

100
Q

bottomness

A

similar rule to strangeness (conserved in strong)

101
Q

3 families of particles in the standard model

A
  1. 6 leptons
  2. 6 quarks
  3. mediating particles
102
Q

what does the standard model not include

A

gravity

103
Q

why is Higgs boson needed

A

for non-zero masses

104
Q

electroweak theory

A

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
Q

grand unified theories

A

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
Q

supersymmetric theories and theory of everything

A

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
Q

redshift

A

receding sources shifted to longer wavelengths

108
Q

speed of recession

A

found by rearranging equation for wavelength

v=(λ0/λs)^2 -1 /(λ0/λs)^2+1 c

109
Q

parsec

A

1/3600 degree = 1 arcsecond

110
Q

estimation of age of universe from hubble’s law

A

14 billion years

assumes all speeds constant after Big Bang, ignores change in expansion rate caused by gravitational interactions

111
Q

inflating balloon Universe

A

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
Q

taking inflating balloon idea into 3D space

A

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
Q

further an object is

A

the longer it takes light to get to us and the greater the change in R and λ

114
Q

whether universe continues to expand indefinitely depend on

A

average density of the matter in the Universe

denser=lot of gravitational attraction to slow and eventually stop expansion and contract again

115
Q

critical density

A

needed to just stop the expansion continuing indefinitely

116
Q

ways of working out density of universe

A
  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
Q

dark matter

A

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
Q

candidates for dark matter

A
  1. WIMPs - subatomic particles heavier than others
  2. MACHOs - black holes that might form halos around galaxies
119
Q

proof that universe is continuing to expand

A

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
Q

dark energy

A

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
Q

planck length

A

assumed that at high energies and short distances, gravitation unites with the others.

Plancks length is the length as which this happens.

122
Q

planck time

A

time required for light to travel planck length

123
Q

exoergic reactions

A

release energy, heating up the star

Physics 1 (10 decks)

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