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Physics 1 > Quantum Phenomena 1 > Flashcards

Quantum Phenomena 1 Flashcards

1
Q

Black body

A

Idealisation
Perfect absorber and perfect emitter of radiation

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2
Q

Analogy for black body

A

Hollow box with a small aperture
Light that enters the box is eventually absorbed
Only allowed certain wavelengths- normal modes

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3
Q

Hotter

A

Higher peak at shorter wavelength

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4
Q

Stefan Boltzmann law

A

I=sigma T^4

I=total intensity

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5
Q

Spectral emittance

A

I(lambda)
Intensity per wavelength interval

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6
Q

Rayleigh jeans law

A

I(lambda)=2pickT/ lambda^4

Agrees with experiment at long wavelength but fails at short

Predicts intensity per wavelength that tends to infinity (UV catastrophe)

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7
Q

Planck hypothesis

A

Assumes oscillator with frequency f can only have energies E=nhf

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8
Q

Planck’s radiation law

A

Used cavity model for black body but his hypothesis that energy was quantised

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9
Q

According to Maxwell Boltzmann distribution, for a system in thermal equilibrium at T

A

A state with energy E has population
nE=Ae^-E/kT

n1/n0=e^-hf/kT

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10
Q

High frequency oscillator

A

Bigger gaps between energy levels so most likely in ground state

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11
Q

From Planck’s law, can derive

A

Wiens law by finding lambda for I(lambda) is minimum
Stefan Boltzmann Law by integrating over lambda
Ray,eigh jeans law

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12
Q

Comments on Planck hypothesis

A

Assumed oscillators emitting radiation could only take quantised values so energy of EM field emitted by black body was quantised

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13
Q

Photoelectric effect

A

Forcing electrons out of surface by shining light

Must supply enough energy to overcome work function

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14
Q

Photoelectric effect experiment

A

Electrons given kinetic energy
Can change intensity of light, frequency of light and potential difference

She notes for diagram but basically just anode and cathode with potential difference across and light shining on

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15
Q

Work done in moving charge q across potential difference

A

E=qV

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16
Q

Work energy theorem

A

Change in electron Ek= Wtot=-eV=eVac

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17
Q

Stopping voltage

A

Vac=-V0 at which no electrons reach the anode

Delta Ek=0-kmax=-eV0

K ax=eV0

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18
Q

Photo current does depend on frequency

A

For given material, light with frequency below threshold frequency produces no photo current, regardless of intensity

Above threshold photo current is proportional to intensity for large positive V

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19
Q

What wave model cannot explain about photoelectric effect

A

Fact there is no time delay before photo current detected (cumulative energy)

Would expect stopping potential to increase with increasing light intensity ie more energy, more Ek so more voltage to stop

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20
Q

Einstein’s photon explanation

A

A beam of light is made up of discrete packages of energy (photons) each with energy E=hf

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21
Q

Work function

A

Amount of energy an electron needs to escape surface

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22
Q

Relating work function and threshold frequency

A

hf the= work function (just E=hf)

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23
Q

Above threshold frequency, maximum kinetic energy of an electron

A

Given by excess energy
eV0=hf- work function

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24
Q

Applications of photoelectric effect

A

Photon momentum eg comets (photons from sun have sufficient energy)

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25
Photon momentum
P=E/c=hf/c=h/ lambda
26
X ray production experiment
Heated cathode accelerate e to anode Electrons crashing into anode emits radiation in the form of X-rays
27
What were X-rays produced as
Bremsstrahlung “breaking radiation” When electrons are slowed abruptly or deflected
28
Bremsstralung spectra
Vertical axis is x ray intensity per unit wavelength Horizontal axis is x ray wavelength Shows that eVac=hf max which is what the photon model predicted
29
Compton scattering
X-ray source Photons incident on target Scattered towards detector
30
Compton scattering Change in wavelength depends on
Angle at which the photons are scattered
31
Compton scattering- wave model predicts
Scattered light has same frequency as incident light
32
Compton scattering Particle model predicts
Scattered light has lower frequency than incident light (think snooker balls)
33
Photons scattered from tightly bound electrons
Undergo a negligible wavelength shift
34
Photons scattered from loosely bound electrons
Undergo a wavelength shift given by eq lambda’ - lambda = h/mc (1-cos theta) **m is mass of electron**
35
Single photon diffraction
Monochromatic light incident on slit Shine onto screen with movable photomultiplier detector - can count individual photons
36
De Broglie wavelength for massive particles
If waves can behave like particles, can particles behave like waves Lambda =h/p=h/mv
37
Relativistic particles
Lambda=h/ gamma mv
38
Electron diffraction experiment
Heated filament emits electrons Electrons accelerated by electrodes and directed at a crystal Electrons strike nickel crystal Detector can be moved to detect scattered electrons at any angle
39
Peak in intensity of scattered electrons is due to
Constructive interference between electron waves scattered by different surface atoms
40
Transmission electron microscope
High voltage supply Cathode where electron beam starts Accelerating anode Condensing lens Objective lens Projection lens Final image in image detector
41
Superposition of two waves
Algebraic sum Spatially finite wave packets are formed
42
Relating wave number and momentum
p=h/ lambda = hk/2 pi = h bar k
43
Heisenberg’s uncertainty principle
Trade off in how well position and momentum can be simultaneously defined
44
Overall size of atom
Of the order of 10^-10m
45
Thomson’s plum pudding model
Electrons embedded in sphere of positive charge Offered an explanation of line spectra (atoms collide, e oscillates around equilibrium at characteristic frequency and emits light at this f)
46
Rutherford’s experiment
Alpha particles emitted by radioactive element such as radium Small holes in pair of lead screens create a narrow beam of alpha particles Alpha strike foil and are scattered by gold atoms Scattered alpha produces a flash of light when it hits scintillation screen, showing direction of scattering
47
Rutherford’s model of the atom
Large angle scattering led Rutherford to develop model where mass and + charge concentrated in nucleus
48
Classical predictions and problems with Rutherford model
Atoms should emit light continuously Should be unstable- if radiating energy should lose energy, orbit get smaller Should emit at all frequencies, further out e less energy, closer = more energy
49
Atoms are stable and therefore must have
Ground level
50
Each wavelength in spectrum corresponds to
Transition between two specific energy levels
51
Bohr model assumption
Allowed energy levels correspond to circular orbits of electron around nucleus ie Fcoulmb=Fcentripetal
52
Quantisation of angular momentum
On=mvnrn=no/2pj = n h bar
53
De broglie wave in an allowed orbit
Standing wave Fixed number of wavelengths should fit into circle
54
Bohr model kinetic and potential energies
Using quantisation of angular momentum and circular orbits gives relationships for radius and velocity Bohr radius given by n=1 Can be used in EK and EP formulae
55
Energy levels predicted by Bohr model
En=Kn+Un
56
Reduced mass of atom
Assuming nucleus at rest Using reduced mass (ie both orbiting centre of mass) gives mr=m1m2/m1+m2
57
Wave function
¥(x,y) Actual symbol is psi, ¥ was closest on keyboard
58
¥(x,t)
Describes distribution of a particle in space
59
|¥( x,t)|^2
Probability distribution function
60
|¥(x,t)|^2 dx
Probability of finding a particle between x and x+dx at time t
61
Mathematical properties of the wave function
Wave function and it’s derivative must be continuous The sum of all probabilities must be 1 (ie integral between negative and positive infinity of erdivative of wave function dx =1)
62
Why is continuity important
Idealised: object hits barrier and instantaneous change in velocity Real: velocity changes quickly and continuously, not abruptly
63
If velocity was discontinuous
Acceleration would be undefined
64
Derivative of wave function
Momentum
65
Second derivative of wave function
Kinetic energy
66
Potential energy diagrams
U(x) against x Looks like valley
67
Particles attracted to places of
Low energy
68
Wave function outside box
0
69
Wave function at edges of box
0 Continuous Si cannot suddenly go to 0 outside box
70
Allowed wavelengths in box
n lambda/ 2=L Integer number of half wavelengths Lambda = 2L/n
71
Time independent Schrodinger equation
Mathematical description of the wave nature of particles and is a statement of conservation of energy KE+PE=Etot
72
H bar
H/ 2pi
73
Capital psi
x and t
74
lower case psi
for just x
75
Simplest example to discuss complete solution to time independent Schrodinger equation
Infinite potential well
76
Potential given by
U= infinity when x is between -infinity and zero U=0 when x is between 0 and L U=infinity when x is between L and infinity
77
Energy barriers at walls is infinite so
Particle cannot escape
78
Potential barrier
Particle does not have enough energy to make it over the barrier Non zero portability of finding it on other side thiugh
79
Analogy: frustrated total internal reflection
EM field falls off at boundary between two media but it is not discontinuous
80
Potential barrier: limiting cases
Zero probability of finding particle where L tends to infinity Continuous wave when l tends to zero
81
Probability as a function of barrier width
Probability walls off exponentially as a function of barrier width
82
Transmission coefficient
When T<<1 T=Ae^-2kL A and k constants given
83
Quantum tunnelling
A particle on the left of the barrier has a non zero probability of being found on the right of the barrier, not possible classically
84
Scanning tunnelling microscope
Sharp needle kept at positive potential relative to surface If needle close enough to surface electrons can tunnel across and be detected as current Needle moves across surface and perpendicular to it to maintain constant tunnelling current
85
Alpha decay
Made possible by quantum tunnelling Potential seen by alpha in nucleus is due to strong nuclear force Alpha particle does not have sudpfficient energy classically

Physics 1 (10 decks)

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