Introduction to modern physics - FSU Physics Department

Introduction to modern physics:
Physics of the 20 th and 21 st centuries
Lectures:
• Quantum physics
• Nuclear and particle physics
• some condensed matter physics
• Relativity – special, general
• Cosmology
Lab experiments: some of the following:
• Earth’s magnetic field
• Geiger Müller counter, half life measurement
• operational amplifier
• mass of the K 0 particle
• e/m of electron
• Franck-Hertz experiment
• Hall effect
• Planck’s constant from LED’s
Homework problems
problem solving, modeling, simulations
website http://www.physics.fsu.edu/courses/Summer13/YSP
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Quantum physics
(quantum theory, quantum mechanics)
Part 1:
2

Outline
Introduction
Problems of classical physics
emission and absorption spectra
Black-body Radiation
• experimental observations
• Wien’s displacement law
• Stefan – Boltzmann law
• Rayleigh - Jeans
• Wien’s radiation law
• Planck’s radiation law
photoelectric effect
• observation
• studies
• Einstein’s s explanation
Summary
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Question: What do these have in common?
• lasers
• solar cells
• transistors
• computer chips
• CCDs in digital cameras
• Ipods
• superconductors
• .........
Answer:
• They are all based on the quantum physics
discovered in the 20th century.
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Why Quantum Physics?
“Classical l Physics”:
• developed in 15 th to 20 th century;
• provides very successful description of “every
day, ordinary objects”
o motion of trains, cars, bullets,….
o orbit of moon, planets
o how an engine works,..
• subfields: mechanics, thermodynamics,
electrodynamics,
• Quantum Physics:
o developed early 20 th century, in response to
shortcomings of classical physics in describing certain
phenomena (blackbody radiation, photoelectric effect,
emission i and absorption spectra…)
o describes “small” objects (e.g. atoms and their
constituents)
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“Classical” vs “modern” physics
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Quantum Physics
QP is “weird and counterintuitive”
But:
o “Those who are not shocked when they first come
across quantum theory cannot possibly have
understood it” (Niels Bohr)
o “Nobody feels perfectly comfortable with it “
(Murray Gell-Mann)
o “I can safely say that nobody understands quantum
mechanics” (Richard Feynman)
o QM is the most successful ssfu theory ever developed by
humanity
o underlies our understanding of atoms, molecules,
condensed d matter, nuclei, elementary particles
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o Crucial ingredient in understanding of stars, …

Features of QP
Quantum physics is basically the recognition
that there is less difference between waves
and particles than was thought before
key insights:
o light can behave like a particle
o particles (e.g. electrons) are indistinguishable
i i o particles can behave like waves (or wave
packets)
o waves gain or lose energy only in "quantized
amounts“
o detection (measurement) of a particle
wave will change suddenly into a new wave
o quantum mechanical interference – amplitudes
add
o QP is intrinsically probabilistic
o what you can measure is what you can know
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emission spectra
continuous spectrum
o solid, liquid, or dense gas emits continuous
spectrum of electromagnetic radiation
(“thermal radiation”);
o total intensity and frequency dependence
of intensity change with temperature
(Kirchhoff, Bunsen, Wien, Stefan,
Boltzmann, Planck)
line spectrum
o rarefied gas which is “excited” by heating,
or by passing discharge through it, emits
radiation consisting of discrete wavelengths
(“line spectrum”)
o wavelengths of spectral lines are
characteristic of atoms
9

Emission spectra:
11

Absorption spectra
• first seen by Fraunhofer in light from Sun;
• spectra of light from stars are absorption
spectra (light emitted by hotter parts of
star further inside passes through colder
“atmosphere” of star)
• dark lines in absorption spectra match
bright lines in discrete emission spectra
• Helium discovered by studying Sun's
spectrum
• light from continuous-spectrum source
passes through colder rarefied gas before
reaching observer;
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Fraunhofer spectra
13

Spectroscopic studies
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Kinetic theory of heat
Molecules are in constant random motion,
Average kinetic energy depends only on temperature
In thermal equilibrium, energy is equally shared
between all “degrees of freedom” of the possible
motions, ons, ave. kinetic energy per degree of freedom
=
= ½k B T (k B = Boltzmann’s constant)
Degrees of freedom: translational motion in 3
dimensions i has 3 degrees of freedom (dof);
Rotational and vibrational motion: nb. of dof depends
on number of atoms and their configuration in
molecule
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0th law of thermodynamics
• between bodies of different temperature (i.e. of different
average internal thermal energy), heat will flow from the
body of higher temperature to the body of lower
temperature until the temperatures of the two bodies are
the same;
• then the bodies are in “thermal equilibrium”
• two bodies are in thermal equilibrium (at same temperature)
if there is no heat flow between them;
• corollary: if two bodies are in thermal equilibrium with a
third body, then they are in thermal equilibrium with each
other.
• can use thermometer to compare temperature
• note:
o observation only shows that temperatures equalize -
heat flow is hypothesis
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temperature
Temperature:
• was measured long before it was understood;
• Galilei (around 1592): “device to measure degree of
hotness”; inverted narrow-necked flask, warmed in
hand, put upside down into liquid; liquid level
indicates temperature; OK, but not calibrated.
• Hooke, Huygens, Boyle (1665): “fixed points” -
freezing or boiling point of water;
• C. Renaldini (1694): use both freezing and boiling
point
• Modern point of view: temperature is measure of
kinetic energy of random motion of molecules,
atoms,..
• http://en.wikipedia.org/wiki/Temperature
ped / emperature
• http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html
• http://eo.ucar.edu/skymath/tmp2.html
• http://www.visionlearning.com/library/module_viewer.php?mid=48
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Thermal energy, heat, temperature
observation of ”Brownian motion” ” (1827):
• small seeds (e.g. burlap) suspended in liquid show erratic
motion (“random motion”)
• http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html
h i i i / l ss s/109N/m st l ts/b i /b i html
• http://www.aip.org/history/einstein/brownian.htm
kinetic theory of heat (Boltzmann, Maxwell,...)
• heat is a form of energy;
• internal energy = thermal energy of material bodies is
related to random motions of molecules or atoms
• temperature is a measure of this internal energy .
• explanation of Brownian motion: Albert Einstein (1905):
calculated speed of “diffusion” from kinetic theory of
heat - found in agreement with experimental
measurements
• strong support for atomic picture of matter
• http://en.wikipedia.org/wiki/Theory //en.wikipedia.org/wiki/Theory_of_heatof heat
• http://en.wikipedia.org/wiki/Kinetic_theory
• http://www.vias.org/physics/bk2_03_02.html
• http://www.youtube.com/watch?v=-n90pfbiBJE
• http://galileo.phys.virginia.edu/classes/252/kinetic_theory.html
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Fahrenheit, Celsius scale
Fahrenheit scale:
• Gabriel Daniel Fahrenheit (Danzig, 1686-1736),
glassblower and physicist;
o reproducible thermometer using mercury (liquid
throughout range) (around 1715)
o 0 point: lowest temperature of winter of 1709, (using mix
of water, ice, salt −17.8 8 °C )
o 96 o = body temperature (96 divisible by 12, 8),
o water freezes at 32 o F, boils at 212 o F
o
http://inventors.about.com/od/tstartinventions/a/History-Of-The-Thermometer.htmnt t tin nti ns/ /Hist m m t htm
Celsius scale:
• Anders Celsius (Swedish astronomer, 1701 - 1744)
• 0 o C = ice point (mixture of water and ice at 1 atm)
• 100 o C = boiling point of water at 1 atm. (1742)
relation between Fahrenheit and Celsius degrees:
• T C
= (5/9)(T F
- 32 ) , T F
= (9/5)T C
+ 32
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Temperature (2)
thermodynamic temperature scale
• (absolute, Kelvin scale)
• pressure vs temperature t of gas at constant t volume
and volume vs temperature of gas at constant
pressure extrapolate to zero at - 273.15 o C
• this is “absolute zero”
• unit: Kelvin
• Size of unit of Kelvin scale = that of Celsius scale,
only shift of zero-point
• This is the temperature scale which is used in most of
physics
• http://en.wikipedia.org/wiki/Kelvin
• http://abyss.uoregon.edu/~js/glossary/temperature_scale.html
edu/~js/glossary/temperature scale html
• http://lamar.colostate.edu/~hillger/temps.htm
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Range of temperatures
• Universe 5×10 −44 s after the Big Bang: T 1.4×10 32 K
• core of hottest stars, 410 9 K; seems maximum now
• hydrogen bomb ignites at , 410 7 K;
• interior of Sun , 1.510 6 K;
• plasma 10 5 K;
• 10 5 K : clouds of atoms, ions, e, occasional molecule;
• 5800 K: surface of the Sun; 5000 K: cool spots at surface of the
Sun; evidence for some molecules;
• 3000 K: water steam: about 1/4 of water molecules ruptured into
atoms;
• 2800 K: W light bulb filament;
• 2000 K: molten lava;
• 1520 o C: iron melts; 327 o C: lead melts;
• 100 o C (373.15 K): water boils;
• 252 K (-21.1 o C = 5.8 o F): temp. of salt-ice saltwater mix;
• 234 K: mercury freezes; 194 K: dry ice freezes;
• 77 K: nitrogen boils
• 4 K: helium boils.
• ;
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Thermal radiation
thermal radiation = e.m. radiation emitted by a body by virtue
of its temperature
spectrum is continuous, comprising all wavelengths
thermal radiation formed inside body by random thermal
motions of its atoms and molecules, repeatedly absorbed and
re-emitted on its way to surface original character of
radiation obliterated spectrum of radiation depends only on
temperature, not on identity of object
amount of radiation actually emitted or absorbed depends on
nature of surface
good absorbers are also good emitters (why??)
• http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/absrad.html
html
• http://casswww.ucsd.edu/archive/public/tutorial/Planck.html
• http://panda.unm.edu/Courses/Finley/P262/ThermalRad/ThermalRad.html
• http://csep10.phys.utk.edu/astr162/lect/light/radiation.html
• http://www.youtube.com/watch?v=CDncSyDvpdQ
• http://www.enotes.com/topic/Kirchhoff's_law_of_thermal_radiation
• http://ip.anndannenberg.com/IPHandouts/Heattransfernotes.pdf
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warm bodies emit radiation
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Black-body radiation
“Black body”
• perfect absorber
o ideal body which absorbs all e.m. radiation that
strikes it, any wavelength, any intensity
o such a body would appear black “black
body”
• must also be perfect emitter
o able to emit radiation of any wavelength at any
intensity i -- “black-body b radiation”
i “Hollow cavity” (“Hohlraum”) kept at
constant T
o hollow cavity with small hole in wall is good
approximation to black body
o thermal equilibrium inside, radiation can escape
through hole, looks like black-body radiation
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Studies of radiation from hollow cavity
In 2 nd half of 19 th century,
behavior of radiation within a
heated cavity studied d by many
physicists, both theoretically
and experimentally
Experimental findings:
• spectral density ρ(f,T)
(= energy per unit volume
per unit frequency) of the
heated cavity depends on
the frequency f of the
emitted light and the
temperature T of the cavity
and nothing else.
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Thermal radiation
“Global description”, i.e without frequency dependence:
• Descriptions successful, i.e. in agreement with observations
total power output of black body: Stefan-Boltzmann law:
• For an “ideal” radiator (“black body”)
),
total emitted power (per unit emitting area), P/A
P/A = σ·T 4 σ = 5.672 · 10 -8 W m -2 K -4
(Josef Stefan, Ludwig Boltzmann 1879, 1884)
• http://csep10.phys.utk.edu/astr162/lect/light/radiation.htmlphys edu/astr162/lect/light/radiation html
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html
http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html
Wien’s displacement law (1893)
peak vs temperature:
max ·T = C, C= 2.898 · 10 -3 mK
inverse relationship between the wavelength of the peak of the
emission i of a black body and its temperature when expressed as
a function of wavelength
• http://en.wikipedia.org/wiki/Wien's_displacement_law hyperphysics.phy-
astr.gsu.edu/hbase/quantum/wien2.html
html
http://scienceworld.wolfram.com/physics/WiensDisplacementLaw.html
http://webphysics.davidson.edu/faculty/dmb/blackbody/Wiendemo.html
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Intensity vs frequency
Wilhelm Wien (1896)
(f, T) = af 3 exp(-bf/T) bf/T),
(a and b constants).
• OK for high frequency but fails for low frequencies
• http://en.wikipedia.org/wiki/Wien_approximation
http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf
m p p http://bado-shanai.net/map%20of%20physics/mopWienslaws.htm
http://physics.info/planck/
Rayleigh-Jeans Law (1900)
(f,T) = af 2 T (a = constant)
• (constant found to be = 8k/c
3 by James Jeans, in 1906)
• OK for low frequencies, but “ultra – violet catastrophe” t at high h
frequencies, i.e. intensity grows f 2 for f
(corresponding to limit of wavelength 0)
• http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html http://hyperphysics.phyastr.gsu.edu/hbase/mod6.html
http://scienceworld.wolfram.com/physics/Rayleigh-JeansLaw.html
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Ultraviolet catastrophe
(Rayleigh-Jeans)
29

Planck’s quantum hypothesis
Max Planck (Oct 1900) found formula that
reproduced the experimental results
2
8
f
( f, T) E
3 osc
c
hf
Eosc
hf / kT
e 1
is the average
energy of a cavity
“oscillator”
derivation from classical thermodynamics, but
required assumption that oscillator energies can
only take specific values E = 0, hf, 2hf, 3hf, …
for a multi-state system of particles in thermal
equilibrium, probability for particle to be in state
with energy E,
P(E) = (1/Z)e -E/kT (“Boltzmann factor” )
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Black-body radiation spectrum
Measurements of
Lummer and Pringsheim
(1900)
calculation
schematisch
32

Consequences of Planck’s hypothesis
oscillator energies E = nhf, n = 0,1,…;
• h = 6.626626 10 -34
Js = 4.13 10 -15 eV·s
now called Planck’s constant
• oscillator’s s energy can only change by
discrete amounts, absorb or emit energy
in small packets –“quanta”;
E quantum = hf
• average energy of oscillator
= hf/(e x – 1) with x = hf/kT;
for low frequencies get classical result
= kT, k = 1.38 · 10 -23 J·K -1
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Frequencies in cavity radiation
cavity radiation = system of standing waves produced by
interference of e.m. waves reflected between cavity walls
many more “modes” per wavelength band
at high frequencies (short wavelengths)
than at low frequencies
• for cavity of volume V, n = (8πV/ 4 )
or n = (8πV/c 3 ) f 2 f
if energy continuous, get equipartition, = kT all modes
have same energy spectral density grows beyond bounds as
f
If energy related to frequency and not continous (E = nhf),
the “Boltzmann factor” e
-E/kT
leads to a suppression of high
frequencies
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Problems
estimate Sun’s surface temperature assuming:
• Earth and Sun are black bodies
• Stefan-Boltzmann law
• Earth in energetic equilibrium
(i.e. rad. power absorbed b = rad. power
emitted) , mean temperature T = 290K
• Sun’s angular size Sun = 32’
show that for small frequencies, Planck’s average
oscillator energy yields classical equipartition result
= kT
show that for standing waves on a string, number of
waves in band between and + is n = (2L/ 2 )
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Summary
classical physics explanation of black-body
radiation failed
Planck’s ad-hoc assumption of “energy quanta”
of energy E quantum = h, modifying Wien’s radiation
law, leads to a radiation spectrum which agrees with
experiment.
old generally accepted principle p of “natura non facit
saltus” violated
Opens path to further developments
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