7/28/2019 54348510 Modern Physics
1/37
Modern Physics
An excursion into the
development of new ideas
7/28/2019 54348510 Modern Physics
2/37
BBRThings to know
What is a black body
Sketch the spectrum of BB at different
temperatures
Note that
Wavelength at peak intensity (lmax)
decreases with increase temperature
Relationship lmaxis proportion to absolute
Temperature Wiens law (constant 2.898x10-3 m.K)
7/28/2019 54348510 Modern Physics
3/37
Black Body Radiation
http://rh5.clemson.edu/ropermtn/naturalEM.php
Credits
7/28/2019 54348510 Modern Physics
4/37
Total power per unit area is the area under the curve
This increases with temperature
Stefans law gives the relationship (P = eAs T4) I = sT4
Rayleigh-Jean Law
Attempt to derive spectral intensity by considering
standing waves in the cavity
Ultraviolet catastrophe (small wavelength)
Infinite total power
4
2),(
l
l
TkcTI B
7/28/2019 54348510 Modern Physics
5/37
Plancks Solution
Assumptions Cavity Walls are oscillators
Oscillators have range of fundamental
frequencies Oscillators exchange radiation with cavity
Each oscillator of fund. Freq. f can absorb or
emit energy
E = n h f where n = 0,1,2,3
Novel Idea
Led to the correct eqn
1
2),(
5
2
Tk
hc
Be
hcTI
ll
l
7/28/2019 54348510 Modern Physics
6/37
Photoelectric Effect
http://www.physics.umd.edu/perg/qm/qmcourse/NewModel/research
/pe_jcmst/Jcmst00.htm
Credits
http://www.physics.umd.edu/perg/qm/qmcourse/NewModel/researchhttp://www.physics.umd.edu/perg/qm/qmcourse/NewModel/research7/28/2019 54348510 Modern Physics
7/37
Classical Expectations
Light is a wave so its energy must dependon the intensity and independent of itsfrequency.
Emission of photoelectrons should notdepend on the frequency, but on theintensity
KE should depend on its intensity A delay should be expected as electrons
absorb enough energy from the wave
7/28/2019 54348510 Modern Physics
8/37
Graphs
http://library.thinkquest.org/28383/nowe_teksty/htmla/1_8a.html
Credits
http://phycomp.technion.ac.il/~webteach/phys3/ph114053/adler/photo.html
7/28/2019 54348510 Modern Physics
9/37
Observations
No current for frequency below threshold (Cutoff)
frequency. Independent of intensity
The amount of saturation current depends on the light
intensity
The maximum kinetic energy (or stopping voltage ) is
proportional to frequency, independent of intensity
Threshold frequency depends on the metal
Stopping voltage depends only on metal and frequency ,not on intensity
Instantaneous emission of electrons on illumination
7/28/2019 54348510 Modern Physics
10/37
Conclusions
Light consists of discrete photons
Energy of a photon E = hf
Atom absorbs total photon Energy equal to the work function needed
to remove electron from atom
WF depends on the metal used Energy of photon in excess of WF goes
into K.E of electron (Cons. Of Energy)
7/28/2019 54348510 Modern Physics
11/37
Compton Effect
Monochromatic X-rays scattered fromelectrons in Graphite
Observed change in wavelength which
varied with scattering angle (not expected)
)cos(112 ll cm
h
e
7/28/2019 54348510 Modern Physics
12/37
Diagram
7/28/2019 54348510 Modern Physics
13/37
Explanation
Light consists of discrete particles
These particles collide with the stationary
electrons of the graphite
Relativistic energy and momentum are
conserved (similar to particle-particle
collision)
7/28/2019 54348510 Modern Physics
14/37
The Sun emits energy at a rate of 3.9x1026
W.(i) If the radius is 6.96x108 m, determinethe mean temperature.(ii) If the average
wavelength of its radiation is 550 nm,
determine the average number of photons
emitted by the sun in a second.
The wavelength associated with the cutoff
frequency of silver is 325 nm. Find themaximum kinetic energy and the stopping
potential for electrons emitted when silver is
illuminated by ultraviolet light of wavelength
Class Exercises
7/28/2019 54348510 Modern Physics
15/37
Atomic Spectra Sunlight has continuous spectrum
When electric arc passed through gas, the gas
emits a line (emission) spectrum
White light passing through low density gas resultsin absorption spectrum
http://academic.kellogg.cc.mi.us/herbrandsonc/bio111/metabolism.htm
www.prophotolife.com
7/28/2019 54348510 Modern Physics
16/37
Atomic Spectra
http://www.ruf.rice.edu/~mcannon/Research%20Home/Research%20Home%20Pictures/Spectrum.jpg
The Absorption and
emission spectraare characteristic of the
element.
Applications:Study of elements in The
Sun and Stars
Analysis of heavy metal
contamination in food
Neon Signs
Fluorescent lamps
http://www.ruf.rice.edu/~mcannon/Research%20Home/Research%20Home%20Pictures/http://www.ruf.rice.edu/~mcannon/Research%20Home/Research%20Home%20Pictures/7/28/2019 54348510 Modern Physics
17/37
Spectral Series of Hydrogen
RH is Rhdberg constant = 1.097373x107 m-1
nf = 2 Balmer series ( first observed and equation
deduced by school teacher)
nf = 1 Lyman series (UV range)
nf = 3 Paschen Series
Note ni > nf
Note n 0
Equation was empirical (not based on Theory)
22
111
if
Hnn
Rl
7/28/2019 54348510 Modern Physics
18/37
Bohrs Postulates
Atom consists of electrons in circular orbits around
positive nucleus with Newtonian physics applying to
orbit.
The electron can only exist in stationary states. In these
states no energy is emitted
If an electron moves from one stationary state to that of
lower energy a photon is emitted with
E1 - E2 = h f (f is the frequency of the photon) The stationary states are such that angular momentum is
quantised mvr = n h/2(pi) n = 1,2,3,4,.
7/28/2019 54348510 Modern Physics
19/37
Derivation of Bohrs atom
Coulomb Force Centripetal Acceleration
Energy E = PE + KE
Fourth Postulate
Obtain
rn = a n2
a = 52.92 pm En= 13.60 eV /n2
7/28/2019 54348510 Modern Physics
20/37
Class Exercises
Determine the energy required to ionise a
hydrogen atom from the state n= 3. A
photon transitions from n=6 to n= 2.
Calculate the (i) Energy (ii) Wavelength ofthe emitted photon.
Discuss ground state, excited states
Draw the energy level diagram, theionisation energy and the first Bohr radius
for Singly ionised helium (-54.4eV n =1)
7/28/2019 54348510 Modern Physics
21/37
Limitations of Bohr Atom
The Bohr Model
has flat circle but observation shows spherical
electronic orbit
Has minimum angular momentum of h/2
however Lmin = 0 Cannot explain spectra of more complex atoms
Cannot account for the variation of intensity or
splitting of spectral line under magnetic fields Cannot account for the wave nature of the
electron
7/28/2019 54348510 Modern Physics
22/37
Nature of Light
Interference of light seemed conclusiveevidence for wave nature of light
Photoelectric effect discrete localised
energy Compton Effect proved localised p, E
Both confirm particle nature of light
Reduce light intensity in Youngsexperiment
Individual particles detected on screen
Conclude wave-particle duality for light
7/28/2019 54348510 Modern Physics
23/37
De Broglie
Particle has a wavelength = h/p
Observed by Davisson Germer
Interference pattern observed for e, p, n, I2& buckyballs
Applications
Electron & Neutron diffraction used todetermine atomic structure liquids &solid
Electron diffraction used to study surfaces of
solids
7/28/2019 54348510 Modern Physics
24/37
Class Exercises
In the typical television set the electrons
are accelerated through a potentialdifference of 25.0kV. Ignoring relativistic
effect, determine their De Broglie
wavelength and compare it to that of atennis ball served by Serena Williams
(m=56.7 g v= 120 mph)
1 mph = 0.447 m/s
p: www you u e com wa c v= e
http://www.youtube.com/watch?v=ZUI3lhRje_0http://www.youtube.com/watch?v=ZUI3lhRje_07/28/2019 54348510 Modern Physics
25/37
p: www.you u e.com wa c v= e_
Observe Individual particles at detector
Low intensity area has low probabilityof particle
Interference pattern emerge over
time
Deduce e- detected as particles, but their
probability of arrival at a point on thescreen is determined by theinterference of a pair of waves
Image Credit
http://scienceblogs.com/startswithabang/upload/2009/05/
a_tale_of_two_slits/electron_two_slit.jpg
http://www.youtube.com/watch?v=ZUI3lhRje_0http://scienceblogs.com/startswithabang/upload/2009/05/http://scienceblogs.com/startswithabang/upload/2009/05/http://www.youtube.com/watch?v=ZUI3lhRje_07/28/2019 54348510 Modern Physics
26/37
Complimentarity
The double slit experiment with reduced
particle number showed that the electron
is detected as a particle but their arrival at
a point on the screen is determined by theinterference of two waves.
Thus both wave and particle properties are
required to explain the particle.
Cannot observe both properties
simultanteously
7/28/2019 54348510 Modern Physics
27/37
Cover one slit
No interference
http://www.youtube.com/watch?v=DfPeprQ7oGc
http://www.youtube.com/watch?v=DfPeprQ7oGchttp://www.youtube.com/watch?v=DfPeprQ7oGchttp://www.youtube.com/watch?v=DfPeprQ7oGc7/28/2019 54348510 Modern Physics
28/37
Quantum Mechanics
Matter wave?
Is complex
Has everything knowable about particle
Satisfy Schrdinger Equation
Interpretation of wave function
7/28/2019 54348510 Modern Physics
29/37
Poetry in Physics Origin German
Erwin kann mit seinem Psi
kalkulieren wie noch nie.
Doch wird jeder gleich einsehn:
Psi lsst sich nicht recht verstehn
English translation that does not run as
smoothly, but may be easier to understand for
some. :-)
Erwin with his psi can docalculations quite a few.
But one thing has not been seen:
Just what does psi really mean?
7/28/2019 54348510 Modern Physics
30/37
What Psi means
dxxdxxP2
)()(
7/28/2019 54348510 Modern Physics
31/37
Review Standing Wave
Standing wave on a string of length L
l = 2L/n with n = 1,2,3
Note wavelengths are quantised For standing wave y = sin(kx)
Express y in terms of L & n
7/28/2019 54348510 Modern Physics
32/37
Particle in a box
Particle in 1-D box with Infinitely hard walls Infinite potential well
Width of well L
Mass of particle m Particle exists only in certain stationary states
Stationary states are standing waves
Determines the possible wavelengths
L = ln/2 n = 1,2,3
The wave function is standing wave
Wave-function defines the probability distribution
of the particle
7/28/2019 54348510 Modern Physics
33/37
Quantised Energy Levels
By DeBroglie the wavelength determines
the momentum
p determines KE for that state
Recall V= 0 so total E =
Derive E
Only quantised energy possible Note n 0 thus lowest energy state n = 1
ground state energy.
7/28/2019 54348510 Modern Physics
34/37
Wave Function for PiB
Sketch
(x)
||2
7/28/2019 54348510 Modern Physics
35/37
Class Exercises An electron is trapped in an infinite potential well
(particle in 1-D box) 250 pm wide and is in the
ground state. How much energy must it absorb if it is
to jump to the state n = 4. Determine the wavelength
of the photon emitted when it subsequently drops
back down to the n = 2 energy level.
A particle of mass m is in an infinite potential well of
width L. The particle is in the first excited state. Findthe ratio of the probability of finding the particle in a
small interval about point x = L/3 to that of finding
the particle in an interval of equal size around the
point x = L/4.
7/28/2019 54348510 Modern Physics
36/37
Black Body Radiation
Temperature Wiens law
Stefans law
Plancks Solution
Photoelectric Effect
Experiment
Classical Expectations
Graphs
Observations
Einsteins Solution
Compton Effect
Experiment
Results
Explanation
7/28/2019 54348510 Modern Physics
37/37
Atomic Spectra
Emission/Absorption
Spectral Series of Hydrogen Bohrs Postulates
Bohrs atom
De Broglies Hypothesis Quantum Mechanics
Wave function
Wave function interpretation Particle in a box