The Description of the microscopic world
Previous Lecture: Quantization of light, photonsPhotoelectric effectParticle-Wave dualism
This Lecture: Matter wavesUncertainty Principle Wave functionsStart the atom
MTE3 on Wed 23, 5:30-7:00 pm, Ch 2103 and SH 180, same sessions in each room
Alternate Exams on Wed2:30-4:00 pm6:00-7:30 pmin the Lab room
Send your requests for Alternate Examsby email specifying the class conflict
MTE 3 Contents
Amperes Law and force between wires with current (32.6, 32.8) Faradays Law and Induction (ch 33, no inductance 33.8-10) Maxwell equations, EM waves and Polarization (ch 34, no 34.2) Photoelectric effect (38.1-2-3) Matter waves and De Broglie wavelength (38.4) Atom (37.6, 37.8-9, 38.5-7) Wave function and Uncertainty (39)
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Quantization of light
Light is made of quanta of energy called photons
quantum of energy: E=hf f = frequency of light
Photon is a particle, but moves at speed of light!
This is possible because it has zero mass.
Zero mass, but it does have momentum:
Photon momentum p=E/c (remember U/c for radiation)
Photoelectric effect (1905)
No matter how intense is the light: until the light wavelength passes a certain threshold, no electrons are ejected.
Kmax = h
How much is a quantum of green light?
One quantum of energy for 500 nm light (green)
E = hf = hc
=6.634 1034 Js( ) 3108m /s( )
500 109m= 4 1019J
We need a convenient unit for such a small energy!
1 electron-volt = 1 eV = |charge on electron|x (1 volt) = 1.602x10-19 J
Energy of an electron accelerated in a potential difference of 1 V
In these units,
E(1 green photon) = (4x10-19 J)x(1 eV / 1.602x10-19 J) = 2.5 eV
hc =1240 eV nm so you can use 1240 eV nm/500nm = 2.5 eV
Quiz on photoelectric effectWhich of the following is not true of photoelectric emission?A. increasing the light intensity causes no change in the kinetic energy of photoelectronsB. the max energy of photoelectrons depends on the frequency of light illuminating the metalC. increasing the intensity of the light will increase the KE of photoelectronsD. Doubling the light intensity doubles the number of photoelectrons emitted
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A. is true because the intensity is connected to the number of electrons not to the energy of each onesB. is true because Kmax fC. is false because Kmax depends on fD. Intensity = Power/Area = energy/(time x A) = (Nhf/time x Area)
Is Light a Wave or a Particle?
Wave Electric and Magnetic fields act like waves Superposition, Interference and Diffraction
Particle Photons Photo-electric effect Compton Effect
Sometimes Particle Sometimes Wavedepending on the experiment!
Wave properties of particles
1924 graduate student Nobel Prize in 1929
de Broglie wavelength
De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,...
Should be able to see interference and diffraction for any material particle!!
Wavelength of an electron of 1 eV
de Broglie wavelength
Result: = 1.23 nm
Solve forIf m of particle is large small and wave properties not noticeable
me = 9.1 x 10-31 = 0.511 MeV/c2
De Broglie question
10
Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each have 10 Joules of kinetic energy.
A) bowling > golfB) bowling = golfC) bowling < golf
The largest the mass of the object the less noticeable are
the quantistic effects!Football launched by Brett Favre can go at 30m/s and m = 0.4kg
=hp
=6.6 1034 Js0.4kg 30m /s
= 5.5 1035m
Light properties as a wave
Light has wavelength, frequency, speed f = speed
Light shows interference and diffraction phenomena
Is an Electron a Particle or a Wave? Particle: you can bounce things off them. How would know if electron was a wave?
Look for interference!
This is what we observe like if 1 electron passes through both slits!!
We destroy interference illuminatingto determine the slit they go through
Electron Diffraction: the experiment Parallel beams of mono-energetic electrons on a double slit slit widths
Davisson-Germer experiment
Diffraction of electrons from a nickel single crystal.
Found pattern by heating just by chance. Nichel formed a crystalline structure.
Established that electrons are waves.
54 eV electrons (=0.17nm)
Bright spot: constructive interference
Davisson: Nobel Prize 1937
15
Whats your view of atoms?
16
Hystory of Atoms
Thompsons classical model - raisin-cake (1897): cloud of + charge with embedded e-
Problem: charges cannot be in equilibrium
Planetary model Positive charge concentrated in the nucleus ( 10-15 m) Electrons orbit the nucleus (r~10-10 m)
Problem1: emission and absorption at specific frequenciesProblem2: electrons on circular orbits radiate
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Rutherfords experiment (1911)
Most of the alpha-particles (ionized He nuclei made of 2p+2n) not deflected much but a few bounced back
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Bohrs Model of Hydrogen Atom (1913)Postulate 1: Electron moves in circular orbits where it does not radiate (stationary states)
Postulate 2: radiation emitted in transitions between stationary states
Orbit radius: rn = n2 a0
orbital angular momentum quantized L = mvr = n h/2
Ei E f = hf
Notice: Sometimes fis indicated by
Ef
Ei
Emitted photon has energy hf
a0 = 0.053 nm
En = -13.6 eV/n2
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Emitting and absorbing lightZero energy
n=1
n=2
n=3n=4
E1 = 13.612
eV
E2 = 13.622
eV
E3 = 13.6
32 eV
n=1
n=2
n=3n=4
E1 = 13.612
eV
E2 = 13.622
eV
E3 = 13.6
32 eV
Photon absorbed hf=E2-E1
Photon emittedhf=E2-E1
Ener
gy
axis
20
Question
This quantum system has equally-spaced energy levels as shown. Which photon could possibly be absorbed by this system?
E1=1 eV
E2=3 eV
E3=5 eV
E3=7 eV
Ephoton =hc
=1240 eV nm
A. 1240 nm
B. 413 nm
C. 310 nm
D. 248 nm
2eV 1240 /4132eV 1240 /3102eV 1240 /2484eV 1240 /12404eV 1240 /4134eV =1240 /310
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Why quantized orbits?
Electron is a wave. Its propagation direction is
around circumference of orbit. Wavelength = h / p
Waves on a circular orbit?
Incorporating wave nature of electron gives an intuitive understanding of quantized orbits
22
Standing waves on a string
Fundamental, wavelength 2L/1=2L, frequency f
1st harmonic, wavelength 2L/2=L, frequency 2f
2nd harmonic, wavelength 2L/3,frequency 3f
/2
/2
/2
n =2Ln
Standing wavedisplacement:Boundary conditions:
D(x, t) = 2Asinkxcost
sinkx = 0
sinkL = 0
A guitar vibrates at frequency that depends on string length
freq
uenc
yn=1
n=2
n=3
n=4
Vibrational modes equally spaced in f
. .
.
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Waves in a circular Donut flute
Blow in here
Wavelength
Integer number of wavelengths around circumference.
Otherwise destructive interference occurs when wave travels around ring and interferes with itself
Wind instrument with particular fingering plays a particular pitch (or wavelength)
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Quantization from de Broglie
Circumference
deBroglie:
Result:
giving
L=angular momentum = ,quantized!
= 2rn = n
Integer number wavelengths along circumference of radius rn
=hp
=hmev
2rn =nhmev
mevr = nh2
= nh
Bohr H atom question Peter Flanarys sculpture Wave outside Chamberlin What quantum state of H?
25
Integer number of wavelengths around circumference.
L = pr = n h2
h
= n h2r
2r = n
A. n =2B. n = 3C. n = 4
Lets demonstrate E= -13.6Z2 eV /n2
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F = k Ze2
r2= m v
2
rmvr = nh
k Ze2
r= mv 2
Total energy = kinetic energy + potential energy = kinetic energy + eV
r = k Ze2
mv 2
v = nhmr
Substitute (2) in (1):
(1)
(2)
r = k Ze2m2r2
mn2h2 r = n
2
Zh2
me2k=n2
Z(1.055 1034 )2
9.111031 (1.6 1019)2 9 109=n2
Z0.531010m
r = n2
Za0
E = p2
2m k Ze
2
r=mv 2
2 k Ze
2
r= k Ze
2
2r= k Ze
2
2Zme2kn2h2
= Z 2
n2k 2me4
2h2= 13.6eV Z
2
n2
E = Z2
n2(9 109)2 9.111031 (1.6 1019)4
2 (1.055 1034 )2=
Z 2
n22.2 1018J = Z
2
n213.6eV
a0 = Bohr radius = 0.53 x 10-10 m = 0.53
Z=n. of protons in nucleus of H-like atom
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