physics 214 4: introduction to quantum physics blackbody radiation and planck’s hypothesis the...
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Physics 214Physics 214
4: Introduction to Quantum Physics
•Blackbody Radiation and Planck’s Hypothesis•The Photoelectric Effect•Compton Effect•Atomic Spectra•The Bohr Quantum Model of the Atom
•Classical Physics•Material objects obey Newtons Laws of Motion•Electricity and Magnetism obey Maxwells Equations•Position and momentum are defined at all times •Initial Position and momentum plus knowledge of all forces acting on system predict with certainty the position and momentum at all later times.
•Could not explain•Black Body Radiation•Photo Electric Effect•Discrete Spectral Lines
Blackbody Radiation and Planck’s Hypothesis
Any object with a temperature T>0 K radiates away thermal energy through
the emission of electromagnetic radiation
Classical explanationheat causes accelerated charges (Maxwell like distribution of accelerations) that emit
radiation of various frequencies
Incandescent Spectra produced from Thermal Radiation
frequency
intensity
Wiens Displacement Law
maxT2.898 mK
Rayleigh-Jeans Law
I(,T)2ckT4
Intensity of radiation of wavelength at temp T
However this only agrees with experiment at long
Lim 0
I(,T) Ultraviolet Catastrophe
( total energy density)
Planck ' s Function
I ,T 2hc2
5 ehckT 1
h 6.626 10 34 Js Planck 's Constant
Planck’s Assumptions
Oscillating molecules that emit the radiation only have discrete energies
En = nhn = quantum number
En = energy of quantum state n of molecule
Molecules emit or absorb energy in discrete units of light called QUANTA
E1
h
E2
E2E1
h
The Photoelectric Effect
LightElectron
VG
A
•A is maintained at a positive potential by battery. •IG = 0 until monochromatic light of certain is incident
V
I
-V0
plate A has negative potential Stopping Potential
high intensity light
low intensity light
•When A is negative only electrons having K.E. > eV0 will reach A, independent of light intensity
•Maximum K.E. of ejected electrons Kmax= eV0
1. No electrons ejected if c (cut off frequency )
2. If c
the number of photo electrons light intensity
3. Kmax is independent of light intensity
4. Kmax
as
5. Electrons are emitted instantaneously even at low
light intensities
Observed Properties
Wave theory of light does not predict such properties
Einstein explained this by the hypothesis
that light is quantized in
energy packets = QUANTA with energy E = h
he called such quanta PHOTONS .
The intensity of the light is proportional to the number
of such quanta i .e.
I nh
In order for electrons to be emitted they must pass through
surface . use amount of energy to overcome surface
barrier Ionization Potential Work Function
Kmax
h - = h h c
1 . Kmax
h - ; so Kmax
depends on
2 . h ; for emission of electrons
3 . h - only depends on not on intensity
4. Kmax
as
5 . single electrons are excited by light
(not many gradually) instantaneous emission
Einsteins Theory Predicts
Kmax
c
slope = h
Kmax = h
Compton Effect
scattered photon
scattered electron
More Evidence that light is composed of particles
Observed scattering intensity I
I = I , ;
incident 0 scattered - this contradicts classical theory
= - 0
Compton (1923 ) suggested treating photon as particle
E = h =hc
The Special Theory of Relativity gives E = pc
p is the magnitude of the momentum of the photon
pc =hc
p =
h
Etot
= ptot
= 0
=hm
ec
1 cos
; ; Ephoton
during collision
Compton Wavelength of electron =h
mec
What is Light?
What is Light?
Youngs Double Slit Experiment
Light is composed of waves
Photo Electric Effect
Light is composed of particles
Compton Effect
Light is composed of particles
Paradox?
Wave Particle Duality
Atomic Spectra
gas
gas
Absorption Spectra
Emission Spectra
1R
H
1n
1
2 1n
2
2
; n
2n
11,n
12,
RH1.097373210
m-1 Rydberg Constant
n11 Lyman
n12 Balmer
n13 Paschen
n14 Brackett
Bohr Model
1. Electron moves in circular orbit about nucleus
2. Electron can only exist in specific orbits determined by
L mev r I nh
2 n; n1,2,
Imr 2 ; vr
3. Electrons in such orbits DO NOT radiate energy
although they are accelerating.
Such orbits are thus called STATIONARY STATES
4. Atoms radiate only when electron jumps from higher
energy (large radius) to lower energy (smaller radius)
orbits. The frequency of light they radiate is given by
=Eh E
l
h
Angular Momentum Quantization
U r kq1q
2
r ke
2
rkcoulombs constant
E r K U12mev 2 ke
2
r
If electrons speed is constant
Fcm
eacmev 2
rke2
r2m
ev2 k
e2
r
12mev2 1
2ke2
r
E r 12ke2
r
r
+
-
Quantization of Angular Momentum
r n m e v
v =n me r
mev2
n2 2
mer 2
ke 2
r
r n 2 2
me ke2 ; n 1 , 2 ,
r rn i . e . r depends on n
Bohr radius is defined as r0
2
m e ke 2
so that rn
n2 r0
using these values for rn in the expression
for the energy we obtain
En
mek2e 4
2 2
1n2
; n 1, 2 ,
13 . 6 eV1
n 2
thus the frequencies of emitted photons are
21E2 E 1
hmek 2e 4
2h 2
1n
12 1n
22
1
cmek 2e 4
2h 2c
1
n12
1
n22
Theoretical expression for Rydberg constant
RHm ek 2e 4
2h 2cwhich is in good agreement with experimental value
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