Physics 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
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4: Introduction to Quantum Physics
Any object with a temperature T>0 K radiates away thermal energy through the emission of electromagnetic radiation
Classical explanation
heat causes accelerated charges (Maxwell like distribution of accelerations) that emit radiation of various frequencies
mK
l
T
=
2
.
898
max
Rayleigh

Jeans Law
2
p
ckT
I
(
l
,
T
)
=
4
l
Intensity of radiation of wavelength
l
at temp
T
However this only agrees with experiment at long
l
Lim
I
(
l
,
T
)
=
¥
Ultraviolet Catastrophe
l
¯
0
(
Þ
¥
total energy density
)
Oscillating molecules that emit the radiation only have discrete energies
En = nhn
n = quantum number
En = energy of quantum state n of molecule
Molecules emit or absorb energy in discrete units of light called QUANTA
Light
A
Electron
G
V
Animation
I
low intensity light
V0
V
plate A has negative potential
Stopping Potential
1
.
No electrons ejected if
n
£
n
(cut off frequency
)
c
2
.
If
n
³
n
the number of photo electrons
µ
light intensity
c
3
.
K
is independent of light intensity
max
4.
K
as
n
max
5
.
Electrons are emitted instantaneously even at low
light intensities
Wave theory of light does not predict such properties
that light is quantized in
energy packets
=
QUANTA with energy E
=
h
n
he called such quanta PHOTONS
.
The intensity of the light is proportional to the number
of such quanta i
.
e
.
I
µ
nh
n
In order for electrons to be emitted they must pass through
surface
.
\
use
f
amount of energy to overcome surface
barrier
º
Ionization Potential
º
Work Function
K
=
h
n

f
=
h
n

h
n
max
c
1
.
K
=
h
n

f
;
so K
depends on
n
max
max
2
.
h
n
³
f
;
for emission of electrons
3
.
h
n

f
only depends on
n
not on intensity
4.
K
as
n
max
5
.
single electrons are excited by light
(not many gradually)
Þ
instantaneous emission
Kmax = hnf
slope = h
Kmax
nc
scattered photon
q
f
scattered electron
More Evidence that light is composed of particles
(
)
I
=
I
l
,
q
;
incident
l
¹
scattered
l

this contradicts classical theory
0
D
l
=
l

l
0
Compton
(
1923
) suggested treating photon as particle
hc
E
=
h
n
=
l
The Special Theory of Relativity gives E
=
pc
[
]
p is the magnitude of the momentum of the photon
hc
h
\
pc
=
Þ
p
=
l
l
D
E
=
D
p
=
0
tot
tot
h
(
)
Þ
D
l
=
1

cos
q
m
c
e
Þ
l
;
n
;
E
during collision
¯
¯
photon
h
Compton Wavelength of electron
=
m
c
e
ö
1
1
1
ç
÷
=
R

;
n
=
n
+
1
,
n
+
2
,
K
l
n
n
2
2
è
ø
H
2
1
1
1
2
7
R
=
1
.
0973732
´
10
º
Rydberg Constant
m1
H
n
=
1
Û
Lyman
1
n
=
2
Û
Balmer
1
n
=
3
Û
Paschen
1
n
=
4
Û
Brackett
1
.
Electron moves in circular orbit about nucleus
2
.
Electron can only exist in specific orbits determined by
Angular Momentum Quantization
h
n
L
=
m
v
r
=
I
w
=
n
=
;
n
=
1
,
2
,
K
h
e
2
p
v
é
ù
I
=
mr
;
w
=
2
ë
r
û
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
E

E
Animation
n
=
h
l
h
q
e
2
(
)
U
r
=
=

k
1
2
r
r
k
=
coulombs constant

1
e
2
(
)
r
E
r
=
K
+
U
=
m
v

k
2
2
r
e
+
If electrons speed is constant
m
v
e
e
2
2
2
F
=
m
a
=
=
k
Þ
m
v
=
k
e
2
c
e
c
r
r
e
r
2
1
1
e
2
\
m
v
=
k
2
2
2
r
e
1
e
2
(
)
Þ
E
r
=

k
2
r
ß
n
n
h
h
r
=
Û
v
=
m
v
m
r
e
e
n
ke
h
2
2
2
\
m
v
=
=
2
m
r
r
e
2
e
n
h
2
2
Þ
r
=
;
n
=
1
,
2
,
K
2
m
ke
e
\
r
=
r
i
.
e
.
r
depends on
n
n
h
2
Bohr radius is defined as
r
=
m
ke
0
2
e
so that
r
=
n
r
2
n
0
r
in the expression
n
for the energy we obtain
2
4
m
k
e
1
æ
ö
e
E
=

;
n
=
1
,
2
,
K
è
ø
2
n
n
h
2
2
1
æ
ö
=

13
.
6
eV
è
ø
n
2
thus the frequencies of emitted photons are
æ
E

E
m
k
e
ö
1
1
2
4
ç
÷
2
1
e
n
=
=

h
2h
n
n
21
è
ø
h
2
2
2
1
2
æ
1
n
m
k
e
1
1
ö
2
4
ç
÷
=
=

e
l
c
n
n
è
ø
h
2
2
2
2h
c
1
2
Theoretical expression for Rydberg constant
m
k
e
2
4
e
R
=
H
2
2h
h
c
which is in good agreement with experimental value