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Extra Nuclear Structure
Photoelectric effect ( 光電效應 )
• Evidence of light quanta 光量子的證明
• Introduction of the concept of photons 光子
• wave – particle duality of light
Light is wave(EM wave):
Proof: Young’s double slit experiment
Light is also particle, called photon.
Proof: photoelectric effect
Light
electrons
Photocurrent
K
A
Photocell
K= Cathode, emitter
A = Anode, collector
Light
K
Photocurrent
A
Photocell
K=(photoelectrons
Cathode, emitter
Electrons
光電子 ) are
= Anode,metal
collectorsurfaces when
ejectedA from
EM radiation of high enough
frequency falls on them.頻率足夠高
的電磁輻射
光電流
臨閾頻率
Now we try to study the effect of
frequency 頻率 & intensity 光強度
of EM radiation in this phenomenon.
By changing the position of
the sliding contact on the
potentiometer, we can
change V, voltage across
the photocell.
Light
I, f
A
I
Voltmeter: measure V
+V : higher voltage at A
Microammeter: Measure
photocurrent I
8 V
0V
+12 V
I
P3
P2
P1
-VS
0
Same f
Different
intensity
V
•I  No. of photoelectrons reaching A
•V > 0, I = constant
all photoelectrons reach A
•When V = 0, I  0
electrons emitted are having KE.
I
P3
P2
P1
-VS
0
V
V<0
electrons will be decelerated by the E-field
some of them will even be rejected back to K.
At V = -VS (stopping potential遏止電勢 ), I = 0
the most energetic (highest KE) electrons just
fail to reach the collector A
By energy conservation, the stopping potential
and the maximum KE of the photoelectrons
are then related by the equation
W.D. by E-field = loss of KE
eVS = KEmax
0V
-Vs
K
KEmax
e-
KE=0 A
e-
E-field
I
P3
P2
P1
-VS
0
V
• P1, P2, P3 :different intensities of incident
light with the same frequency
• P1 < P2 < P3.
• For same f, intensity   I 
I
f1
f2
f3
-VS3
-VS2 -VS1 0
V
Different frequency: f3 > f2 > f1
V
S
3 lines for 3 different metals
0
f
f "
0
f '
0
f
0
f   Vs 
(more –ve stopping potential)
The black dashed line is
not the result of the
experiment.
It is just an extension.
y = mx + c  Vs = hf + c
Vs = hf  hf0
KEmax = hf  F
Laws of photoelectric emission
( 光電發射效應 )
1. No. of photoelectrons  intensity
2. f   KE of electron (Vs) 
independent of intensity
3. For a given metal,
minimum fo , threshold frequency臨閾頻率
for f < fo , no photoelectron
Failure of classical wave theory
波動理論
Wave theory:
Predictions by wave theory
Energy  intensity
Intensity   KE (Vs) 
exp. result: KE is independent of intensity
large enough intensity
e must escape
exp. result: existence of threshold frequency fo
e is small
Take time to absorb energy
exp. result: no time delay
Einstein’s explanation
Einstein suggested that light have dual nature.
During transmission, they behave as waves.
When they are emitted or absorbed, they
behave as particles.
He assumed that EM radiation consists of lumps
of energy called photons 光子.
Energy of photon E = hf
f = The frequency of light
h = 6.625  1034 J s = Planck constant ( 普朗克常數 )
Einstein’s photoelectric equation
KEmax = hf  F
KEmax : Max KE of photoelectron
hf : energy of photon with frequency f
F: Work function
The intensity of light  nhf
 n = No. of photons
 No. of photoelectrons
 Photocurrent
since each photon is absorbed by one electron
(1)
(2) If hf > work function F ,
photoelectrons will be emitted instantly. There
should not be any time lag.
F
hf0 = F  f 0 
h
I
double P, same f
P, f
same P, double f
0
Intensity P  nhf
Same P, double f
V
 P  (n/2) h (2f)
 n  n/2
 photocurrent halved
The most energetic photoelectrons, KE = KEmax
• absorbed the energy of the photons, hf
• jump out of the metallic surface directly, without
losing their energy in making collision with
other particles inside the metal
• except in overcoming the surface barrier of the
metal.(work function 功函數 F )
KEmax = hf  F
or KEmax = hf  hf0
VS
0
slope = h/e
f
f0" f0'
F/e
f0
eVS = Kemax
KEmax = hf  F
eVS = hf  F
h
F
VS  f 
e
e
Application of photoelectric effect
Light-dependent resistor / Photocell /
photoelectric cell:
1. Reproduction of sound from movie films
2. As a light-sensitive switch
3. To be a count detector (conveyor belt)
AL MC 99-40
AL MC 00-41
AL MC 01-39
AL MC 02-35
Energy levels of hydrogen atom
氫原子的能級
•Line spectra of monoatomic gases
•Explanation in terms of light quanta (photons)
& energy levels
•Hydrogen spectrum: energy level equations
En = -13.6/n2 eV
Why H atom?
H atom is the simplest atom.
H atom contains one electron only.
H atom is the only atom so far scientist
can fully understand and explain its
orbital electron motion and energy
levels.
He atom is already too complicated.
Emission & absorption spectra
發射光譜 和吸收光譜
• Atoms in a substance can be excited when
the substance is heated, bombarded by
electrons or illuminated with radiation.
• These excited atoms return to lower
energy states accompanying with emission
of radiation.
• monoatomic gas  line
spectrum
Energy Levels 能級 of hydrogen
atom氫原子
Spectrometer
Energy Levels 能級 of hydrogen
atom氫原子
Hydrogen spectrum (visible part)
400nm
500nm
600nm
Balmer series: n = 2
700nm
Energy levels of
hydrogen atom
n = 1:
n

E / eV
0
4
3
0.85
1.51
2
3.40
ground state
n = 2: 1st excited state
n = 3: 2nd excited state
:
:
:
:
1
13.6
Discrete lines in hydrogen spectrum
Existence of energy level in
hydrogen atom
The value of the allowed energy levels能
級 of atomic hydrogen is:
2.176  10
En  
2
n
13.6
E n   2 eV
n
n = 1, 2, 3, ………
18
J or
n
13.6
E n   2 eV
n
n = 1: E1= -13.6 eV ground state基態
(lowest energy state)
n = 2: E2= -3.4 eV 1st excited state
n = : E  = 0 eV
H atom is ionized.
Electron is escaped
from the atom
Ionization energy電離能 of atom
• The least energy required to remove an
electron completely from an atom in
ground state.
• Also called binding energy of the atom
• Electron:
E1  E
• For H atom, ionization energy = E- E1
= 0 – (-13.6)
= 13.6 eV
Transition of electron in H atom
• In H atom, an electron can move from energy
level En to energy level Em with an energy
change E = Em - En .
m
• For m > n, E = Em - En > 0
energy is increased (absorb energy) n e
• For m < n, E = Em - En < 0
n e
energy is decreased (release energy)
m
• a photon with energy E will be
absorbed but photons with energies
other than E will be scattered away.
e.g. photon with E = hf = 10.2 eV
(photon is absorbed
& electron transition from E1 to E2)
photon with E = 11.5 eV
(scattered away & no e transition)
However, a photon of energy greater
than ionization energy電離能 will be
absorbed and the extra energy will
store as the initial KE of the escaped
electron逃逸電子的初動能 .
E.g photon with E = 20.6 eV > 13.6 eV
photon is absorbed
H atom is ionized (e escape逃逸 )
KE of escaped e = 7.0 eV
• Apart from photons, electrons and other
particles can also excite other atoms by
bombardment.
Just like the collision of snooker balls. Energy is
transferred from one ball to the other.
• E.g.
In Franck-Hertz experiment
( 法蘭赫茲 ), we use energetic
electron to excite atoms
Excited atoms (n > 1)
• lasting no longer than a ms (short time)
• finally return to its ground state
• associated with the emission of one or
more photons.
Wavelength of the emitted/absorbed photon:
hf  E  E n  E m
hc
13.6
13.6
 ( 2 )  ( 2 )

n
m
1 13.6  1
1 

 2  2

hc  n
m 
Easier to remember
that
18
2.176  10
E


J
or
n
2
hf = E = |Enm – En|
13.6
E n   2 eV
n
e move from energy level En to Em
f : frequency of photon absorbed or emitted
AL MC 01-40
AL MC 02-37
AL MC 02-36
AL MC 98-42
Franck-Hertz experiment
( 法蘭克赫茲 )
• Evidence for energy level能級
• Excitation energy激發能
• Elastic and inelastic collisions of
electrons with atoms
• Principle of Franck-Hertz type
experiments.
VG >VK
VP < VG (slightly)
Gas atoms (e.g. Hg 汞
atoms) at low pressure
K
G
electron
P
• Thermionic emission
• Accelerating voltage can be varied.
• the accelerating voltage (between G &
K) must be larger than the retarding
potential減速電勢(between G & P).
VG - VK > VG – VP
• Typically, VG - VP  1V
• I (microammeter)
 amount of electrons reach P
Suppose that at the ground state, the
outermost electron of the Hg atom is
in the electron shell n.
Energetic
electron collide
with Hg atom
n+2
n+1
eVi
KE = eVGK
n
eVj
Hg atom
Results: Vi, Vj = The excitation
potentials of the atom
I
0
V i Vj
2Vi
2Vj3Vi V
In the notes, V = VGK is measured by the
voltmeter.
for V < VGP (retarding potential), I = 0
For VGP < V < Vi,
V  I
elastic collision彈性碰撞
e have no KE loss
At V = Vi, I drops rapidly  inelastic collision
 e lose all KE
 atoms is excited
For Vi < V < Vj,
I again as V
V – Vi > retarding potential  e reach P
At V = Vj,
I drops rapidly again
 inelastic collision
 e lose all KE
 atoms is excited (another energy level)
At V = 2Vi, 2Vj, 3Vi, 3Vj, Vi + Vj,………
 I drops
 successive inelastic collisions with 2
or more atoms
Most likely, in Franck-Hertz experiment, we
get the following result. The result depend on
the gas density and the temperature of the gas.
AL MC 00-40
Ionization energy
(ionization by collision)
When the H atoms are ionized (13.6V),
H ions (+ve ion) are attracted to the
anode.
Line spectra (線狀光譜 )
• monatomic gases單原子氣體 only
• The line spectrum of a gas consists of the
characteristic lines of the gas
• 一氣體的明線光譜是該氣體的特徵線
Line spectra
(線狀光譜 )
EHT
In a gas discharge tube
( 放電管 ) a high voltage
(  1 kV ) is applied across
electrodes in a tube
containing a low pressure
gas.
diffraction
grating
discharge tube
Results(observation):
1. There are lines of discrete frequencies f
radiated in emission spectrum.
2. Emission lines ( 發射線 ) are closer at
lower end (shorter wavelength) of the
spectrum.
3. Intensities of lines are different.
He emission spectrum
400nm
500nm
600nm
700nm
Production mechanism產生機制
• Gas atoms are excited by the bombardment of
bullet electrons, or by heating.
e transit to higher energy level (較高能級)
• electron:
higher energy level En  a lower energy level Em
• Emission of radiation then occurs
• a photon of frequency f = ( En  Em )/h is
emitted.
explanations
The energy levels are getting closer and
closer for higher energy state.
the emission spectrum is discrete and lines
are closer at lower end. (short wavelength)
The intensities of lines depend on transition
probability躍遷的機會率 . For line spectra,
the emissions are mostly spontaneous自發
的 .  different intensities
Absorption spectrum ( 吸收光譜 )
• When white light passes through “cool”
dilute gases, and absorption spectra will
be obtained.
• “cool”  does not glow
 most atoms at ground state
cotton
wool
white
light
source
iodine
vapour
diffraction
grating
He emission & absorption spectrum
‘Dark’ lines because they are not as bright
as the ‘unabsorbed’ light.
H absorption and emission spectrum
The emission and absorption spectra of the same
element are complementary to one another.
Production mechanism
• Only photons of certain frequencies
f = ( En  Em )/h can excite the
corresponding gas atoms.
• The excited atoms will return to ground state
quickly.
• For the other photons (other frequencies),
they just pass or are scattered away.
explanation
• The atoms of the gas absorb incident
photons of certain wavelength and re-emit
photons of the same wavelength almost
immediately, but in all directions.
• Consequently, the intensity of light of these
wavelengths, in the original direction is
reduced and ‘dark’ lines are produced.
Continuous spectra ( 連續光譜 )
• In solid, liquid and compressed (dense) gas
 continuous spectra
• Molecular gases or chemical compounds
 band帶狀 spectra
• excited atoms or molecules are not wholly
independent of one another, energy levels of
the atoms will have interaction among them.
radiation of more wavelengths are emitted.
Continuous spectra ( 連續光譜 )
• The spectra produced by a hot filament wire
or the sun is continuous.
• Because at high temperature, there is obvious
interaction between atoms as a result of
overlapping of energy levels between atoms.
Fraunhöfer lines ( 夫琅和費譜線 )
• a series of dark absorption lines in solar
spectrum  vaporized elements
• light from the core of the sun
(photosphere), passing through the
chromosphere色球 (the solar atmosphere
太陽大氣層 ), is absorbed selectively by
the relatively cool gases in it.
Fraunhöfer lines ( 夫琅和費譜線 )
• Fraunhöfer lines are readily
observable before an eclipse takes
place, because the chromsphere is
only visible when the light from the
photosphere is blocked by moon.
• hydrogen, helium, sodium氫、氦、鈉
etc, in the chromosphere
X-rays (X 射線)
•
•
•
•
•
Production & properties
Maximum frequency
X-ray spectra
Energy interpretation of line spectra
Uses in medicine, industry &
crystallography
Properties of X-rays:
• High penetrating power ( 貫穿能力 )
• High ionization power ( 致電離能力 )
• High frequency EM wave
Effect of X-rays on human body
•
•
•
•
Deep-seat burns
Destruction of living cells
Unpredictable chemical changes
Genetic changes
Applications of X-rays
• Medical uses in diagnosis and therapy
• X-ray crystallography in analysis of
molecular structure
• Industrial radiography in locating
internal imperfections.
• Inspection of suitcases at airports
How to produce EM wave?
One of the ways:
When a charged particle is accelerating, EM
radiation (energy) is released.
X-ray:
high energy EM radiation
require high acceleration
In physics, acceleration is the same as
deceleration.
Production using X-ray tube X射線管
_
high voltage +
V
filament
target
electrons
filament
leads
anode
cooling
liquid
Evacuated glass
tube
X-rays
• electrons emitted from the hot filament
• Electrons are accelerated by a high voltage
V ( >6 kV  1MV).  high velocity
• X-rays are emitted when the target metal
(a metal of high atomic number e.g.
tungsten ) in the anode is bombarded by
these electrons. (deceleration)
• Target metal of high atomic number
 numerous electron shells
 X-rays of high frequency
Cooling system 
prevent the target from
melting
X-ray spectrum (X射線譜)
• continuous spectrum ( 連續譜 )
• a line spectrum ( 線狀譜 )
• Minimum wavelength min (highest
frequency)
Relative
intensity
Line spectrum
Continuous
spectrum
K
L
min

Production mechanism for
continuous spectrum
• due to the deceleration of the bombarding
electrons
• The energies of the emitted x-ray photons
equal to the lost KE of the bombarding
electrons during deceleration.
(conservation of energy)
• different electrons lose different amount of
energy by having one or more collisions
minimum wavelength 波長最小值 min
• an electron loses its KE completely in a
single collision
• all its KE is converted into just one X-ray
photon
1 2
c
mv  eV  hf  h
2
 min
 min
hc

eV
V: accelerating potential
1 2
c
mv  eV  hf  h
2
 min
 min
hc

eV
• For V = 500000 V, min = 0.02484 Å
• a TV tube of V = 25000 V, min = 0.497 Å
• Higher V  shorter min  Higher energy
Production mechanism for line spectrum
• the inner shell electrons of the target atoms
being knocked out by the bombarding electrons
(inner e move to higher energy levels)
• followed by the transitions of the outer shell
electrons to fill the inner vacancies.
• Photons of definite frequencies are emitted某
些確定頻率的光子
Production mechanism for line spectrum
N
M
X-ray photons
K
L
K
K
factors affecting the X-rays spectrum
• Temperature of filament 燈絲的溫度 
 intensity 
• Accelerating voltage V 
 min  & intensity 
• Material target metal 靶的物質
different line spectra but same min
Laser激光
• Light Amplification by Stimulated
Emission of Radiation (LASER)
受激輻射的光放大激光的作用
• Brief qualitative discussion of laser
action
• The uses of lasers
Properties of laser
•
•
•
•
•
•
Monochromatic單色光 (single frequency)
Coherent相干
High intensity高強度
Long coherent length (a few meter)
Beam is parallel / uni-directional單向性
(some laser can produce polarized radiation)
偏振
Spontaneous emission ( 自發發射 )
• An excited atom falls back to its ground state
randomly.受激原子會隨機地回落到基態
• The radiation emitted is incoherent ( 不相干 )
& in all directions.
• The probability of spontaneous emission is
proportional to the number of excited atoms.
• It occurs in light bulb燈泡, discharge tube放
射管 etc.
Stimulated emission ( 受激發射 )
• a photon of energy hf , where hf = En  E1
is capable of stimulating a excited atom to
pass from an excited state to the ground
state.
(electron: En  E1)
En
Photon: hf
E1
The probability of stimulated emission
depends on
• the no. of excited atom
• the no. of photons of energy hf
available
difficulty
• Stimulated emission doesn’t happen easily
• Naturally, most atoms are at ground
states
• Solution :
population inversion
Population Inversion ( 粒子分佈倒置 )
• Population inversion is a situation where the
majority of atoms are excited to a higher
state. (higher energy level)
大部份的原子是在受激態的情況
• This state must be a metastable state ( 亞
穩 態 ) in which the electrons remain
longer than usual (~3ms)
• the transition to the lower state occurs by
stimulated emission rather than spontaneous
emission.
Ground state:
electrons occupy the
lowest energy levels
Population inversion:
More electrons are at
higher energy level
P(stimulated emission) > P(absorption)
En
hf = En - E1
E1
Production mechanism
• Atoms are excited to an unstable energy
level by absorbing photons of flashes of
light (optical pumping).
• Population inversion occurs when excited
atoms reach metastable state (by emitting
photons hf1. )
• Apart from optical pumping, there are
other ways of pumping, like electrical
pumping in CD & DVD players
(pumping)
stimulated
absorption
of a photon
of
hf = Em E1
spontaneous
emission of
a photon of
hf1 = Em En
excited
state Em
metastable
state En
ground
state E1
• Some of the excited atoms in metastable
state emit photons hf2 spontaneously.
• These photons stimulate the emission of
other photons of same frequency f2 (light
amplification) and in phase.
stimulated emission by
photon of hf2 = En  E1
atom 1
atom2
electron
n  hf2
(n+1)  hf2
(n+2)  hf2
mirror
Optical pumping:
Laser
beam
partial
mirror
• As the process continues, large number of
photons is built up ( also due to the fact that
light is reflected between the two end mirrors.)
• The coherent laser beam is emitted from a
small hole of one of the mirror to be more
unidirectional.
applications
• Optical fibre communication, Laser diode
for telephone communication
• Printing
• reading digital information (DVD,
CD….)
• Ranging, Welding, Drilling, Pointer for
instructor, Holography
• Cutting of cornea for short, long sight,
Treatment of detached retina