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Modern Physics
MOHAMMAD IMRAN AZIZ
Assistant ProfessorPHYSICS DEPARTMENT
SHIBLI NATIONAL COLLEGE, AZAMGARH (India).
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Relativity in ClassicalPhysics
Galileo and Newton dealt with theissue of relativity
The issue deals with observing naturein different reference frames, that is,with different coordinate systems
We have always tried to pick a
coordinate system to ease calculations
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Relativity and ClassicalPhysics
We defined something called aninertial reference frame
This was a coordinate system inwhich Newtons First Law was valid
An object, not subjected to forces,moves at constant velocity (constantspeed in a straight line) or sits still
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Relativity and ClassicalPhysics
Coordinate systems that rotate oraccelerate are NOT inertial referenceframes
A coordinate system that moves atconstant velocity with respect to aninertial reference frame is also an
inertial reference frame
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Moving Reference Frames
While the motion of a dropped coinlooks different in the two systems,the laws of physics remain the same!
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Classical Relativity
The relativity principle is that thebasic laws of physics are thesame in all inertial reference
frames
Galilean/Newtonian Relativity restson certain unprovable assumptions
Rather like Euclids Axioms andPostulates
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Classical Assumptions
The lengths of objects are the samein all inertial reference frames
Time passes at the same rate in all
inertial reference frames Time and space are absolute and
unchanging in all inertial reference
frames Masses and Forces are the same in
all inertial reference frames
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Measurements of Variables
When we measure positions in different inertialreference frames, we get different results
When we measure velocities in different inertial
reference frames, we get different results When we measure accelerations in different
inertial reference frames, we get the SAMEresults
The change in velocity and the change in timeare identical
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Classical Relativity
Since accelerations and forces andtime are the same in all inertialreference frames, we say thatNewtons Second Law, F = masatisfies the relativity principle
All inertial reference frames are
equivalent for the description ofmechanical phenomena
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Classical Relativity
Think of the constant accelerationsituation
x=x0+v0t+1
2at2
v=v0+at
Changing to a new movingcoordinate system meanswe just need to change theinitial values. We make acoordinatetransformation.
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The Problem!!!
Maxwells Equations predict the velocityof light to be 3 x 108 m/s
The question is, In what coordinate
system do we measure it? If you fly in an airplane at 500 mph and
have a 200 mph tailwind in the jetstream, your ground speed is 700 mph
If something emitting light is moving at1 x 108 m/s, does this means that thatparticular light moves at 4 x 108 m/s?
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The Problem!!
Maxwells Equations have no way toaccount for a relative velocity
They say that
Waves in water move through amedium, the water
Same for waves in air What medium do EM waves move in?
c
=
1/00
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The Ether
It was presumed that the medium in which lightmoved permeated all space and was called theether
It was also presumed that the velocity of lightwas measured relative to this ether
Maxwells Equations then would only be true inthe reference frame where the ether is at rest
since Maxwells Equations didnt translate toother frames
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The Ether
Unlike Newtons Laws of Mechanics,Maxwells Equations singled out a uniquereference frame
In this frame the ether is absolutely at rest So, try an experiment to determine the
speed of the earth with respect to the ether
This was the Michelson-Morley Experiment
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Michelson-Morley
Use an interferometer to measurethe speed of light at different timesof the year
Since the earth rotates on its axisand revolves around the sun, wehave all kinds of chances to observe
different motions of the earth w.r.t.the ether
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Michelson-Morley
We get an interferencepattern by adding thehorizontal path light to thevertical path light.
If the apparatus moves w.r.t.the ether, then assume thespeed of light in thehorizontal direction ismodified. Then rotate the
apparatus and the fringes willshift.
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Michelson-Morley
Calculation in the text
Upshot is that no fringe shift was seen so thelight had the same speed regardless ofpresumed earth motion w.r.t. the ether
Independently, Fitzgerald and Lorentz proposedlength contraction in the direction of motionthrough the ether to account for the null resultof the M-M experiment
Found a factor that worked Scientists call this a kludge
1
v2/c2
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Einsteins Special Theory
In 1905 Einstein proposed the solutionwe accept today
He may not even have known about the
M-M result He visualized what it would look like
riding an EM wave at the speed of light
Concluded that what he imaginedviolated Maxwells Equations
Something was seriously wrong
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Special Theory of Relativity
The laws of physics have the sameform in all inertial reference frames.
Light propagates through emptyspace (no ether) with a definitespeed c independent of the speed ofthe source or observer.
These postulates are the basis ofEinsteins Special Theory of Relativity
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Gedanken Experiments
Simultaneity
Time Dilation
Length Contraction (Fitzgerald &Lorentz)
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Simultaneity
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Simultaneity
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Simultaneity
Time is NOT absolute!!
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Time Dilation
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Time Dilation
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Time Dilation
Clocks moving relative to an observer are measured by thatobserver to run more slowly compared to clocks at rest by anamount
1v2
/c2
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Length Contraction
A moving objects length is measuredto be shorter in the direction ofmotion by an amount
1
v2
/c2
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Wave-Particle Duality
Last time we discussed severalsituations in which we had to concludethat light behaves as a particle called
a photon with energy equal to hf Earlier, we discussed interference anddiffraction which could only beexplained by concluding that light is a
wave Which conclusion is correct?
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Wave-Particle Duality
The answer is that both are correct!!
How can this be???
In order for our minds to grasp concepts we
build models These models are necessarily based onthings we observe in the macroscopic world
When we deal with light, we are moving into
the microscopic world and talking aboutelectrons and atoms and molecules
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Wave-Particle Duality
There is no good reason to expect thatwhat we observe in the microscopic worldwill exactly correspond with the
macroscopic world We must embrace Niels Bohrs Principle of
Complementarity which says we must useeither the wave or particle approach tounderstand a phenomenon, but not both!
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Wave-Particle Duality
Bohr says the two approachescomplement each other and both arenecessary for a full understanding
The notion of saying that the energyof a particle of light is hfis itself anexpression of complementarity since
it links a property of a particle to awave property
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Wave -Particle Duality
Why must we restrict this principle tolight alone?
Might microscopic particles likeelectrons or protons or neutronsexhibit wave properties as well asparticle properties?
The answer is a resounding YES!!!
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Wave Nature of Matter
Louis de Broglie proposed thatparticles could also have waveproperties and just as light had a
momentum related to wavelength, soparticles should exhibit a wavelengthrelated to momentum
= hmv
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Wave Nature of Matter
For macroscopic objects, thewavelengths are terrifically short
Since we only see wave behaviorwhen the wavelengths correspond tothe size of structures (like slits) wecant build structures small enough
to detect the wavelengths ofmacroscopic objects
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Wave Nature of Matter
Electrons have wavelengthscomparable to atomic spacings inmolecules when their energies are
several electron-volts (eV) Shoot electrons at metal foils and
amazing diffraction patterns appear
which confirm de Broglieshypothesis
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Wave Nature of Matter
So, what is an electron? Particle? Wave?
The answer is BOTH
Just as with light, for some situations we
need to consider the particle properties ofelectrons and for others we need to considerthe wave properties
The two aspects are complementary
An electron is neither a particle nor a wave,it just is!
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Electron Microscopes
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Models of the Atom
It is clear that electrons arecomponents of atoms
That must mean there is somepositive charge somewhere insidethe atom so that atoms remainneutral
The earliest model was called theplum pudding model
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Plum Pudding Model
We have a blob of positive chargeand the electrons are embedded inthe blob like currants in a plumpudding.
However, people thought that theelectrons couldnt just sit still insidethe blob. Electrostatic forces wouldcause accelerations. How could itwork?
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Rutherford Scattering
Ernest Rutherford undertook experimentsto find out what atoms must be like
He wanted to slam some particle into anatom to see how it reacted
You can determine the size and shape of anobject by throwing ping-pong balls at theobject and watching how they bounce off
Is the object flat or round? You can tell!
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Rutherford Scattering
Rutherford used alpha particles which are thenuclei of helium atoms and are emitted from someradioactive materials
He shot alphas into gold foils and observed the
alphas as they bounced off
If the plum pudding model was correct, you wouldexpect to see a series of slight deviations as thealphas slipped through the positive pudding
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Rutherford Scattering
Instead, what was observed wasalphas were scattered in alldirections
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Rutherford Scattering
In fact, some alphas scatteredthrough very large angles, comingright back at the source!!!
He concluded that there had to be asmall massive nucleus from whichthe alphas bounced off
He did a simple collision modelconserving energy and momentum
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Rutherford Scattering
The model predicted how manyalphas should be scattered at eachpossible angle
Consider the impact parameter
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Rutherford Scattering
Rutherfords model allowed calculating theradius of the seat of positive charge inorder to produce the observed angulardistribution of rebounding alpha particles
Remarkably, the size of the seat ofpositive charge turned out to be about 10-15 meters
Atomic spacings were about 10-10
metersin solids, so atoms are mostly emptyspace
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Rutherford Scattering
From the edge of the atom, the nucleusappears to be 1 meter across from adistance of 105 meters or 10 km.
Translating sizes a bit, the nucleusappears as an orange viewed from adistance of just over three miles!!!
This is TINY!!!
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Rutherford Scattering
Rutherford assumed the electrons mustbe in some kind of orbits around thenucleus that extended out to the size ofthe atom.
Major problem is that electrons would beundergoing centripetal acceleration andshould emit EM waves, lose energy andspiral into the nucleus!
Not very satisfactory situation!
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Light from Atoms
Atoms dont routinely emitcontinuous spectra
Their spectra consists of a series ofdiscrete wavelengths or frequencies
Set up atoms in a discharge tube andmake the atoms glow
Different atoms glow with differentcolors
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Atomic Spectra
Hydrogen spectrum has a pattern!
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Atomic Spectra
Balmer showed that the relationshipis
1
=R1
221
n2
forn=3,4,5,...
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Atomic Spectra
Lyman Series
Balmer Series
Paschen Series1
=R1
221
n2
forn=3,4,5,...
1
=R1
121
n2
forn=2,3,4,...
1
=R1321n2
forn=4,5,6,...
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Atomic Spectra
Lyman Series
Balmer Series
Paschen Series So what is going on here???
This regularity must have some
fundamental explanation Reminiscent of notes on a guitar
string
1
=R1
221
n2
forn=3,4,5,...
1
=R1
121
n2
forn=2,3,4,...
1
=R1321n2
forn=4,5,6,...
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Atomic Spectra
Electrons can behave as waves
Rutherford scattering shows tiny nucleus
Planetary model cannot be stable classically
What produces the spectral lines of isolatedatoms?
Why the regularity of hydrogen spectra?
The answers will be revealed next time!!!
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Summary of 2nd lecture
electron was identified as particle emitted in photoelectriceffect
Einsteins explanation of p.e. effect lends further credenceto quantum idea
Geiger, Marsden, Rutherford experiment disproves
Thomsons atom model Planetary model of Rutherford not stable by classical
electrodynamics
Bohr atom model with de Broglie waves gives somequalitative understanding of atoms, but
only semiquantitative no explanation for missing transition lines
angular momentum in ground state = 0 (1 )
spin??
O tli
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Outline more on photons
Compton scattering Double slit experiment
double slit experiment with photons andmatter particles interpretation Copenhagen interpretation of quantum
mechanics
spin of the electron Stern-Gerlach experiment
spin hypothesis (Goudsmit, Uhlenbeck)
Summary
Photon properties
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Photon properties
Relativistic relationship between a particlesmomentum and energy: E2 = p2c2 + m0
2c4
For massless (i.e. restmass = 0) particles
propagating at the speed of light: E
2
= p
2
c
2
For photon, E = h =
angular frequency = 2
momentum of photon = h /c = h/ = k
wave vector k = 2/
(moving) mass of a photon: E=mc2m = E/c2m = h /c2 = /c2
Compton scattering 1
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Compton scattering 1
Expectation from classical
electrodynamics: radiation incident on
free electrons electrons oscillate at
frequency of incidentradiation emit light ofsame frequency lightscattered in alldirections
electrons dont gainenergy
no change in frequencyof light
Scattering of X-rays on free
electrons;Electrons supplied by graphitetarget;Outermost electrons in C looselybound; binding energy
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Compton scattering 2Compton (1923) measured intensity of
scattered X-rays from solid target, asfunction of wavelength for differentangles. Nobel prize 1927.
X-ray source
Target
Crystal(selects
wavelength)
Collimator(selects
angle)
Result: peak in scattered radiation shifts tolonger wavelength than source. Amount dependson (but not on the target material).
A.H. Compton,Phys. Rev. 22 409 (1923)[email protected]
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Compton scattering 3 Classical picture: oscillating electromagnetic field causes
oscillations in positions of charged particles, which re-radiate in alldirections at same frequencyas incident radiation. No change inwavelength of scattered light is expected
Comptons explanation: collisions between particles of light (X-ray photons) and electrons in the material
Oscillating electronIncident light wave Emitted light wave
ep
p Before After
Electron
Incoming photon
p
scattered photon
scattered [email protected]
Compton scattering 4
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p g
ep
p Before After
Electron
Incoming photon
p
scattered photon
scattered electron
Conservation of energy Conservation of momentum
( )1/ 2
2 2 2 2 4
e e eh m c h p c m c + = + +
e
h
= = +p i p p
( )
( )
1 cos
1 cos 0
e
c
h
m c
=
=
12
Compton wavelength 2.4 10 mce
h
m c
= = =
From this derive change in wavelength:
Compton scattering 5
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Compton scattering 5
unshifted peaks comefrom collision between theX-ray photon and thenucleus of the atom
- = (h/mNc)(1 - cos )
0 sincesince mN >> me
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WAVE-PARTICLE DUALITY OF LIGHT Einstein (1924) : There are therefore now two theories of light,
both indispensable, and without any logical connection. evidence for wave-nature of light:
diffraction
interference
evidence for particle-nature of light:
photoelectric effect
Compton effect
Light exhibits diffraction and interference phenomena that areonlyexplicable in terms of wave properties
Light is always detected as packets (photons); we never observehalf a photon
Number of photons proportional to energy density (i.e. to square ofelectromagnetic field strength)
Double slit experiment
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pOriginally performed by Young (1801) to demonstrate the wave-
nature of light. Has now been done with electrons, neutrons, Heatoms,
D
d
Detecting
screen
y
Alternativemethod ofdetection: scana detector
across the planeand recordnumber ofarrivals at eachpoint
Expectation: two peaks for particles, interference pattern for waves
Fringe spacing in double slit experiment
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Maxima when: sind n =
y D
Dy
d
=
Position on screen: tan y D D =
n
d
d
D >> d use small angleapproximation
So separation between adjacentmaxima:
g p g p
d
sind
D
y
Double slit experiment -- interpretation
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p p
classical:
two slits are coherent sources of light interference due to superposition of secondary waves on screen
intensity minima and maxima governed by optical path differences
light intensity I A2, A = total amplitude
amplitude A at a point on the screen A2 = A12 + A2
2 + 2A1 A2 cos,
= phase difference between A1 and A2 at the point maxima for = 2n
minima for = (2n+1)
depends on optical path difference : = 2/
interference only for coherent light sources; twoindependentlight sources: no interference since not coherent(random phase differences)
Double slit experiment: low intensity
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Double slit experiment: low intensity Taylors experiment (1908): double slit experiment with very
dim light: interference pattern emerged after waiting for few
weeks interference cannot be due to interaction between photons, i.e.
cannot be outcome of destructive or constructive combinationof photons
interference pattern is due to some inherent property of
each photon it interferes with itself while passing fromsource to screen
photons dont split light detectors always show signals ofsame intensity
slits open alternatingly: get two overlapping single-slitdiffraction patterns no two-slit interference
add detector to determine through which slit photon goes: no interference
interference pattern only appears when experiment providesno means of determining through which slit photon passes
double slit experiment with very low
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double slit experiment with very low
intensity , i.e. one photon or atom at a
time:get still interference pattern if we waitlong enough
Double slit experiment QM
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interpretation
patterns on screen are result of distribution of photons
no way of anticipating where particular photon will strike
impossible to tell which path photon took cannot assign specifictrajectory to photon
cannot suppose that half went through one slit and half through other
can only predict how photons will be distributed on screen (or overdetector(s))
interference and diffraction are statistical phenomena associated withprobability that, in a given experimental setup, a photon will strike acertain point
high probability bright fringes
low probability dark fringes
ou e s exp . -- wave vs
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ou e s exp . wave vsquantum
pattern of fringes: Intensity bands due to
variations in square ofamplitude, A2, of
resultant wave oneach point on screen
role of the slits:
to provide two
coherent sources ofthe secondary wavesthat interfere on thescreen
pattern of fringes: Intensity bands due to
variations inprobability, P, of a
photon striking pointson screen
role of the slits:
to present twopotential routes bywhich photon can passfrom source to screen
wavetheory
quantum theory
ou e s exp ., wave
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ou e s exp ., wavefunction
light intensity at a point on screen I depends on number of photons striking the point
number of photons probability P of finding photon there, i.e I P = ||2, = wave function
probability to find photon at a point on the screen : P = ||2 = |1 + 2|
2 = |1|2 + |2|
2 + 2 |1|
|2| cos;
2 |1| |2| cos is interference term; factor cos due to fact that s are complex functions
wave function changes when experimental setup is changed
by opening only one slit at a time
by adding detector to determine which path photon took
by introducing anything which makes paths distinguishable
Waves or Particles?
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Waves or Particles? Youngs double-slitdiffraction experimentdemonstrates the
wave property of light.
However, dimmingthe light results insingle flashes on thescreen representativeof particles.
Electron Double-Slit
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Experiment C. Jnsson (Tbingen,Germany, 1961) showeddouble-slit interferenceeffects for electrons byconstructing very narrow
slits and using relativelylarge distances betweenthe slits and theobservation screen.
experiment demonstrates
that precisely the samebehavior occurs for bothlight (waves) and electrons(particles).
Results on matter wave interferenceResults on matter wave interference
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Neutrons, AZeilinger et al.Reviews of Modern
Physics 60 1067-1073 (1988)
He atoms: O Carnal and JMlynek Physical Review Letters
66 2689-2692 (1991)
C60 molecules: M
Arndt et al.Nature 401, 680-
682 (1999)
With multiple-slit grating
Without grating
Interference patterns can not be explained classically - clear demonstration of matter
Fringevisibilitydecreases asmolecules
are heated.L.Hackermlleret al. , Nature427 711-714
(2004)
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Which slit?
Try to determine which slit the electron went through. Shine light on the double slit and observe with a microscope. After theelectron passes through one of the slits, light bounces off it; observing thereflected light, we determine which slit the electron went through.
The photon momentum is:
The electron momentum is:
The momentum of the photons used to determine which slit the electronwent through is enough to strongly modify the momentum of the electronitselfchanging the direction of the electron! The attempt to identify whichslit the electron passes through will in itself change the diffraction pattern!
Need ph < dto
distinguish the slits.
Diffraction is significantonly when the aperture is~ the wavelength of thewave.
Discussion/interpretation of double sliti t
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experiment
Reduce flux of particles arriving at the slits so that only oneparticle arrives at a time. -- still interference fringesobserved! Wave-behavior can be shown by a single atom or photon.
Each particle goes through both slits at once.
A matter wave can interfere with itself.
Wavelength of matter wave unconnected to any internal sizeof particle -- determined by the momentum
If we try to find out which slit the particle goes through theinterference pattern vanishes! We cannot see the wave and particle nature at the same time.
If we know which path the particle takes, we lose the fringes .
hard Feynman about two-slit experiment: a phenomenon which is impossiblsolutelyimpossible, to explain in any classical way, and which has in it the hea
quantum mechanics. In reality it contains the [email protected]
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Wave particle - duality
So, everything is both a particle and a wave -- disturbing!?? Solution: Bohrs Principle of Complementarity:
It is not possible to describe physical observablessimultaneously in terms of both particles and waves
Physical observables:
quantities that can be experimentally measured. (e.g. position, velocity,momentum, and energy..)
in any given instance we must use either the particle description or thewave description
When were trying to measure particle properties, thingsbehave like particles; when were not, they behave like waves.
Probability, Wave Functions, and the
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yCopenhagen Interpretation
Particles are also waves -- described by wavefunction
The wave function determines the probability offinding a particle at a particular position in space at a
given time.
The total probability of finding the particle is 1.Forcing this condition on the wave function is callednormalization.
The Copenhagen
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The CopenhagenInterpretation Bohrs interpretation of the wave
function consisted of three principles: Borns statistical interpretation, based on
probabilities determined by the wave function
Heisenbergs uncertainty principle
Bohrs complementarity principle
Together these three concepts form a logicalinterpretation of the physical meaning of quantum
theory. In the Copenhagen interpretation, physicsdescribes only the results of measurements.
Atoms in magnetic field
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o s ag e c e d
orbiting electron behaves like current loop magnetic moment interaction energy = B (bothvectors!)
loop current = -ev/(2r)
magnetic moment = current x area = - BL/
B = e /2me = Bohr magneton interaction energy
= m BB
z
(m = z comp of L)
er
IA
L
n
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Splitting of atomic energy levels
Predictions:should always get an oddnumber of levels. An s state (such as theground state of hydrogen, n=1, l=0, m=0)
should not be split.
(2l+1) states withsame energy: m=-l,
+l(Hence the namemagneticquantum numberfor m.)
0B = 0B
B 0: (2l+1) states withdistinct energies
m = 0
m = -1
m = +1
Stern - Gerlach experiment - 1
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p magnetic dipole moment associated with angular momentum
magnetic dipole moment of atoms and quantization of angularmomentum direction anticipated from Bohr-Sommerfeld atommodel
magnetic dipole in uniform field magnetic field feels torque,but nonet force
in non-uniform field there will be net force deflection extent of deflection depends on
non-uniformity of field
particles magnetic dipole moment
orientation of dipole moment relative to mag. field
Predictions:
Beam should split into an odd number of parts (2l+1)
A beam of atoms in an s state (e.g. the ground state ofhydrogen, n = 1, l = 0, m = 0) should not be split.
N
S
Stern-Gerlach experiment (1921)z
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Oven
AgAg-vaporcollim.
screen
x
Ag beam
N
S
Magnet
0
B
N
S
Ag beam
( ) zz ezBB
=non-
uniform z0
#
Aga
toms
B= 0
B B
Stern-Gerlach experiment -
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Stern Gerlach experiment 3 beam of Ag atoms (with electron in s-state
(l =0)) in non-uniform magnetic field force on atoms: F = z Bz/z
results show two groups of atoms,
deflected in opposite directions, withmagnetic moments z = B
Conundrum:
classical physics would predict a continuousdistribution of
quantum mechanics la Bohr-Sommerfeldpredicts an odd number (2 l +1) of groups, i.e.
just one for an s [email protected]
Th t f i
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The concept of spin
Stern-Gerlach results cannot be explained by interaction of magneticmoment from orbital angular momentum
must be due to some additional internal source of angular momentumthat does not require motion of the electron.
internal angular momentum of electron (spin) was suggested in 1925by Goudsmit and Uhlenbeck building on an idea of Pauli.
Spin is a relativistic effect and comes out directly from Diracstheory of the electron (1928)
spin has mathematical analogies with angular momentum, but is not tobe understood as actual rotation of electron
electrons have half-integer spin, i.e. /2
Fermions vs Bosons
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Radioactivity
Radiation
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Radiation: The process of emittingenergy in the form of waves or
particles.
Where does radiation come from?Radiation is generally producedwhen particles interact or decay.
A large contribution of the radiationon earth is from the sun (solar) orfrom radioactive isotopes of theelements (terrestrial).
Radiation is going through you at
this very moment!
http://www.atral.com/U238.ht
Isotopes
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IsotopesWhats an isotope?
Two or more varieties of an elementhaving the same number of protons butdifferent number of neutrons. Certainisotopes are unstable and decay tolighter isotopes or elements.
Deuterium and tritium are isotopes ofhydrogen. In addition to the 1 proton, theyhave 1 and 2 additional neutrons in thenucleus respectively*.
Another prime example is Uranium
238, or just238
U.
Radioactivity
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y
By the end of the 1800s, it was known that certain
isotopes emit penetrating rays. Three types of radiationwere known:
1) Alpha particles ( )2) Beta particles ( )3) Gamma-rays ( )
By the end of the 1800s, it was known that certain
isotopes emit penetrating rays. Three types of radiationwere known:
1) Alpha particles ( )2) Beta particles ( )3) Gamma-rays ( )
Where do these particles come
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from ?
These particles generally comefrom the nuclei of atomic isotopeswhich are not stable.
The decay chain of Uraniumproduces all three of these formsof radiation.
Lets look at them in more detail
Alpha ParticlesNote: This is theatomic weight which
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Alpha Particles( )
Radium
R226
88 protons138 neutrons
Radon
Rn222
atomic weight, whichis the number ofprotons plus neutrons
86 protons136 neutrons
+ n np
p
(4He)2 protons2 neutrons
The alpha-particle( ) is a Helium nucleus.
Its the same as the element Helium, with theelectrons stripped off!
Beta Particles ( )
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( )
CarbonC14
6 protons8 neutrons
NitrogenN14
7 protons7 neutrons
+ e-
electron(beta-particle)
We see that one of the neutrons from the C14 nucleusconverted into a proton, and an electron was ejected.
The remaining nucleus contains 7p and 7n, which is a nitrogen
nucleus. In symbolic notation, the following process occurred:
n p + e ( + )
Yes, the sameneutrino we saw
previously
Gamma particles ( )
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p In much the same way that electrons in atoms can be in anexcited state, so can a nucleus.
NeonNe20
10 protons10 neutrons
(in excited state)
10 protons10 neutrons
(lowest energy state)
+
gamma
NeonNe20
A gamma is a high energy light particle.
It is NOT visible by your naked eye because it is not inthe visible part of the EM spectrum.
A gamma is a high energy light particle.
It is NOT visible by your naked eye because it is not inthe visible part of the EM spectrum.
Gamma Rays
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y
NeonNe20 +
The gamma from nuclear decayis in the X-ray/ Gamma ray
part of the EM spectrum(very energetic!)
NeonNe20
ow o ese par c esdiffer ?
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differ ?Particle Mass*
(MeV/c2)Charge
Gamma ( ) 0 0
Beta ( ) ~0.5 -1
Alpha ( ) ~3752 +2
* m = E / c2* m = E / c2
Rate of Decay
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yBeyond knowing the types of particles which are emittedwhen an isotope decays, we also are interested in how frequently
one of the atoms emits this radiation.
A very important point here is that we cannot predict when aparticular entity will decay.
We do know though, that if we had a large sample of a radioactive
substance, some number will decay after a given amount of time.
Some radioactive substances have a very high rate of decay,while others have a very low decay rate.
To differentiate different radioactive substances, we look toquantify this idea of decay rate
Half-Life
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The half-life (h) is the time it takes for half the atoms of aradioactive substance to decay.
For example, suppose we had 20,000 atoms of a radioactivesubstance. If the half-life is 1 hour, how many atoms of thatsubstance would be left after:
10,000 (50%)
5,000 (25%)
2,500 (12.5%)
1 hour (one lifetime) ?
2 hours (two lifetimes) ?
3 hours (three lifetimes) ?
Time#atoms
remaining% of atomsremaining
Lifetime ( )
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The lifetime of a particle is an alternate definition ofthe rate of decay, one which we prefer.
It is just another way of expressing how fast the substancedecays..
It is simply: 1.44 x h, and one often associates theletter to it.
The lifetime of a free neutron is 14.7 minutes{ (neutron)=14.7 min.}
Lets use this a bit to become comfortable with it
The lifetime of a particle is an alternate definition ofthe rate of decay, one which we prefer.
It is just another way of expressing how fast the substancedecays..
It is simply: 1.44 x h, and one often associates theletter to it.
The lifetime of a free neutron is 14.7 minutes{ (neutron)=14.7 min.}
Lets use this a bit to become comfortable with it
Lifetime (I)
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The lifetime of a free neutron is 14.7 minutes.
If I had 1000 free neutrons in a box, after 14.7minutes some number of them will have decayed.
The number remaining after some time is given by theradioactive decay law
/
0
t N N e =N0 = starting number of
particles = particles lifetime
This is the exponential. Itsvalue is 2.718, and is a very usefulnumber. Can you find it on yourcalculator?
Lifetime (II)
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/
0
t N N e =Note by slight rearrangement of this formula:
Fraction of particles which did not decay: N / N0 = e-t/
#lifetimes
Time
(min)
Fraction ofremaining
neutrons0 0 1.0
1 14.7 0.368
2 29.4 0.135
3 44.1 0.050
4 58.8 0.018
5 73.5 0.007 0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 2 4 6
Lifetimes
FractionS
urvived
After 4-5 lifetimes, almost all of theunstable particles have decayed away!
After 4-5 lifetimes, almost all of the
unstable particles have decayed away!
Lifetime (III)
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Not all particles have the same lifetime.
Uranium-238 has a lifetime of about 6 billion
(6x109) years !
Some subatomic particles have lifetimes that areless than 1x10-12 sec !
Given a batch of unstable particles, we cannot
say which one will decay.
The process of decay is statistical. That is, we canonly talk about either,
1) the lifetime of a radioactive substance*, or2) the probability that a given particle will decay.
Not all particles have the same lifetime.
Uranium-238 has a lifetime of about 6 billion(6x109) years !
Some subatomic particles have lifetimes that areless than 1x10-12 sec !
Given a batch of unstable particles, we cannotsay which one will decay.
The process of decay is statistical. That is, we canonly talk about either,
1) the lifetime of a radioactive substance*, or
2) the probability that a given particle will decay.
Lifetime (IV)
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Given a batch of 1 species of particles, some will decaywithin 1 lifetime (1 ), some within 2 , some within 3 , and
so on
We CANNOT say Particle 44 will decay at t =22 min.You just cant !
All we can say is that: After 1lifetime, there will be (37%) remaining After 2 lifetimes, there will be (14%) remaining After 3 lifetimes, there will be (5%) remaining After 4 lifetimes, there will be (2%) remaining, etc
Lifetime (V)
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Lifetime (V)
If the particles lifetime is very short, the particles decay away veryquickly.
When we get to subatomic particles, the lifetimesare typically only a small fraction of a second!
If the lifetime is long (like 238 U) it will hang around for a very longtime!
If the particles lifetime is very short, the particles decay away veryquickly.
When we get to subatomic particles, the lifetimesare typically only a small fraction of a second!
If the lifetime is long (like 238 U) it will hang around for a very longtime!
Lifetime (IV)
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t if we only have 1 particle before us? What can we sayut it?
Survival Probability = N / N0 = e-t/
Decay Probability = 1.0 (Survival Probabili
# lifetimes Survival Probability
(percent)
Decay Probability =1.0 Survival Probability
(Percent)
1 37% 63%
2 14% 86%
3 5% 95%
4 2% 98%
5 0.7% 99.3%
Summary
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Certain particles are radioactive and undergo decay.
Radiation in nuclear decay consists of , , and particles
The rate of decay is give by the radioactive decay law:
Survival Probability = (N/N0)e-t/
After 5 lifetimes more than 99% of the initial particleshave decayed away.
Some elements have lifetimes ~billions of years.
Subatomic particles usually have lifetimes which arefractions of a second Well come back to this!
Certain particles are radioactive and undergo decay.
Radiation in nuclear decay consists of , , and particles
The rate of decay is give by the radioactive decay law:
Survival Probability = (N/N0)e-t/
After 5 lifetimes more than 99% of the initial particleshave decayed away.
Some elements have lifetimes ~billions of years.
Subatomic particles usually have lifetimes which arefractions of a second Well come back to this!
Ionization sensors
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(detectors)
In an ionization sensor, the radiationpassing through a medium (gas or solid)creates electron-proton pairs
Their density and energy depends on theenergy of the ionizing radiation.
These charges can then be attracted toelectrodes and measured or they may be
accelerated through the use of magneticfields for further use.
The simplest and oldest type of sensor isthe ionization chamber.
Ionization chamber
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Ionization chamber
The chamber is a gas filled chamber
Usually at low pressure
Has predictable response to radiation.
In most gases, the ionization energy for the outerelectrons is fairly small 10 to 20 eV.
A somewhat higher energy is required since someenergy may be absorbed without releasing chargedpairs (by moving electrons into higher energy bandswithin the atom).
For sensing, the important quantity is the W value.
It is an average energy transferred per ion pairgenerated. Table 9.1 gives the W values for a fewgases used in ion chambers.
W l f
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W values for gases
Table 9.1. W va lues for var ious gases used in ionization chambers (eV/ion pair)
Gas Electrons (fast) Alpha particlesArgon (A) 27.0 25.9
Helium (He) 32.5 31.7
Nitrogen (N2) 35.8 36.0
Air 35.0 35.2
CH4 30.2 29.0
Ionization chamber
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Ionization chamber
Clearly ion pairs can also recombine. The current generated is due to an average rate of
ion generation.
The principle is shown in Figure 9.1.
When no ionization occurs, there is no current as thegas has negligible resistance.
The voltage across the cell is relatively high andattracts the charges, reducing recombination.
Under these conditions, the steady state current is a
good measure of the ionization rate.
Ionization chamber
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Ionization chamber
Ionization chamber
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Ionization chamber
The chamber operates in the saturationregion of the I-V curve.
The higher the radiation frequency andthe higher the voltage across thechamber electrodes the higher thecurrent across the chamber.
The chamber in Figure 9.1. is
sufficient for high energy radiation For low energy X-rays, a better
approach is needed.
Ionization chamber -
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applications The most common use for ionization chambers
is in smoke detectors.
The chamber is open to the air and ionizationoccurs in air.
A small radioactive source (usually Americum241) ionizes the air at a constant rate
This causes a small, constant ionization currentbetween the anode and cathode of thechamber.
Combustion products such as smoke enter thechamber
Ionization chamber -
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applications Smoke particles are much larger and heavier than air They form centers around which positive and negative charges
recombine.
This reduces the ionization current and triggers an alarm.
In most smoke detectors, there are two chambers.
One is as described above. It can be triggered by humidity, dustand even by pressure differences or small insects, a second,reference chamber is provided
In it the openings to air are too small to allow the large smokeparticles but will allow humidity.
The trigger is now based on the difference between these two
currents.
Ionization chambers in a
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residential smoke detector
Ionization chambers -
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application Fabric density sensor (see figure). The lower part contains a low energy radioactive
isotope (Krypton 85) The upper part is an ionization chamber.
The fabric passes between them. The ionization current is calibrated in terms of
density (i.e. weight per unit area). Similar devices are calibrated in terms of
thickness (rubber for example) or other quantitiesthat affect the amount of radiation that passesthrough such as moisture
A nuclear fabric density
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sensor
Proportional chamber
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Proportional chamber
A proportional chamber is a gas ionization chamber but: The potential across the electrodes is high enough to
produce an electric field in excess of 106 V/m.
The electrons are accelerated, process collide withatoms releasing additional electrons (and protons) in a
process called the Townsend avalanche. These charges are collected by the anode and because
of this multiplication effect can be used to detect lowerintensity radiation.
Proportional chamber
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Proportional chamber
The device is also called a proportionalcounter or multiplier.
If the electric field is increased further,the output becomes nonlinear due toprotons which cannot move as fast aselectrons causing a space charge.
Figure 9.2 shows the region of
operation of the various types of gaschambers.
Operation of ionizationh b
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chambers
Geiger-Muller counters
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Geiger Muller counters
An ionization chamber Voltage across an ionization chamber is very high
The output is not dependent on the ionizationenergy but rather is a function of the electric field inthe chamber.
Because of this, the GM counter can count singleparticles whereas this would be insufficient totrigger a proportional chamber.
This very high voltage can also trigger a false
reading immediately after a valid reading.
Geiger-Muller counters
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Geiger Muller counters
To prevent this, a quenching gas is added to the noble gasthat fills the counter chamber.
The G-M counter is made as a tube, up to 10-15cm longand about 3cm in diameter.
A window is provided to allow penetration of radiation.
The tube is filled with argon or helium with about 5-10%alcohol (Ethyl alcohol) to quench triggering.
The operation relies heavily on the avalanche effect
UV radiation is released which, in itself adds to theavalanche process.
The output is about the same no matter what the
ionization energy of the input radiation is.
Geiger-Muller counters
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Geiger Muller counters
Because of the very high voltage, a single particle canrelease 109 to 1010 ion pairs.
This means that a G-M counter is essentially guaranteedto detect any radiation through it.
The efficiency of all ionization chambers depends on thetype of radiation.
The cathodes also influence this efficiency
High atomic number cathodes are used for higherenergy radiation ( rays) and lower atomic numbercathodes to lower energy radiation.
Geiger-Muller sensor
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Geiger Muller sensor
Scintillation sensors
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Scintillation sensors
Takes advantage of the radiation to lightconversion (scintillation) that occurs in certainmaterials.
The light intensity generated is then a measure
of the radiations kinetic energy. Some scintillation sensors are used as detectorsin which the exact relationship to radiation isnot critical.
In others it is important that a linear relationexists and that the light conversion be efficient.
Scintillation sensors
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Scintillation sensors
Materials used should exhibit fast light decayfollowing irradiation (photoluminescence) to allowfast response of the detector.
The most common material used for this purposeis Sodium-Iodine (other of the alkali halide crystals
may be used and activation materials such asthalium are added)
There are also organic materials and plastics thatmay be used for this purpose. Many of these have
faster responses than the inorganic crystals.
Scintillation sensors
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Scintillation sensors
The light conversion is fairly weak because itinvolves inefficient processes.
Light obtained in these scintillating materials isof light intensity and requires amplification to
be detectable. A photomultiplier can be used as the detectormechanism as shown in Figure 9.5 to increasesensitivity.
The large gain of photomultipliers is critical inthe success of these devices.
Scintillation sensors
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Sc a o se so s
The reading is a function of many parameters. First, the energy of the particles and the
efficiency of conversion (about 10%) defines howmany photons are generated.
Part of this number, say k, reaches the cathode ofthe photomultiplier.
The cathode of the photomultiplier has aquantuum efficiency (about 20-25%).
This number, say k1is now multiplied by the gain
of the photomultiplier G which can be of the orderof 106 to 108.
Scintillation sensor
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Semiconductor radiationd t t
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detectors
Light radiation can be detected insemiconductors through release of chargesacross the band gap
Higher energy radiation can be expected do
so at much higher efficiencies. Any semiconductor light sensor will also be
sensitive to higher energy radiation
In practice there are a few issues that have
to be resolved.
Semiconductor radiationdetectors
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detectors First, because the energy is high, the lower bandgapmaterials are not useful since they would produce currents
that are too high.
Second, high energy radiation can easily penetrate throughthe semiconductor without releasing charges.
Thicker devices and heavier materials are needed.
Also, in detection of low radiation levels, the backgroundnoise, due to the dark current (current from thermalsources) can seriously interfere with the detector.
Because of this, some semiconducting radiation sensorscan only be used at cryogenic temperatures.
Semiconductor radiationdetectors
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detectors When an energetic particle penetrates into asemiconductor, it initiates a process which releases
electrons (and holes) through direct interaction with the crystal
through secondary emissions by the primary electrons
To produce a hole-electron pair energy is required: Called ionization energy - 3-5 eV (Table 9.2).This is only about 1/10 of the energy required to release an ion pair in
gases
The basic sensitivity of semiconductor sensors is anorder of magnitude higher than in gases.
Properties of
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semiconductors
Table 9.2. Properties of some common semiconductors
Material Operating
temp [K]
Atomic
number
Band gap [eV] Energy per electron-
hole pair [eV]
Silicon (Si) 300 14 1.12 3.61
Germanium (Ge) 77 32 0.74 2.98
Cadmium-teluride
(CdTe)
300 48, 52 1.47 4.43
Mercury-Iodine (HgI2) 300 80, 53 2.13 6.5
Gallium-Arsenide
(GaAs)
300 31, 33 1.43 4.2
Semiconductor radiationdetectors
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detectors Semiconductor radiation sensors are essentiallydiodes in reverse bias.
This ensures a small (ideally negligible) background(dark) current.
The reverse current produced by radiation is then a
measure of the kinetic energy of the radiation. The diode must be thick to ensure absorption of the
energy due to fast particles.
The most common construction is similar to the PIN
diode and is shown in Figure 9.6.
em con uctor ra at onsensor
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Semiconductor radiationdetectors
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detectors In this construction, a normal diode is built but with amuch thicker intrinsic region.
This region is doped with balanced impurities so that itresembles an intrinsic material.
To accomplish that and to avoid the tendency of drift
towards either an n or p behavior, an ion-driftingprocess is employed by diffusing a compensatingmaterial throughout the layer.
Lithium is the material of choice for this purpose.
Semiconductor radiationdetectors
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detectors Additional restrictions must be imposed: Germanium can be used at cryogenic temperatures
Silicon can be used at room temperature but:
Silicon is a light material (atomic number 14)
It is therefore very inefficient for energetic radiation such as
rays. For this purpose, cadmium telluride (CdTe) is the most often
used because it combines heavy materials (atomic numbers48 and 52) with relatively high bandgap energies.
Semiconductor radiationdetectors
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detectors Other materials that can be used are the mercuric iodine (HgI2)and gallium arsenide (GaAs).
Higher atomic number materials may also be used as a simpleintrinsic material detector (not a diode) because thebackground current is very small (see chapter 3).
The surface area of these devices can be quite large (some as
high as 50mm in diameter) or very small (1mm in diameter)depending on applications.
Resistivity under dark conditions is of the order of 108 to 1010 .cm depending on the construction and on doping, if any(intrinsic materials have higher resistivity).
.
Semiconductor radiationdetectors notes
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detectors - notes The idea of avalanche can be used to increase
sensitivity of semiconductor radiation detectors,especially at lower energy radiation.
These are called avalanche detectors and operate
similarly to the proportional detectors While this can increase the sensitivity by about two
orders of magnitude it is important to use theseonly for low energies or the barrier can be easilybreached and the sensor destroyed.
Semiconductor radiationdetectors notes
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detectors - notes Semiconducting radiation sensors are the most sensitiveand most versatile radiation sensors
They suffer from a number of limitations.
Damage can occur when exposed to radiation over time.
Damage can occur in the semiconductor lattice, in the
package or in the metal layers and connectors. Prolonged radiation may also increase the leakage (dark)
current and result in a loss of energy resolution of thesensor.
The temperature limits of the sensor must be taken into
account (unless a cooled sensor is used).
History of Constituents of
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Matter
AD
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In Nuclear Reactions momentum and mass-energy isconserved for a closed system the total momentumand energy of the particles present after the reaction isequal to the total momentum and energy of theparticles before the reaction
In the case where an alpha particle is released from anunstable nucleus the momentum of the alpha particleand the new nucleus is the same as the momentum ofthe original unstable nucleus
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0
0
0
1
1
1
1
0 ++ epnLarge variations in the emission velocities of the particleseemed to indicate that both energy and momentum were notconserved.
This led to the proposal by Wolfgang Pauli of another particle,the neutrino, being emitted in decay to carry away the
missing mass and momentum.
The neutrino (little neutral one) was discovered in 1956.
Wolfgang Pauli
__
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0
0
0
1
1
1
1
0 ++
epn1.008665 u 1.007825 u 0.0005486 u27
10660.1 1 u =
1 J = 19106.1
__
kg
eV
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0002914.0
)0005486.0007825.1(008665.1
=
+=Mass difference
2710660.10002914.0 =
311083724.4
=
kg
kg
u
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It has been found by experiment that the emitted beta particlehas less energy than 0.272 MeVNeutrino accounts for the missing energy
2mcE =2831 )100.3)(1083724.4( =
14
10353516.4
=
271755
10602.1
10353516.4
19
14
=
=
J
J
eV
272.0= MeV
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Ancient Greeks:
Earth, Air, Fire,Water
By 1900, nearly 100
elementsBy 1936, back to threeparticles: proton,
neutron [email protected]
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The Four Fundamental Forces
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Particle
zoo
2cEm =
-
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Classification of Particle
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Thomson (1897): Discovers electron
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mx 10101
mx 15101
mx 15107.0
mx 18107.0
( )
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0001
6028
6027 ++ eNiCo
Q = -1e almost all trapped in atoms
Q= 0 all freely moving through universe
_
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Just as the equation x2=4 can have two possiblesolutions (x=2 OR x=-2), so Dirac's equation
ld h l i f l
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could have two solutions, one for an electronwith positive energy, and one for an electron
with negative energy.
Dirac interpreted this to mean that for everyparticle that exists there is a correspondingantiparticle, exactly matching the particle butwith opposite charge. For the electron, forinstance, there should be an "antielectron"called the positron identical in every way butwith a positive electric charge.
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1928 Dirac predicted existence of antimatter
1932 antielectrons (positrons) found in conversion ofenergy into matter
1995 antihydrogen consisting of antiprotons andpositrons produced at CERN
+ + ee
In principle an antiworld can be built from
antimatterProduced only in accelerators andin cosmic rays
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++
eerays
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hfee 2+
+
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31=Q
3
2+=Q 1+=Q
0=Q
http://membres.lycos.fr/geryon/bio.htm -
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James Joyce
Murray Gell-Mann
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3
1
3
1
3
1
32+
3
2+
3
2
+
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13
1
3
2
3
2+=++
03
1
3
1
3
2=+
3
2
+
3
1
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