modern physics by imran aziz

8/8/2019 Modern Physics by imran aziz

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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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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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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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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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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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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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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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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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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 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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Instead, what was observed wasalphas were scattered in alldirections

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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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The model predicted how manyalphas should be scattered at eachpossible angle

Consider the impact parameter

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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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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 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??

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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

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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

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Compton scattering 1


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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]



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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:

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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)

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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

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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

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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)

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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

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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

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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

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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

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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

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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.

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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).

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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.

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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.

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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.

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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.

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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

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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

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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

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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


+ 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


(in excited state)


(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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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.



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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.



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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.



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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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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.



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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.



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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.



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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.



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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



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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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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.



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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.



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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

[email protected]


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[email protected]


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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

[email protected]


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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

__

[email protected]


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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

[email protected]


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0002914.0

)0005486.0007825.1(008665.1

=

+=Mass difference

2710660.10002914.0 =

311083724.4

=

kg

kg

u

[email protected]


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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

[email protected]


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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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[email protected]

The Four Fundamental Forces


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[email protected]


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[email protected]


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[email protected]


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Particle

zoo

2cEm =

[email protected]


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[email protected]

Classification of Particle


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[email protected]

Thomson (1897): Discovers electron


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mx 10101

mx 15101

mx 15107.0

mx 18107.0

( )

[email protected]


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0001

6028

6027 ++ eNiCo

Q = -1e almost all trapped in atoms

Q= 0 all freely moving through universe

_

[email protected]


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[email protected]


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[email protected]

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.

[email protected]


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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

[email protected]


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++

eerays

[email protected]


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hfee 2+

+

[email protected]


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[email protected]


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31=Q

3

2+=Q 1+=Q

0=Q

[email protected]
http://membres.lycos.fr/geryon/bio.htm


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James Joyce

Murray Gell-Mann

[email protected]
http://membres.lycos.fr/geryon/bio.htm


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3

1

3

1

3

1

32+

3

2+

3

2

+

[email protected]


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13

1

3

2

3

2+=++

03

1

3

1

3

2=+

3

2

+

3

1

[email protected]


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modern physics by imran aziz

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