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Please be notified that we will hold our first test Please be notified that we will hold our first test on 16 Jan 2004, Friday, 5.00 – 5.50 pm (which on 16 Jan 2004, Friday, 5.00 – 5.50 pm (which was previously scheduled for the 3rd tutorial). was previously scheduled for the 3rd tutorial).

The test paper comprises of The test paper comprises of 20 objective 20 objective questions on (1) SR, (2) particle properties of questions on (1) SR, (2) particle properties of radiation, (3) wave properties of particles. Tutors radiation, (3) wave properties of particles. Tutors will monitor the process of the test. will monitor the process of the test.

Please make sure that you bring along your Please make sure that you bring along your pencil can scientific calculator, and don’t miss pencil can scientific calculator, and don’t miss the test. Thanks. the test. Thanks.

Notice of first testNotice of first test

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Notification of “ Constructive Web-Notification of “ Constructive Web-Based Learning” Based Learning”

Please be notified that the “computer-based test” as Please be notified that the “computer-based test” as mentioned earlier on is now readymentioned earlier on is now ready

Each student taking the course ZCT 104/3E please fill up Each student taking the course ZCT 104/3E please fill up your name in the registration lists that have been put up your name in the registration lists that have been put up outside the “Makmal Kumputer Fizik Gunaa” in the 2nd outside the “Makmal Kumputer Fizik Gunaa” in the 2nd level, School of Physicslevel, School of Physics

You only need to sit the “test” once. The “test” will be lasting You only need to sit the “test” once. The “test” will be lasting for about an hour. No prior preparation is neededfor about an hour. No prior preparation is needed

The dates this test will be conducted are as the followed The dates this test will be conducted are as the followed (choose a date and time that suits your preference)(choose a date and time that suits your preference)

3/1/04 (Sat) 4/1/04 (Sun) 9/1/04 (Fri) 3/1/04 (Sat) 4/1/04 (Sun) 9/1/04 (Fri) 10/1/04 (Sat) 11/1/04 (Sun) 17/1/04 (Sat) 10/1/04 (Sat) 11/1/04 (Sun) 17/1/04 (Sat) 18/1/04 (Sun)18/1/04 (Sun)

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Pair Production: Energy into Pair Production: Energy into mattermatter

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Conservational laws in pair-Conservational laws in pair-productionproduction

The pair-production must not violate some very The pair-production must not violate some very fundamental laws in physics:fundamental laws in physics:

Charge conservation, total linear momentum, Charge conservation, total linear momentum, total relativistic energy are to be obeyed in the total relativistic energy are to be obeyed in the processprocess

Due to kinematical consideration (energy and Due to kinematical consideration (energy and linear momentum conservations) pair production linear momentum conservations) pair production cannot occur in empty spacecannot occur in empty space

Must occur in the proximity of a nucleus (check Must occur in the proximity of a nucleus (check out the detail yourself in the text book if out the detail yourself in the text book if interested)interested)

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Energy threshold Energy threshold Due to conservation of relativistic energy, pair Due to conservation of relativistic energy, pair

production can only occur if Eproduction can only occur if E is larger than 2 is larger than 2 mmee = 2 x 0.51 MeV = 1.02 MeV = 2 x 0.51 MeV = 1.02 MeV

Any additional photon energy becomes kinetic Any additional photon energy becomes kinetic energy of the electron and positron, energy of the electron and positron, KK

KcmhcE e 22

nucleus

PP

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ExampleExample What is the minimal wavelength of a EM radiation What is the minimal wavelength of a EM radiation

to pair-produce an electron-positron pair?to pair-produce an electron-positron pair? Solutions: minimal photon energy occurs if the Solutions: minimal photon energy occurs if the

pair have no kinetic energy after being created, pair have no kinetic energy after being created, K K = 0= 0

Hence,Hence,

m1021.1MeV51.02eVnm1240

212

2min

cm

hc

e

These are very energetic EM radiation called gamma rays and are found in nature as one of the emissions from radioactive nuclei and in cosmic rays.

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Pair-annihilationPair-annihilation

The inverse of pair production occurs The inverse of pair production occurs when a positron is near an electron and when a positron is near an electron and the two come together under the influence the two come together under the influence of their opposite electric chargesof their opposite electric charges

ee++ + e + e-- + + Both particles vanish simultaneously, with Both particles vanish simultaneously, with

the lost masses becoming energies in the the lost masses becoming energies in the form of two gamma-ray photons:form of two gamma-ray photons:

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Initial energy = 2mec2 + K

Final energy = hc/hc/

Conservation of relativistic energy:

2mec2 + K = 2 hc/

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The total relativistic energy of the eThe total relativistic energy of the e---e+ pair is -e+ pair is EE = 2 = 2mmeecc22 + + KK = 1.02 MeV + = 1.02 MeV + KK, where , where K K the total kinetic energy of the the total kinetic energy of the electron-positron pair before annihilation electron-positron pair before annihilation

Each resultant gamma ray photon has an energy Each resultant gamma ray photon has an energy hh = = 0.51 MeV + 0.51 MeV + KK/2/2

Both energy and linear momentum are automatically Both energy and linear momentum are automatically conserved in pair annihilation (else it wont occur at all)conserved in pair annihilation (else it wont occur at all)

The gamma photons are always emitted in a back-to-back The gamma photons are always emitted in a back-to-back manner due to kinematical reasons (conservation of linear manner due to kinematical reasons (conservation of linear momentum)momentum)

No nucleus or other particle is needed for pair annihilation No nucleus or other particle is needed for pair annihilation to take placeto take place

Pair annihilation always occurs whenever a matter comes Pair annihilation always occurs whenever a matter comes into contact with its antimatterinto contact with its antimatter

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As a tool to observe anti-worldAs a tool to observe anti-world What is the characteristic energy of a gamma-ray that is What is the characteristic energy of a gamma-ray that is

produced in a pair-annihilation production process? What produced in a pair-annihilation production process? What is its wavelength?is its wavelength?

Answer: 0.51 MeV, Answer: 0.51 MeV, annihannih = = hchc / 0.51 MeV = 0.0243 nm / 0.51 MeV = 0.0243 nm The detection of such characteristic gamma ray in The detection of such characteristic gamma ray in

astrophysics indicates the annihilation of matter-astrophysics indicates the annihilation of matter-antimatter in deep spaceantimatter in deep space

May indicate the existence of ‘anti-matter world’May indicate the existence of ‘anti-matter world’ However, none of this is observedHowever, none of this is observed Our observed universe does not contain any anti-matter Our observed universe does not contain any anti-matter

worldworld

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Wave particle dualityWave particle duality

““Quantum nature of light” refers to the Quantum nature of light” refers to the particle attribute of lightparticle attribute of light

““Quantum nature of particle” refers to the Quantum nature of particle” refers to the wave attribute of a particlewave attribute of a particle

Light (classically EM waves) is said to Light (classically EM waves) is said to display “wave-particle duality” – it behave display “wave-particle duality” – it behave like wave in one experiment but as particle like wave in one experiment but as particle in others (c.f. a person with schizophrenia)in others (c.f. a person with schizophrenia)

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Not only light does have “schizophrenia”, so are Not only light does have “schizophrenia”, so are other microscopic ``particle’’ such as electron, other microscopic ``particle’’ such as electron, (see later chapters), i.e. particle” also manifest (see later chapters), i.e. particle” also manifest wave characteristics in some experimentswave characteristics in some experiments

Wave-particle duality is essentially the Wave-particle duality is essentially the manifestation of the quantum nature of thingsmanifestation of the quantum nature of things

This is an very weird picture quite contradicts to This is an very weird picture quite contradicts to our conventional assumption with is deeply our conventional assumption with is deeply rooted on classical physics or intuitive notion on rooted on classical physics or intuitive notion on thingsthings

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Whether light displays wave or particle nature Whether light displays wave or particle nature depends on the object it is interacting with, and depends on the object it is interacting with, and also on the experimental set-up to observe italso on the experimental set-up to observe it

If an experiment is set-up to observe the wave If an experiment is set-up to observe the wave nature (such as in interference or diffraction nature (such as in interference or diffraction experiment), it displays wave nature experiment), it displays wave nature

If the experimental set-up has a scale that is If the experimental set-up has a scale that is corresponding to the quantum nature of corresponding to the quantum nature of radiation, then light will displays particle radiation, then light will displays particle behaviour, such as in Compton scatteringsbehaviour, such as in Compton scatterings

When is light wave and when is it When is light wave and when is it particle?particle?

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Compton wavelength as a scale to Compton wavelength as a scale to the quantum nature of light and the quantum nature of light and

matter (electron)matter (electron) As an example of a ‘scale’ in a given As an example of a ‘scale’ in a given

experiment or a theory, let’s consider the experiment or a theory, let’s consider the Compton wavelength in Compton scatteringCompton wavelength in Compton scattering

Compton wavelength is the Compton wavelength is the lengthlength scalescale

which characterises the onset of quantum which characterises the onset of quantum nature of light (corpuscular nature) and nature of light (corpuscular nature) and electron (wave nature) in their interactionselectron (wave nature) in their interactions

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If the wavelength of light is much larger than If the wavelength of light is much larger than the Compton wavelength of the electron it is the Compton wavelength of the electron it is interacting with, light behaves like wave (e.g. interacting with, light behaves like wave (e.g. in interference experiments with visible light). in interference experiments with visible light). Compton effect is negligible in this caseCompton effect is negligible in this case

On the other hand, if the wavelength of the On the other hand, if the wavelength of the radiation is comparable to the Compton radiation is comparable to the Compton wavelength of the interacting particle, light wavelength of the interacting particle, light starts to behave like particle and collides with starts to behave like particle and collides with the electron in an ‘particle-particle’ mannerthe electron in an ‘particle-particle’ manner

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In short the identity manifested by In short the identity manifested by light depends on what it “sees” light depends on what it “sees”

(which in turns depend on its own (which in turns depend on its own wavelength) in a given experimental wavelength) in a given experimental

conditioncondition

Microscopic matter particle (such as Microscopic matter particle (such as electron and atoms) also manifest electron and atoms) also manifest

wave-particle dualitywave-particle duality

This will be the next agenda in our This will be the next agenda in our coursecourse

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Wavelike properties of particleWavelike properties of particle In 1923, while still a graduate In 1923, while still a graduate

student at the University of student at the University of Paris, Louis de Broglie Paris, Louis de Broglie published a brief note in the published a brief note in the journal journal Comptes rendusComptes rendus containing an idea that was to containing an idea that was to revolutionize our revolutionize our understanding of the physical understanding of the physical world at the most fundamental world at the most fundamental level: level: That particle has intrinsic That particle has intrinsic wave propertieswave properties

For more interesting details:For more interesting details: http://www.davis-inc.com/http://www.davis-inc.com/

physics/index.shtmlphysics/index.shtml Prince de Broglie, 1892-1987

1919

de Broglie’s postulate (1924)de Broglie’s postulate (1924) The postulate: there should be a symmetry The postulate: there should be a symmetry

between matter and wave. The wave aspect of between matter and wave. The wave aspect of matter is related to its particle aspect in exactly matter is related to its particle aspect in exactly the same quantitative manner that is in the case the same quantitative manner that is in the case for radiation. The total energy for radiation. The total energy EE and momentum and momentum p p of an entity, for both matter and wave alike, is of an entity, for both matter and wave alike, is related to the frequency related to the frequency nn of the wave of the wave associated with its motion via by Planck constantassociated with its motion via by Planck constant

E E = = hh; p ; p = = hh//

2020

= = hh//pp is the de Broglie relation predicting the is the de Broglie relation predicting the

wave length of the matter wave wave length of the matter wave associated with the motion of a material associated with the motion of a material particle with momentum particle with momentum pp

Particle with linear momentum p

Matter wave with de Broglie wavelength

= p/h

A particle with momentum p is pictured as a wave

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A physical entity possess both A physical entity possess both aspects of particle and wave in a aspects of particle and wave in a

complimentary mannercomplimentary manner

BUT why is the wave nature of material particle

not observed?

Because …

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Because…we are too large and quantum effects are too Because…we are too large and quantum effects are too smallsmall

Consider two extreme cases: Consider two extreme cases: (i) an electron with kinetic energy K = 54 eV, de Broglie (i) an electron with kinetic energy K = 54 eV, de Broglie

wavelenght, wavelenght, = h/p = = h/p = h / (2mh / (2meeK)K)1/21/2 = 1.65 Angstrom = 1.65 Angstrom

(ii) a billard (100 g) ball moving with momentum p = mv = (ii) a billard (100 g) ball moving with momentum p = mv = 0.1 kg x 10 m/s = 1 Ns, de Broglie wavelenght, 0.1 kg x 10 m/s = 1 Ns, de Broglie wavelenght, = h/p = = h/p = 1010-34-34 m, too small to be observed in any experiments m, too small to be observed in any experiments

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Matter wave is a quantum Matter wave is a quantum phenomenaphenomena

This also means that this effect is difficult to observe in This also means that this effect is difficult to observe in our macroscopic world (unless with the aid of some our macroscopic world (unless with the aid of some specially designed apparatus)specially designed apparatus)

The smallness of The smallness of hh in the relation in the relation = = hh//pp makes wave makes wave characteristic of particles hard to be observedcharacteristic of particles hard to be observed

The statement that when The statement that when h h 0, 0, becomes vanishingly becomes vanishingly small means that small means that

the wave nature will becomes effectively ``shut-off’’ and the wave nature will becomes effectively ``shut-off’’ and there would appear to loss its wave nature whenever the there would appear to loss its wave nature whenever the relevant scale (e.g. the relevant scale (e.g. the pp of the particle) is too large in of the particle) is too large in comparison with comparison with hh ~ 10-34 Js ~ 10-34 Js

In other words, the wave nature will of a particle will only In other words, the wave nature will of a particle will only show up when the scale show up when the scale pp is comparable (or smaller) to is comparable (or smaller) to the size of the size of hh