Download lecture 15 (zipped power point) (update: 2 Jan 03)

Notice of first test

Please be notified that we will hold our first test
on 16 Jan 2004, Friday, 5.00 – 5.50 pm (which
was previously scheduled for the 3rd tutorial).
 The test paper comprises of 20 objective
questions on (1) SR, (2) particle properties of
radiation, (3) wave properties of particles. Tutors
will monitor the process of the test.
 Please make sure that you bring along your
pencil can scientific calculator, and don’t miss
the test. Thanks.
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Notification of “ Constructive WebBased Learning”
Please be notified that the “computer-based test” as
mentioned earlier on is now ready
 Each student taking the course ZCT 104/3E please fill up
your name in the registration lists that have been put up
outside the “Makmal Kumputer Fizik Gunaa” in the 2nd
level, School of Physics
 You only need to sit the “test” once. The “test” will be
lasting for about an hour. No prior preparation is needed
 The dates this test will be conducted are as the followed
(choose a date and time that suits your preference)



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3/1/04 (Sat)
4/1/04 (Sun)
10/1/04 (Sat) 11/1/04 (Sun)
18/1/04 (Sun)
9/1/04 (Fri)
17/1/04 (Sat)
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Pair Production: Energy into
matter
3
Conservational laws in pairproduction

The pair-production must not violate some very
fundamental laws in physics:
 Charge conservation, total linear momentum,
total relativistic energy are to be obeyed in the
process
 Due to kinematical consideration (energy and
linear momentum conservations) pair production
cannot occur in empty space
 Must occur in the proximity of a nucleus (check
out the detail yourself in the text book if
interested)
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Energy threshold

Due to conservation of relativistic energy, pair
production can only occur if Eg is larger than 2
me = 2 x 0.51 MeV = 1.02 MeV
 Any additional photon energy becomes kinetic
energy of the electron and positron, K
Eg 
hc

 2me c  K
2
PP
nucleus
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Example

What is the minimal wavelength of a EM
radiation to pair-produce an electron-positron
pair?
 Solutions: minimal photon energy occurs if
the pair have no kinetic energy after being
created, K = 0
 Hence,
min
hc
1240nm  eV
12


 1.2110 m
2
2me c
2  0.51MeV
These are very energetic EM radiation called gamma
rays and are found in nature as one of the emissions
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from radioactive nuclei and in cosmic rays.
Pair-annihilation
 The
inverse of pair production occurs
when a positron is near an electron and
the two come together under the influence
of their opposite electric charges
e+ + e-  g + g
 Both particles vanish simultaneously, with
the lost masses becoming energies in the
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 e--e+ pair is E =
2mec2 + K = 1.02 MeV + K, where K the total kinetic
energy of the electron-positron pair before annihilation
Each resultant gamma ray photon has an energy hn =
0.51 MeV + K/2
Both energy and linear momentum are automatically
conserved in pair annihilation (else it wont occur at all)
The gamma photons are always emitted in a back-toback manner due to kinematical reasons (conservation
of linear momentum)
No nucleus or other particle is needed for pair
annihilation to take place
Pair annihilation always occurs whenever a matter
comes into contact with its antimatter
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As a tool to observe anti-world

What is the characteristic energy of a gamma-ray that is
produced in a pair-annihilation production process?
What is its wavelength?
 Answer: 0.51 MeV, annih = hc / 0.51 MeV = 0.0243 nm
 The detection of such characteristic gamma ray in
astrophysics indicates the annihilation of matterantimatter in deep space
 May indicate the existence of ‘anti-matter world’
 However, none of this is observed
 Our observed universe does not contain any anti-matter
world
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Wave particle duality
 “Quantum
nature of light” refers to the
particle attribute of light
 “Quantum nature of particle” refers to the
wave attribute of a particle
 Light (classically EM waves) is said to
display “wave-particle duality” – it behave
like wave in one experiment but as particle
in others (c.f. a person with schizophrenia)
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Not only light does have “schizophrenia”, so are
other microscopic ``particle’’ such as electron,
(see later chapters), i.e. particle” also manifest
wave characteristics in some experiments
 Wave-particle duality is essentially the
manifestation of the quantum nature of things
 This is an very weird picture quite contradicts to
our conventional assumption with is deeply
rooted on classical physics or intuitive notion on
things

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When is light wave and when is it
particle?

Whether light displays wave or particle nature
depends on the object it is interacting with, and
also on the experimental set-up to observe it
 If an experiment is set-up to observe the wave
nature (such as in interference or diffraction
experiment), it displays wave nature
 If the experimental set-up has a scale that is
corresponding to the quantum nature of
radiation, then light will displays particle
behaviour, such as in Compton scatterings
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Compton wavelength as a scale to
the quantum nature of light and
matter (electron)

As an example of a ‘scale’ in a given
experiment or a theory, let’s consider the
Compton wavelength in Compton scattering

Compton wavelength is the length scale
which characterises the onset of quantum
nature of light (corpuscular nature) and
electron (wave nature) in their interactions
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
If the wavelength of light is much larger than
the Compton wavelength of the electron it is
interacting with, light behaves like wave (e.g.
in interference experiments with visible light).
Compton effect is negligible in this case

On the other hand, if the wavelength of the
radiation is comparable to the Compton
wavelength of the interacting particle, light
starts to behave like particle and collides with
the electron in an ‘particle-particle’ manner
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In short the identity manifested by
light depends on what it “sees”
(which in turns depend on its own
wavelength) in a given experimental
condition
Microscopic matter particle (such as
electron and atoms) also manifest
wave-particle duality
This will be the next agenda in our
course
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Wavelike properties of particle



In 1923, while still a graduate
student at the University of
Paris, Louis de Broglie
published a brief note in the
journal Comptes rendus
containing an idea that was to
revolutionize our
understanding of the physical
world at the most fundamental
level: That particle has intrinsic
wave properties
For more interesting details:
http://www.davisinc.com/physics/index.shtml
Prince de Broglie, 18921987
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de Broglie’s postulate (1924)

The postulate: there should be a symmetry
between matter and wave. The wave aspect of
matter is related to its particle aspect in exactly
the same quantitative manner that is in the case
for radiation. The total energy E and momentum
p of an entity, for both matter and wave alike, is
related to the frequency n of the wave
associated with its motion via by Planck constant
 E = hn; p = h/
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 = h/p
 is
the de Broglie relation predicting the
wave length of the matter wave 
associated with the motion of a material
particle with momentum p
A particle with momentum p
is pictured as a wave
Particle with linear
momentum p
Matter wave with de
Broglie wavelength
 = p/h
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A physical entity possess both
aspects of particle and wave in a
complimentary 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
small

Consider two extreme cases:
 (i) an electron with kinetic energy K = 54 eV, de Broglie
wavelenght,  = h/p =
h / (2meK)1/2 = 1.65 Angstrom

(ii) a billard (100 g) ball moving with momentum p = mv =
0.1 kg x 10 m/s = 1 Ns, de Broglie wavelenght,  = h/p =
10-34 m, too small to be observed in any experiments
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Matter wave is a quantum
phenomena

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This also means that this effect is difficult to observe in
our macroscopic world (unless with the aid of some
specially designed apparatus)
The smallness of h in the relation  = h/p makes wave
characteristic of particles hard to be observed
The statement that when h  0,  becomes
vanishingly small means that
the wave nature will becomes effectively ``shut-off’’
and there would appear to loss its wave nature
whenever the relevant scale (e.g. the p of the particle)
is too large in comparison with h ~ 10-34 Js
In other words, the wave nature will of a particle will
only show up when the scale p is comparable (or
smaller) to the size of h
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