Overview of Modern Physics

1
Overview of Modern Physics

• Quantum Mechanics Special Relativity

2
Summary of Important Equations to understand for
the HW

1. c ? f
2. E h f
3. ? h/mv
4. ?t' ?t/v(1 - v2/c2)
5. E m c2

3
Three ways to transfer energy

• With a Particle
• With a Wave
• With a Field

4
Summary of Waves

• Properties
• Wavelength (l) distance between two successive
  crests
• Frequency (f) number of wave crests passing per
  second
• Speed of wave vfl
• Amplitude (A) maximum displacement
• Energy E µ A2

5
Interference

• Only waves experience interference ? this is just
  adding up the parts of a wave
• Where two crests (or troughs) meet, they add
• Where a crest and trough meet, they cancel

6
Introduction (Reference The Feynman Lectures,
Vol. 1, p. 37-3)

• Water waves, like all waves, experience
  interference when diffracted by two slits
• As seen here http//www.warren-wilson.edu/escerbo
  /Diffraction/2-slit.htm and here
  http//www.phy.davidson.edu/introlabs/labs220-230/
  html/lab10diffract.htm
• Imagine a pond in which we start a water wave
  ripple. The ripple starts out near the center
  and spreads radially outward (Water Ripples
  Movie and also video from The Examined Life)
• Very far away, the water wave ripple will look
  like a straight line. Something interesting
  happens to these plane waves (in this case, water
  waves) when they hit two slits.
• The water wave ripple will divide up into two new
  ripples when it hits the slits and, if the slits
  are spaced just right, the two new water wave
  ripples will experience interference (Double
  Slit Movie and Great Java Applet)
• We can represent it graphically by plotting the
  big and small parts as a graph

7
Light Particles vs. Waves

• Light was originally thought to be a particle
• E.g., look at sharp shadows, photoelectric
  effect, etc. ? also, Newton endorsed the view
  that light was made up of particles
• Particles behave completely differently when
  they encounter slits...
• E.g., suppose you fired bullets at one slit?
  What does that look like? Just a simple curve...
  
• What if you fired bullets at two slits? Just two
  separate curves
• So what happens when you fire light at it?
  Interference like water waves!

8
Quantum Particle Wave AND Particle

• Okay, so maybe light is a wave since it exhibits
  this wave behaviour.
• But we also know light is made up of particles
  (photons).
• So okay, light is nutty... light, like all
  matter, is actually a quantum particle
• It exhibits both wave and particle aspects
  (wave-particle duality)
• But that's not all there is to the quantum
  strangeness... what happens when you fire
  electron (quantum) particles?
• Same interference pattern even though you detect
  individual electron "particles" at the other end!
  
• Well, then electrons are simple waves, right? No!
  
• Reduce flow to a single electron (or photon) at a
  time and you still get the same pattern!
• And we definitely pick up particles at the other
  end (particle detectors)
• Each particle somehow knows where it should go...
  
• welcome to the quantum reality, welcome to the
  real nature of existence itself, which we will
  now explore in detail...

9
What Happens at the Slits?
-Top is what we get when slit 1 is
covered -Bottom is what we get when slit 2 is
covered -What do we get when both are open?
10
What Happens at the Slits?

• The blue curve is what we would get if each
  electron made a random choice of which slit to
  pass through
• The orange curve is what we actually get
• Conclusion?
• The electron passes through both slits at the
  same time
• The electron behaves both as a wave and as a
  particle

11
Something is rotten in the state of Denmark

• Three problems at the turn of the century were
  the first clues that all was not how it seemed

12
Ultra-Violet Catastrophe

• As the temperature of a BlackBody goes up, more
  energy is emitted per second at each wavelength
  and the peak wavelength shifts to smaller values
• Plot of UV catastrophe versus reality
  (experimental results are shown in Ch. 8 and is
  also shown in Fig. 10.1 on p. 373 and here)
• Why doesn't theory match reality (experiment)?

13
The Photoelectric Effect

• When light hits certain metals, e- are ejected
• Hypothesis brighter (higher intensity) light
  should cause more e- to be ejected with higher
  energies
• But, more light caused more e- to be ejected but
  it didn't increase their energy
• Only the frequency (colour) of the light
  affected the energy of the ejected e-
• Higher frequency light ejected e- with higher
  energy
• But even extremely dim light of the right
  frequency caused e- to be emitted
• Why does the energy of the ejected e- depend on
  the frequency of the light?

14
Can We Explain This?
Predictions of the Wave Model -For high enough
intensity, any wavelength of light should produce
the photoelectric effect. -The maximum kinetic
energy of the photoelectrons should scale with
light intensity. -The maximum kinetic energy
should be independent of the frequency. -The
photoelectrons need a measurable amount of time
to gain enough energy to be ejected.
Not what we see.
Not what we see.
Not what we see.
Not what we see.
15
The Atomic Spectra

• Light from bulbs, stars, etc. show a continuous
  spectrum when seen through a prism
• A hot gas, however, has an emission line spectrum
  made of a few, discrete lines of colour
• Why don't hot gases show continuous spectra?

Emission
Absorption
16
Quantum Hypothesis Energy is quantized

• What is quantization? It only comes in discrete
  chunks instead of a continuous range of energies
• Transparency 1 Figure 10.3 on p. 373
• If you assume the Energy of each atomic
  oscillator is quantized, you can get the correct
  BlackBody curve
• Planck suggested Energy is quantized in units of
  h and was proportional to the oscillators
  frequency E hf
• As is common in physics, he originally just came
  up with an equation to fit the curve without
  knowing anything about the underlying mechanism
  (he addressed the what but not the how)
• This quantization of energy arose as a necessary
  condition of the equation Planck derived to fit
  the correct curve
• Although he developed a model (energy is
  quantized) he had no idea why this should be so!

Continuous
Discrete
17
Quantum Hypothesis Light is quantized

• Einstein proposed that light is also quantized
  and its energy is also determined by its
  frequency via E hf
• Each individual packet of light energy is called
  a photon and an EM wave is made of these
  individual "particles"
• Brighter light ? more photons strike metal each
  second ? more e- ejected/sec (but it does not
  increase the energy of each e-)
• Higher frequency light ejects e- with more energy
  because each photon has more energy to give

18
Quantum Hypothesis Orbits are quantized

• Bohr suggested that the orbits of electrons are
  also quantized
• An electron can go from one level to another by
  absorbing or emitting a photon of light
• If light energy is quantized and electron orbits
  are also quantized, that would explain why atomic
  spectra are discrete (since atoms/electrons only
  absorb or emit a single photon at a time)

The Bohr Model of the Hydrogen Atom
19
Energy, Light, Orbits are quantized!

• So all three problems at the turn of the century
  had the same solution quantization of the
  fundamental aspects of nature!
• This is why it's called quantum mechanics
  everything is quantized (comes in discrete chunks
  instead of a continuous range of values) --
  matter (the Bohr "orbitals"), light, and even
  energy are ALL quantized!
• DeBroglie further hypothesized that since
  electrons also behave as waves, they must also
  have a wavelength ? h/mv
• This was part of his doctoral thesis which won
  him a Nobel prize
• He also came to physics late in life, contrary to
  the popular notion of physics being a young man's
  game
• E mc2 hf cvelectron and f v/? ? mv2
  hv/? ? ? hv/mv2 h/mv (see
  http//www.chemistrycoach.com/BohrAssump.htm)

20
In Class Exercise 1

• Compare the energies associated with a quantum
  of
• IR light (f 3 x 1013Hz),
• Blue light (f 6.3 x 1014Hz), and
• X-Rays (f 5 x 1018Hz)
• Note h 6.63 x 10-34J-s 4.136 x 10-15eV/Hz
  (see p. 375)

Known Unknown


fIR 3 x 1013Hz fBlue 6.3 x 1014Hz fX-Rays
5 x 1018Hz
E ?J
h 6.63 x 10-34J-s 4.136 x 10-15eV/Hz

• E hf

21
Quantum Mechanics in a nutshell

• Matter, it seems, is nutty at the sub-microscopic
  level
• Quantum particles behave like both waves and
  particles even energy comes in packets or
  chunks!
• Look at them one way, they're particles another
  way, they're waves!
• Transparency 2 Fig. 10.6 on p. 375 (reproduce)
• If you pass light through slits, it's a wave if
  you aim it at metals, it behaves like a particle
• "They could but make the best of it, and went
  around with woebegone faces sadly complaining
  that on Mondays, Wednesdays, and Fridays they
  must look on light as a wave on Tuesdays,
  Thursdays, and Saturdays as a particle. On
  Sundays, they simply prayed." -- Banesh Hoffmann
• Electrons are the same way they behave as both
  particles and waves
• All particles have a wave-aspect higher the
  momentum, shorter the wavelength
• But the incredibly tiny value of h ensures this
  is only a microscopic effect

22
Heisenberg Uncertainty Principle

• Heisenberg proposed that the wave aspect of an
  electron makes it impossible to know both the
  position and momentum to arbitrary precision
• Heisenberg Uncertainty Principle (HUP) ?x
  ?(mv) h/4p
• E.g., if you have a periodic wave (or a standing
  wave) you can't really tell what its position is
  (it's spread out over the whole string, e.g.).
  But you can tell exactly what its wavelength is.
  Now if you send a wave pulse down the string, you
  can't tell what its wavelength is (doesn't make
  sense for a pulse) but you can tell exactly what
  its position is. (With thanks to Prof. Griffiths)
  

23
The Atomic Structure

• So we can't say where exactly the electron is
  (it's not like a billiard ball, or like a wave,
  or like a puffy cloud, or like anything else we
  know from ordinary experience)
• "Now we know how the electrons and light behave.
  But what can I call it? If I say they behave like
  particles I give the wrong impression also if I
  say they behave like waves. They behave in their
  own inimitable way, which technically could be
  called a quantum mechanical way. They behave in a
  way that is like nothing that you have ever seen
  before. Your experience with things that you have
  seen before is incomplete. The behavior of things
  on a very tiny scale is simply different. An atom
  does not behave like a weight hanging on a spring
  and oscillating. Nor does it behave like a
  miniature representation of the solar system with
  little planets going around in orbits. Nor does
  it appear to be somewhat like a cloud or fog of
  some sort surrounding the nucleus. It behaves
  like nothing you have ever seen before." --
  Richard P. Feynman, The Character of Physical Law
  
• Since we can't talk about its exact location,
  it's more useful to concentrate on the electron's
  energy

24
Predicted Energy Levels

• Instead of looking at orbits, we now look at
  energy levels, which are the certain, allowed
  energy states
• Lowest energy level (corresponding to innermost
  orbit in Bohr theory) is called the ground state
  and higher energy states are excited states
• The structure of the atom is shown schematically
  on an energy-level diagram labeled with a quantum
  number n
• Transparency 3 Fig. 10.31 on p. 390
• As quantum number ?, Energy associated with that
  state ?
• Transition of the electron from one orbit to
  another is now represented as the atom going from
  one energy level to another
• Transition achieved by absorption or emission of
  a photon with an energy corresponding to the
  difference in energy between the two levels, or
  states
• When white light hits an atom, only photons with
  the right energy are absorbed!

25
In Class Exercise 2

• What is the frequency and wavelength of the
  photon absorbed by a hydrogen atom that takes it
  from the n1 state to the n2 state (see Fig.
  10.30 on p. 390)? Note c ? f (see p. 391)

Known Unknown






ni 1
f ?Hz
nf 2
? ?m
Ei E1 eV
Ef E2 eV
h 6.63 x 10-34J-s 4.136 x 10-15eV/Hz
c 3 x 108m/s

• DE E2 E1 hf ? f DE/h
• c lf ? l c/f
• l hc/DE

26
Some Atomic Physics

• Atom can gain or lose energy by absorption or
  emission of photons or by collisions
• Pauli Exclusion Principle two electrons cannot
  occupy the same quantum state at the same time
• Number of quantum states in a given energy level
  given by 2n2
• If even one electron is in a higher energy level,
  the atom is said to be in an excited state
• Properties of each element determined by the
  ground-state configuration of its atoms (e.g.,
  valence electrons, etc.)
• What about relativity?

27
Everything is relative

• In conversation, this implies there is no correct
  answer, no preferred point of view, nothing is
  fixed or constant.
• In physics, the meaning is quite different if I
  know how your motion and mine differ, I can
  predict exactly what you will see when you
  observe me.
• Some things look the same to all viewers
  everywhere at any time (invariants). Others do
  not. Thus, very important to find these
  invariants.

One essence of science PREDICTIONS
28
Inertial Reference Frames

• Describing a Physical Phenomenon requires
• Event
• Observer
• Frame of reference (the Point of View!)
• A reference frame is a coordinate system and a
  clock.
• An inertial reference frame is one that is not
  accelerated.
• Newtons Laws are valid in inertial reference
  frames only.
• An underlying assumption in Newtonian mechanics
  The laws of physics are the same in all inertial
  reference frames (Relativity).

29
Galilean vs. Special Relativity

• Galilean relativity throw ball from a speeding
  truck and the speeds add.
• In the late 19th century, Michelson and Morley
  designed an experiment that replaced the football
  with light, and the truck was replaced by the
  entire Earth. 
• But what they found was not the obvious solution
  ?they found that light travelled at a constant
  speed.
• If the quarterback shines a flashlight from a
  standing position, it goes at the same speed as
  if the quarterback shines the flashlight from the
  back of a moving truck.

30
Invariance of Maxwells Equations (Skip)

• Einstein noticed a contradiction between
  classical mechanics and electromagnetism
• Consequence of reconciling them (i.e., invariance
  of Maxwell's equations) leads to the constancy of
  the speed of light
• Maxwells equations showed that light is
• An electromagnetic wave
• EM waves dont need a medium
• EM waves propagate at speed c
• They also said that EM waves ALWAYS propagate at
  the same speed, c
• Newtonian mechanics predicts that any motion
  relative to empty space will reveal a different
  value for the speed of electromagnetic waves.
• THIS HAS NEVER BEEN OBSERVED
• Maxwells equations say changing E ? changing B
  ? changing E
• They look like

31
Laws of Mechanics must be the same in all
Inertial Frames of References (Skip)

• No Experiment involving laws of mechanics can
  differentiate between any two inertial frames of
  reference
• Only the relative motion of one frame of ref.
  w.r.t other can be detected
• Notion of ABSOLUTE motion is meaningless
• There is no such thing as a preferred frame of
  reference
• Some good links
• "Unlike Newton's equation, however, Maxwell's
  equations were not invariant under the Galilei
  transformation. This is evident from the fact
  that Maxwell's equations predicted the speed of
  light. But the speed of something depends on
  which inertial frame you were observing it from.
  So Maxwell's equations could only be correct in
  one particular inertial frame!This did not go
  well with the belief that the laws of physics
  should be the same regardless of which inertial
  frame you were making the observation from." (See
  http//www.phys.vt.edu/hcp/special_relativity/not
  es/section7.html)
• "Another great problem was that Maxwell's
  equations did not appear to obey the principle of
  Galelian Relativity i.e. they were not invariant
  under the Galelian transformations. This means
  that in a moving space ship the electric and
  optical phenomena should be different from those
  in a stationary ship!!! Thus one could use for
  example optical phenomena to determine the speed
  of the ship. One of the consequences of
  Maxwell's equations is that if there is a
  disturbance in the field such that light is
  generated, these electromagnetic waves go out in
  all directions equally and at the same speed c.
  Another consequence of the equations is that if
  the source of the disturbance is moving, the
  light emitted goes through space at the same
  speed c. This is analogous to the case of sound
  being likewise independent of the motion of the
  source. This independence of the motion of the
  source in the case of light brings up an
  interesting problem." (See http//vishnu.mth.uct.a
  c.za/omei/gr/chap1/node2.html)
• "Einstein, in 1905, explained this observation in
  the basis of the assertion that the laws of
  nature including Maxwell's equations with the
  same velocity of light are the same to you
  whether you are moving or not.Fitzgerald and
  Lorentz had shown how to modify the equations of
  ordinary mechanics to give them the same
  invariance properties as Maxwell's equations."
  (see http//www-math.mit.edu/18.013A/chapter29/sec
  tion06.html) "The theory of Electromagnetism,
  summarized and completed by J. Maxwell
  (1831-1879), appeared to alter the situation.
  Maxwell's equations allow a wave solution which
  represents electromagnetic waves propagating with
  the same speed in all directions. The Galilean
  transformation cannot retain the constancy of the
  speed of light and there could be only one
  inertial frame in which the light travels with
  the same speed in all directions. One could
  designate this frame the absolute rest frame.
  However, all experimental searches for this frame
  have failed. Einstein accepted the constancy of
  the speed of light in all inertial frames as a
  postulate and showed that the coordinate
  transformation between inertial frames has to be
  the Lorentz transformation to retain the
  invariance of the speed of light. All inertial
  frames are on the same footing again and the
  concept of relativity can remain. But the problem
  is that Newton's equation of motion, being
  invariant under the Galilean transformation, is
  not invariant under the Lorentz transformation.
  In the process of rescuing the concept of
  relativity in Electromagnetism, one in turn faces
  the possibility of ruining the concept of
  relativity in Mechanics. Einstein, postulating
  that all laws of physics are the same in all
  inertial reference frames, chose to modify
  Newton's equation of motion and invented the
  Relativistic Dynamics which is invariant under
  the Lorentz transformation." (See
  http//hepth.hanyang.ac.kr/kst/lect/relativity/c1
  3.htm)
• "Maxwell's equations are not invariant with
  respect to the Galilean transformation. That
  transformation introduced extra terms into the
  form of the equations, and this meant that
  different inertial observers would observe
  different electromagnetic effects and therefore,
  by performing a suitable experiment you would be
  able to determine your speed with respect to the
  ether. Several experiments were done in order to
  observe the effects that these extra terms
  introduced, in an attempt to measure the speed of
  the ether wind. Naturally, they all failed to
  discover those effects, thus people began to
  believe that, somehow, Maxwell's equations were
  wrong. Interestingly enough, Maxwell's equations
  turn out to be invariant with respect to the
  Lorentz transformation. This was all very
  confusing. Apparently, either Maxwell's equations
  or the Galilean transformation had to be wrong.
  They couldn't possibly both be correct!" (See
  http//mathforum.org/library/drmath/view/56248.htm
  l)
• See also http//www.geocities.com/autotheist/Physi
  cs/

32
Foundation of Relativity

• The laws of physics are the same for all
  observers moving uniformly in an inertial
  reference frame
• I.e., no special places in the universe
  (continuation of Copernican revolution)
• Galileo, Newton, and Einstein all agree that
  mechanics looks the same in all inertial frames
• Einstein added that electromagnetism looks
  identical in all inertial frames (therefore, c is
  invariant)
• Galileo Newton thought time and spatial length
  are invariant
• Einstein, noticing the invariance of c, suggested
  whats invariant is the interval t2 c2t2
  x2
• In addition, time becomes just another coordinate
  (albeit imaginary)
• Perceived order in which events occur depends on
  the observers frame of reference

33
Special Theory of Relativity

• Consequences of the invariance of the speed of
  light, c
• Two observers, in uniform relative motion, find
  space and time behave differently for them
• These effects are
• Time dilation
• Length contraction
• Mass increase
• Totally real effects!
• Not an illusion of perspective or apparent
  effect these are VERY real consequences!

So how does this happen?
34
Light Clocks Time Dilation

• Imagine a clock that uses light pulses
• When its motionless, the light beam goes up and
  down and clicks off one second (tick-tock)
• Now, imagine the clock in motion it still ticks
  off one second just like the ball on the truck
  still goes up and down
• BUT, the distance travelled, for both the ball
  and the clock, is much greater
• What does this mean?

35
Time Dilation slowing down time (OLD)

• Synchronize two light clocks on two ships
• One spaceship moves with a speed, v, relative to
  the observer on the stationary ship on the Earth
  
• Light path on the spaceship, according to the
  observer on Earth, follows a longer zig-zag path
  
• Speed distance/time c (speed of light)
• c is invariant
• Therefore, longer distance means longer time
  (since t d/c) As measured by a stationary
  observer on EARTh
• ? time dilation (as measured by the stationary
  observer on Earth!)
• But to the people on the moving ship, the Earth
  observer's clock runs slower!
• Both observers are correct
• "Time, then, is not an absolute, innate quality
  of nature"
• ?t' ?t/v(1 - v2/c2)

Time, as measured by the STATIONARY OBSERVER
36
Trucks to spaceships

• Synchronize two light clocks on two ships
• One spaceship moves with a speed, v, relative to
  the observer on the stationary ship on the Earth
• Light path on the spaceship, according to the
  observer on Earth, follows a longer zig-zag path
• Just like the guy throwing the ball on the truck
• He saw the ball go straight up and down
• But stationary observer saw it follow a longer,
  parabolic path

37
Stationary vs. Moving

• So the distance of the light beam, as measured by
  the stationary observer on Earth, is the longer
  zig-zag path
• But Speed distance/time c (speed of light)
• And c is invariant and constant
• Therefore, the light, as measured by the
  stationary observer on Earth, has to travel a
  longer distance
• Since time distance/(speed of light), that
  longer distance takes a longer time (as measured
  by a stationary observer on Earth)
• This is time dilation (as measured by the
  stationary observer on Earth!)
• Different observers, different strokes
  observations
• Although the guy on the moving ship still
  measures the tick-tock as taking one second, the
  stationary observer on Earth measures that same
  tick-tock as taking much longer than a second.
• This is just like the guy on the truck he sees
  the ball go straight up an down whereas the
  observer on the sidewalk sees it as taking a
  longer, parabolic path.
• So whos right?
• Both observers are correct
• "Time, then, is not an absolute, innate quality
  of nature"

38
Time Dilation the gruesome derivation

• We can derive this relationship quite easily
• Distance light travels, as seen by the moving
  observer (straight up and down) d ct/2
• Distance light travels, as seen by the stationary
  observer (the longer zig-zag path) cDt/2
• Distance the ship travels, as seen by the
  stationary observer (assume speed v) vDt/2
• Apply Pythagorean theorem c2 a2 b2
• ? (cDt/2)2 (vDt/2)2 (ct/2)2 ? Rearrange
• ?t' ?t/v(1 - v2/c2)

Original distance (tick)
Time, as measured by the STATIONARY OBSERVER
Distance light travels
Distance ship travels
39
Some more consequences

• Time dilation only significant at high speeds
• Transparency 5 Fig. 12.5 on p. 451
• Another consequence length contraction
• ?L' ?L v(1 - v2/c2)
• Yet another consequence rest energy is Eo mo
  c2
• In inelastic collisions, mass is transformed into
  energy and energy may be converted into mass
  because mass and energy are equivalent!
• This means, according to Einstein himself, "Mass
  and energy are only different expressions for
  the same thing."
• Erel KErel mc2 mc2/v(1 - v2/c2)
• Correspondence Principle Special Relativity
  reduces to Galilean Relativity at low speeds
• KErel reduces to ½ mv2 for low speeds (for higher
  speeds, higher the speed, higher the energy/mass)

40
General Relativity

• Einstein further realized that mechanics and
  light should look the same to an observer
  falling freely in a gravitational field as to an
  observer in an inertial frame!
• This is a more general statement of relativity.
• It makes natural the principle of equivalence
• equating inertial and gravitational mass.
• Truly explains gravity
• Matter tells space how to bend and space tells
  matter how to move
• Space is bent by matter

41
Newton vs. Einstein
Newton
Einstein
42
Why Do We Think Einsteins Theories are Correct?

• General relativity predicts exactly the observed
  orbits of the planets. Newtonian mechanics come
  close but do not exactly match observation.
• We have actually observed time dilation with
  highly accurate synchronized clocks.
• His theories account for experimental
  observations for which we have no other
  explanation (i.e. the detection of muons on the
  surface of the Earth).

43
Four Known Forces

• Two familiar kinds of interactions
• gravity (masses attract one another) and
  electromagnetism (same-sign charges repel,
  opposite-sign charges attract)
• What causes radioactive decays of nuclei ?
• Must be a force weak enough to allow most atoms
  to be stable.
• What binds protons together into nuclei ?
• Must be a force strong enough to overcome
  repulsion due to protons electric charge

44
Previously, we peered inside the atom

• We recalled that electrons orbit the atoms
  massive nucleus and determine an elements
  chemical behavior.
• We explored the proton and neutron content of
  nuclei and the phenomena of radioactivity,
  fission, and fusion they make possible.
• Today well look inside the nucleons themselves.
• Fundamental particles in the Standard Model are
• Leptons
• Quarks
• Intermediate Gauge Bosons

45
Anti-matter

• Each kind of elementary particle has a
  counterpart with the same mass, but the opposite
  electric charge, called its anti-particle.
• Electron m .0005 GeV, charge 1, symbol e-
• Positron m .0005 GeV, charge -1, symbol e
• The anti-particle has a bar over its symbol
• Anti-proton is written , anti-neutrino
  is
• Anti-matter is rare in the explored universe
• Its created in cosmic rays and particle
  accelerators and some radioactive decays.
• When a particle and its anti-particle collide,
  they annihilate one another in a flash of
  energy.

46
Where do the elements come from?
47
Stability diagram
Heavy elements can fission into lighter elements.
Elements from helium to iron were manufactured
in the cores of stars by fusion. Heavier
elements are metastable and were made during
supernovae explosions.
Light elements can undergo fusion into heavier
elements.
48
Chain reaction
For reaction to be self-sustaining, must
haveCRITICAL MASS.
49
Nuclear reactors
50
Fission bomb
51
Fusion

• Light nuclei are more stable when combined
• Tremendous energy released
• Hydrogen bombs and Fusion power?