Peter Paul 09/8/05 PHY313-CEI544 Fall-05 1

PHY313 - CEI544The Mystery of Matter

From Quarks to the CosmosFall 2005

Peter PaulOffice Physics D-143

www.physics.sunysb.edu PHY313

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 2

The Energy Scales of Matter

• http://www.jca.umbc.edu/~george/html/courses/glossary/key_energies.html

• Energy units in the standard system is the Joule, 1 W = 1 J/s

• In advanced physics the energy unit is the eV, the energy it takes to accelerate one electric charge with a potential of 1 Volt.

• This unit is very small1 eV = 1.6 10 -19 Joules1000 eV = 1 keV1 Million eV = 1 MeV1 Billion eV = 1 GeV

• A 27-in TV accelerates electrons to 30 keV

,

The Relativistic Heavy Ion Collider accelerates Au ions to 100 GeV x 197 ~ 20 TeV

about 1 Billion times your TV

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 3

What have we learned so far?

• Physics changed around the years 1900 to 1905 by the introduction of energy quantization by Planck and by Einstein’s realization that the speed of light must be the same in all inertial reference frames.

• Thus h = 4.14 x 10-15 eV s and c = 3 x 108 m/s became the two most important constants in nature.

• When a mass moves at v ~ c the laws must change from Newton’s mechanics to Relativity.

• When an action involves an energy and scale close to hc = 1240 eV nm quantum effects become important.

• The concepts that explain matter and mass apply to a huge scale of lengths and energy, of which the small dimensions from nanometers (nm) to femtometer (fm) have become important to our daily life.

• Four known fundamental forcesdescribe all interactions in nature. They differ hugely in their strength and range. They bind quarks into nuclei, nuclei into atoms, atoms into crystals and materials, and hold together the masses in the cosmos.

• At very high energies 3 of these forces approach the same strength.

• Why?

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 4

Planck’s Constant h

• Relativity becomes important when velocity ~ c

• Quantum effects become important when

energy x size ~ h c

• Example from chip design:Energy scale ~ 6 eVSize ~ 1240/6 nm ~ 200 nm

This is a very practical dimension and poses limits for the chip industry.

• The two most important constants in Nature are:

• The speed of light cC = 2.998 x 108 m/s

• Planck’s constant hh = 6.626 x 10-34 J s or

4.137 x 10-15 eV s• h is a very small amount of

“action”

h c = 1240 eV nm

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 5

Energy scale of microscopic matter

• Atoms eV to keV• Materials 0.1 eV to 1 eV• Nuclei MeV• Elementary particles 100 MeV

to GeV• Largest existing accelerator

(LHC) 16 TeV = 1.6 x 103 GeV• Unification scale 1016 GeV• Planck Energy 1.2 x 1019 GeV

Thermal scales: • Room temperature 1/40 eV• Temperature of the sun surface

6000 degrees ~ 0.5 eV• Temperature required to melt

nuclei:

170 MeV = 2000 x Billions of the temperature at the surface of the sun

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 6

1905: The Year of Albert Einstein• http://www.aip.org/history/einstein/• In 1905 Einstein produced 3 break-through

papers:1. Photoelectric effect: Light is an energy

quantum that can be treated like a particle. E = h ν

2. Brownian motion: heat is kinetic energy of small particles moving in a medium:

3. Special Relativity: The speed of light must be the same in all inertial reference frame: E = mc2

4. His Gedanken Experiments established a whole new way to gain physical insight

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 7

The Photo Effect• The energy of the light overcomes the

binding energy (WF) of the electron in the material:

• http://lectureonline.cl.msu.edu/~mmp/kap28/Photoeffect/

• This experiment proves that light can act as a particle.

• The binding energy WF depends on the material and tells us about the binding energy of electrons inside crystals and surfaces.

• Einstein introduced E = h ν to explain the Photo-effect.

• E is a quantum of light energy→photon with frequency ν

• In this process a photon knocks out electrons from material surfaces and gives them kinetic energy.

• The capability of knocking them out depends only on the frequency, i.e. the energy of the photon, not on the number of photons that hit the surface . K = hν −WF

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 8

Review: Properties of Waves

• A wave has a frequency ν= number of oscillations per s (in Hz),

• a wave length λ = distance from one peak to the next (in m or nm).

• A velocity v = λ ν.• An amplitude A.• For sound wave vs = 334 m/s in air• When a supersonic planes velocity

exceeds vs it outruns its own sonic boom!

• A man with a flashlight in a fast car can never do that!

• Velocity of light c must be the same in all uniformly moving frames

• Two or more waves of the same frequency or different frequencies can be added.

• They can be diffracted and interfere with each other:

• Young’s Double slit experiment• http://www.ngsir.netfirms.com/e

nglishVersion.htm• http://www.colorado.edu/physics

/2000/applets/twoslitsa.html

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 9

Special Relativity: The basics• If light is an EM wave the laws of

optics require that speed of light c in free space must be the same in all inertial reference frames.

• There can be no “ether” medium that carries the light. A light wave travels through empty space!

• Otherwise a fast-moving traveler could outrun her own image!

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/star.html - c1• This had been confirmed earlier

experimentally in 1879 by Michelson.

• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/mmexpt6.htm

• The deep basis for Special Relativity is that….

• The laws of physics should be the same in all inertial reference frames.

• EM wave has a frequency ν, a wavelength λ and a speed c.These parameters are related:λν = c

• If c = constant then an increasing ν requires a decreasing λ

http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html - c1

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 10

The Basis for Einstein’s Special Theory of Relativity

• Einstein's theory of special relativity results from two statements -- the two basic postulates of special relativity:

• The speed of light is the same for all observers, no matter what their relative speeds.

• The laws of physics are the same in any inertial (that is, non-accelerated) frame of reference. This means that the laws of physics observed by a hypothetical observer traveling with a relativistic particle must be the same as those observed by an observer who is stationary in the laboratory.

• Given these two statements, Einstein showed how definitions of momentum and energy must be refined and how quantities such as length and time must change from one observer to another in order to get consistent results for physical quantities such as particle half-life. To decide whether his postulates are a correct theory of nature, physicists test whether the predictions of Einstein's theory match observations. Indeed many such tests have been made -- and the answers Einstein gave are right every time!These assumptions lead to a number of unexpected results

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 11

Moving clocks and time dilation• If c is constant, then we must expect

strange new physics when somebody moves at a velocity close to c.

• A moving clock observed by a stationary observer, ticks more slowly when velocity is close to c:

• T’ is the clock time of the observer sitting in the moving frame

• T is the clock time of the observer at rest.

http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf

• A fly lives 1 day inside a car.• If the car moves at a velocity of

v = 0.8 x ci.e. at 80% of the speed of light, the

fly’s lifetime as seen by a road observer will be

t = t’/0.6 = 1.67 days• That means the fly seems to live

longer as measured by the stationary observer.

• The famous twin paradox: The twin that traveled in a spaceship at close to the speed of light, ages less than the one who stays behind.

t = t '

1− v 2

c 2

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 12

The Amazing Atmospheric Mu Mesons• Mu (µ) mesons are created in the upper

atmosphere at h = 10 km at a rate of ~1 per cm2 and sec.

• They live on the average in their rest frame t’ = 2.3 µs.

• They move with a speed of 0.98 c • Their travel time over 10 km is 34 µs and

only 0.3 out 1 Million survive.• However with time dilation their life timeis 5 x 2.3 = 11.5 µs and 49,000 out of a million survive.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/muonatm.html

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html

• Muons can be produced in particle reactions and accelerated rapidly to, say, 30 GeV.

• Their time dilation factor then will be

• Thus the muons live 690 µs as they fly through the stationary atmosphere

ssT

MeVMeV

mcE

cv

µµ 6903.2300

300100

000,30

1

12

2

2

=⋅=

===

−

Haefele and Keating Experimentin 1972 traveling around the globe.

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 13

Moving Objects and Length Contraction• An object of length L’ that moves with a

speed v ~ c will be seen by a stationary observer with its dimensions in the direction of motion shortened

• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf

• A car that is 5 m long at rest and travels at v = 0.8 c will be only

• A Soccer ball will be shaped like a football with the short axis in the flight direction.

= 5m 1− 0.82 = 5m •0.6 = 0.3mL

L = L'• 1− v2

c2

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 14

How Long is the SLAC Accelerator?

• The SLAC electron linear accelerator at Stanford University is 2 miles long on the ground. How long does it appear to the electrons in the beam?

• L’= 2 miles = 3,200 m• The final beam energy is 30 GeV. Thus at

the half point E = 15 GeV

• Thus if I am riding on the electron beam through the accelerator it is only

L = 3,200/3000 ~ 1m long!• Thus it is quite easy to align the machine!

1− v 2

c 2 =0.5MeV

15,000MeV=

13000

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 15

Energy and Momentum in Special Relativity• In Newton’s mechanics every

particle has a kinetic Energy K and a momentum p:

• Because of the condition that c is the same in all frames, these rules need to be changed in Special Relativity

http://galileoandeinstein.physics.virginia.edu/lectures/mass_increase.html

• In Einstein’s mechanics every particle has kinetic energy K, a momentum p, and a mass energy given by mc2.

• Kinetic energy and mass energy add up to a total energy E:

• That means that the moving particle gains mass as it speeds up. It actually becomes heavier

K =m2

v 2 =p2

2mvmp ⋅=

2

2

2

2

1cv

mcE

mcE

−

=

= Stationary particle

Moving particle

42222 cmcpE +=

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 16

Some mass energies at rest and in motion

• Rest energy of electron 511 keV• Rest energy of the muon 106 MeV• Rest energy of pion 140 MeV• Rest energy of proton 938.3 MeV• Rest energy of neutron 939.6 MeV• Rest energy of Au nucleus 183.5 GeV• Rest energy of U nucleus 221.6 GeV• Rest energy of Z boson 80 GeV

• A 30-GeV electron moves with v/c = 0.99999. Its mass is ~ 30 GeV• A 200-GeV proton moves with v/c = 0.99987. Its mass is ~ 200 GeV.

.

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 17

What about the mass of the Photon?

• Since a photon always moves with the speed of light, it must be a very special object.

• Its rest mass must be zero because it can never stand still!

• Einstein writes down for the energy of a particle:

• For p = 0 (i.e. particle at rest) this gives the famous equation

• Mass is Energy!

• Thus for a photon with m = 0

• With De Broglie p = h/λ (see slide 20) this gives:

as Einstein had already postulated.

• Thus it all hangs together.

E 2 = p2c 2 + m2c 4

E = pc

E = mc 2

E = hν

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 18

Doppler Effect and Red shift• If a photon is emitted from a

moving source in my direction, do I see any effect from the moving source, even though c is always the same?

• Yes, if the source is moving toward me, the source is “pushing” the photon in my direction. That adds energy to the photon. Since the energy of the photon is E = hν, the frequency ν increases.

• If the source, like a star, is moving away from me the photon loses energy and ν decreases.

• This is the famous Red Shift observed from receding stars and galaxies all across the Universe.

• http://hubblesite.org/newscenter/newsdesk/archive/releases/2004/07

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 19

Decay of neutral mesons into 2 Photons

What are the energies of the 2 photons?The π0 mass at rest is E = 140 MeV.Thus energy of each of two photons is

half of that: Eg = 70 MeVThe velocity of each photon is c.Its frequency is n = 70 MeV/h = 17 x

1021 Hz or 17 x 1012 GHz

π0γ2γ1

A π0 meson is unstable because it can decay into 2 photons. It so decays with a lifetime of ~ 10-15

s after creation.

12 years later, in 1947, C. F. Powell detected a particle in cosmic rays which fit Yukawa’s hypothesis

In 1935 Hideki Yukawa predicted the existence of a new particle, the pion. It comes in 3 flavors: π+,π-, π0

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 20

The mechanics of quantal systems

• Atoms emit light in discrete steps.• This means electrons inside the

atom must be in discrete orbitals, which cannot be explained by classical physics.

• The size of the orbits is given by the Bohr radius RB = 5.3 x 10 -11 m,

• The emitted photons have energies of ~ 1 eV

• Thus RB x E ~ 5x 10 -2 nm eV< h c and quantum physics must be applied !

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydcn.html- c1

De Broglie

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 21

The Electron as a Wave

• Einstein says: p = E/c = h/ λ for a photon

• De Broglie turns it aroundλ = h/p

for a particle. This trick ascribes wave properties to a particles.

• Proof: Davidson/Germer show experimentally that electron diffraction from metals is the same as that obtained from x-rays.

• However: Because of their mass electrons have a much shorter wave length than X-rays

• For a 100 keV electron beam the wave length isλ = 392 x 10-5 nm ~ 4 pm

This has led to high resolution electron microscopy.

Electron diffraction

X-ray diffractionλ = hc

2mc 2E=

1240eVnm2mc 2E

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 22

Modern Electron Microscopy

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 23

Electrons in Atoms

• Electrons are bound in atoms by the electromagnetic force exerted by the nucleus.

• The question right now is: how will they move around?

• If they remain bound in the atom with a certain energy of motion, does the fact that they must also be considered like waves, have any effect?

• It turns out that this fact alone leads to the conclusion that electrons can move around the nucleus only in certain discrete orbitals.

• Already in 1913 Niels Bohr came to that conclusion.

• At that time the wave character of electrons had neither been syste-matically postulated nor experi-mentally demonstrated.

• It meant that the orbitals of the electrons in atoms are quantized.

Niels Bohr received the Nobel prize in 1922

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 24

Electrons as Strings• Assume electrons are confined in

the atom over a distance L• Let’s look at it as a linear problem,

a particle = a wave in a box.• This is like a string of length L that

is fixed at both ends.• Plucking the string produces

standing waves in the box, with discrete wavelengths:

1. λ = 2L2. λ = L = 2L/23. λ = 2L/3

In general λ = 2L/n with n = 1,2,3…

• http://www.cord.edu/dept/physics/p128/lecture99_35.html

• We call n the principal quantum number of the system.

• Different values of n produce different energies inside the box:

• As the electron jump form a higher n to a lower n it looses energy which is given off as discrete light quanta.

E =p2

2m=

h2c 2

2mc 2n2

2L( )2

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 25

First Homework Set-rev, due Sept. 15, 2005

1. Describe briefly the 3 important discoveries that Einstein published in 1905.

2. Who demonstrated that electromagnetic waves exist. What lead to the discovery that light was an electromagnetic wave?

3. Where was Max Planck’s office when he discovered his quantum theory? ((hint: go to the web!)

4. Give the approximate dimensions of the Earth, an ant, an atom and a nucleus, with their appropriate dimensional prefixes.

5. A light-year is a distance. How long is it? (hint: a year = 31,536,000 s)

6. Name the four forces that we encounter in Nature and describe briefly what action they perform.

Peter Paul 09/8/05 PHY313-CEI544 Fall-05 26

Second Homework Set, due Sept. 15, 2005

1. What is the evidence that photons can be treated like particles?2. Why does the double slit exp’t show that electrons can be treated

like waves?3. If you see a sleek sports car driving by on the road at a speed of

0.99c, would it look stunted, elongated or unchanged to you? Explain!

4. Where was De Broglie when he thought up his famous relationship between wavelength and momentum?

5. Explain why electron microscopy can observe objects that are much smaller than what can be seen with a light microscope.

6. Why do standing waves on a string lead to a quantization?