Announcements HW1: Ch.2-70, 75, 76, 87, 92, 97, 99, 104, 111

*** Lab start-up meeting with TA – “This” Week

*** Lab manual is posted on the course web

*** Course Web Page *** http://highenergy.phys.ttu.edu/~slee/2402/ Lecture Notes, HW Assignments, Schedule for thePhysics Colloquium, etc..

2

A test of General Relativity

•! Can test to see if the path of light appears curved to us

•! Local massive object is the sun

•! Can observe apparent position of stars with and without the sun

3

Other Consequences of GR

•! Time dilation from gravity effects

•! Gravitational Radiation! –! Created when big gravity sources are moved

around quickly

–! Similar to the electromagnetic waves that were caused by moving electron charges quickly

•! Black Holes

•! Expanding Universe (although Einstein missed the chance to predict it! – He didn’t believed)

4

Gravitational Radiation •! When a mass is moved, the curvature of

space-time changes

•! Gravitational radiation carries energy and momentum and wiggles mass in its path

5

Evidence for Gravity Waves •! In 1974, Joseph Taylor and his student

Russell Hulse discovered a binary neutron star system losing energy as expected from gravitational radiation

Phy107 Fall 2006 6

Direct Detection of Gravity Waves LIGO is a collection of large laser interferometers searching for gravity waves generated by exploding stars or colliding black holes

Nobel Prize in 2006 •! For the universe to start small and expand space

and time must be thing that can expand(or contract) –! General relativity was key physics needed to understand

that process

•! However, a simple model of that would predict such a universe would not have clumps of matter(stars, galaxies)

•! Unless those clumping were present very early on

•! 2006 Nobel prize was given to the people who designed the COBE experiment which was sensitive enough to see those clumping in the CMB

Conclusion

Classical

physics

Relativistic

mechanics,

El.-Mag.

(1905)

Quantum

mechanics

(1920’s-)

Relativistic

quantum

mechanics

(1927-)

v/c

h/s

Maxwell’s Equations of

electromagnetism

(1873)

Newtonian Mechanics,

Thermodynamics

Statistical Mechanics

Question:

Should we use relativistic or classical approach to describe the motion of an electron in H atom?

Lecture 6 – Chapter. 3

Wave & Particles I

Outline:

•!Blackbody Radiation (Plank; 1900; 1918*)

•!The Photoelectric Effect (Einstein; 1905; 1921*)

•!The Production of X-Rays (Rontgen;1901; 1901*)

•!The Compton Effect (Compton; 1927; 1927*)

•!Pair Production (Anderson; 1932; 1936*)

•!Is It a Wave or a Particle? ! Duality?

EM-“Waves” behaving like “Particles”

Historical Development

Newton(1704): light as a stream of particles.

Descartes (1637), Huygens, Young, Fresnel (1821), Maxwell: by mid-19th century,the

wave nature of light was established (interference and diffraction, transverse nature

of EM-waves).

Physics of the 19th century: mostly investigation of light waves

Physics of the 20thcentury:interaction of light with matter

One of the challenges – understanding the “blackbody spectrum” of thermal radiation

Black body:

In physics, a black body is an idealized object that absorbs all E&M radiation that falls on it. "

No E&M radiation passes through it and none is reflected. "

Because no light is reflected or transmitted, the object appears black when it is cold. "

However, a black body emits a temperature-dependent spectrum of light. (see Fig)"

This thermal radiation from a black body is termed black-body radiation.

As the temperature decreases, the peak

of the black-body radiation curve moves to lower intensities and longer

wavelengths.

Black Body Radiation(Max Planck 1900)

(More in Appendix C)

Experiment shows that as frequency

increases, the blackbody spectral energy density reaches a max. then

fall off. But, classical theory predicts a

divergence !!

Do we need a new theory?

Historical Development

In 1900, Planck suggested a solution based a revolutionary new idea:

Emission and absorption of E&M radiation by matter has quantum nature:

i.e. the energy of a quantum of E&M radiation emitted or absorbed by a harmonic

oscillator with the frequency f is given by the famous Planck’s formula

,where h is the Planck’s constant

where Also, in terms of the

angular frequency

- at odds with the “classical” tradition, where energy was always associated with amplitude,

not frequency

The Energy (E) in

the electromagnetic radiation

at a given frequency (f)

may take on values restricted to

E = nhfwhere:

n = an integer

h = a constant

(“Planck Constant”)

The Planck’s Black-Body Radiation Law: Blackbody Radiation: A New

Fundamental Constant

Plank’s spectral energy density is the critical link

between temperature and EM radiation.

Interestingly, although the assumption E = nhf might

suggest EM radiation behaving as an integral number of

particles of energy hf, he hesitated at the new frontier -

others carried the revolution forward.

For the discovery, Plank was awarded the 1918 Nobel

prize!!

Experimental Fact:

E = nhf

BUT Why should the energy of an

Electromagnetic wave be

“Quantized”?

(n= integer)

No Explanation

until 1905

Albert Einstein

The Photoelectric Effect

A wave is a

Continuous

Phenomenon

REMINDER:: Waves (based on PHYS 1408/2401)

Wave equation in one dimension

for any quantity !:

Solution: a plane wave traveling in the

negative (positive) direction x with velocity v: x

t = 0 t = t0

vt0

Harmonic plane wave traveling in the positive direction x:

v – the phase velocity

x

!

A0

!

-A0

Electromagnetic waves:

(transverse in free space)

angular

frequency wave

number

t

T

A0

!

-A0

metal

The Photoelectric Effect

(Albert Einstein 1905)

Phenomenon observed long time before Einstein,

and something very strange was observed:

Photoelectric Effect

Historical Note: The photoelectric effect was accidentally discovered by Heinrich Hertz

in 1887 during the course of the experiment that discovered radio waves. Hertz died (at

age 36) before the first Nobel Prize was awarded.

Observation: when a negatively charged body was illuminated with UV light, its charge

was diminished.

J.J. Thomson and P. Lenard determined the ratio e/m for the particles emitted by the

body under illumination – the same as for electrons.

The effect remained unexplained until 1905 when Albert Einstein postulated the

existence of quanta of light -- photons -- which, when absorbed by an electron near the

surface of a material, could give the electron enough energy to escape from the material.

Robert Milliken carried out a careful set of experiments, extending over ten years, that

verified the predictions of Einstein’s photon theory of light. Einstein was awarded the

1921 Nobel Prize in physics: "For his services to Theoretical Physics, and especially for

his discovery of the law of the photoelectric effect." Milliken received the Prize in 1923 for

his work on the elementary charge of electricity (the oil drop experiment) and on the

photoelectric effect.

metal

The Photoelectric Effect(Albert Einstein 1905)

Even With Very strong light of low frequency

NO

electrons

ejected

Contradicting C

lassical

Wave P

hysics

The Photoelectric Effect(Albert Einstein 1905)

Even With Very-Very weak light intensity,

but of high enough frequency

Electrons

ejected

Planck’s Law

(E = nhf)

Albert Einsteinproposed:

Photoelectric Effect

(Threshold frequency)

The light is behaving as a collection of particles

called “photons” each of them having energy

E = hf

The Photoelectric Effect(Albert Einstein 1905)

Even With Very-Very weak light intensity,

but of high enough frequency

Electrons

ejectednhfE

hfE

beam

photon

=

=

What happens

is that

1 PHOTON ejects 1 ELECTRON

NO

Electrons

ejected

nhfE

hfE

beam

photon

=

=

There is no PHOTON capable of

ejecting an ELECTRON

Example (1): Very intensive light beam, low

frequency light

SMALL (below the threshold)

LARGE (n is large)

1 electron

ejected

nhfEE

hfE

photonbeam

photon

==

=

The PHOTON ejects 1 ELECTRON

Example (2): SINGLE PHOTON

Very weak light beam of high frequency

LARGE

(above the threshold)

Energy

Conservation:

hfE photon =

!

!"= hfKEmax

To free an electron from the metal, one has to

“pay” a certain amount of energy

the Work Function

Also known at that time:

nm380=!

VoltsU 2<

Repels electrons

?="?

?

min

max

=

=

f

!

Problems

1. The work function of tungsten surface is 5.4eV. When the surface is illuminated by light

of wavelength 175nm, the maximum photoelectron energy is 1.7eV. Find Planck’s constant

from these data.

2. The threshold wavelength for emission of electrons from a given metal surface is 380nm.

(a)! what will be the max kinetic energy of ejected electrons when "is changed to 240nm?

(b)! what is the maximum electron speed?

Problems

1. The work function of tungsten surface is 5.4eV. When the surface is illuminated by light

of wavelength 175nm, the maximum photoelectron energy is 1.7eV. Find Planck’s constant

from these data.

2. The threshold wavelength for emission of electrons from a given metal surface is 380nm.

(a)! what will be the max kinetic energy of ejected electrons when "is changed to 240nm?

(b)! what is the maximum electron speed?

(a)

(b)

The Production of X-Rays

(Wilhelm Roentgen 1901)

(The “opposite” of the Photoelectric Effect)

Bremsstrahlung

X-rays can be produced by smashing high-

speed electrons into a metal target. When

they hit, these decelerating charge produce

much radiation, called…

We use the name X-rays for EM radiation whose wavelengths are in the 10-2 nm to

10 nm region of spectrum

The Production of X-Rays

(Wilhelm Roentgen 1901)

(The “reverse” of the Photoelectric Effect)

BremsstrahlungCLASSICAL physics:

Radiation covers entire spectrum

SURPRISE:

Experiments indicate a cutoff wavelength:

Frequency f , Energy E=hf

1 photon -> 1 electron

(?) 1 electron -> 1 photon (?)

There is no classical

explanation for so sharp

a termination of the

spectrum

SURPRISE:

Experiments indicate a cutoff wavelength:

Frequency f

INDEED:

If the radiation is quantized, the minimum

E allowed at f is “hf” (single photon). We can’t produce half a photon, so if multiple

electrons don’t combine their Es into a single photon, no photon could be

produced of E > KE of a single electrons.

Setting the KE of an incoming electron

= E of one photon

Frequency f

INDEED:

1 electron -> 1 photon

The Compton effect(Arthur Compton 1927)

Hypothesis:Experiment

?

Is this true? – Compton provided

the 1st experimental evidence!!

momentum

energy

Momentum & Energy when a photon strike a free electron

Before Collision: A photon approaches an electron at rest

Momentum & Energy when a photon strike a free electron

After Collision: The electron scatters at speed u, angle #. A

photon of wavelength "’ scatters at angle $ Energy and Momentum Conservation

Momentum & Energy when a photon strike a free electron

The Compton Effect

Photons carry momentum like particles

and scatter individually with other particles

indeed, the wavelength shift is independent of the target material

and the initial photon wavelength.

target (light atoms,

e.g. graphite)

e-

X-ray detector

X-ray tube