Warning!

Test on Feb 19 (Monday after next Monday)

1. 5 homework type problems

2. 5 short problems (multiple choices/ fill in the blanks etc.)

Compton effect (Text 2.7)We can eliminate pelectron and θ from these three equations and obtain a relationship between ν, ν’, and φ (all properties of the photon):

( )

) cos-(1 mch '-

)cos1)('h)(h(2'hhmc2

mc - cm csin'hcos'hh 'h h

:(1)in p thengSubstituti

p sin'hcos'hh )3((2)

, eliminate To

2

2422222

2electron

2electron

222

22

φλλ

φνννν

φνφνννν

φνφνν

θ

=⇒

−=−⇒

+⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛ −+=

=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛ −⇒+

ccc

ccc

(See course webpage for algebraic details)

Compton effect (Text 2.7)Remember:

has a length scale. i.e. The unit

of is meter. Is called Compton

Wavelength (λC).

mch

mch

mch

In Compton scattering, if the change in wavelength equals to Compton wavelength, what is the scattering angle φ for the photon?

Compton effect (Text 2.7)

Agreement between calculation and experiment demonstrate the particle property of electromagnetic wave.

Can we use proton instead of electron? What will be the differences?

Pair production (Text 2.8)

1. Relativity allows the conversion of energy to mass, so a photon (energy) can be converted to other particles (mass).

2. In the process, conservative laws (e.g. conservation of energy, conservation of momentum, conservation of charge etc.) have to be followed. Created particles are most likely pair of particle and antiparticle, like electron and positron pairs.

Pair production

Bremsstrahlung

Compton electron

Pair production (Text 2.8)Pair production cannot occur in vacuum because conservation of momentum and energy cannot be satisfied at the same time.

θ

θ

e+

e-

p

pAssume it is possible

!impossible (1) eq.energy ofon conservati makes Thish mc 2

1 coscv Since

coscvmc 2 h

(2)--- mvcos 2 cos 2p c

h

:momentum ofon Conservati(1)--- mc 2 h

:energy ofon Conservati

2

2

2

νγ

θ

θγν

θγθν

γν

<∴

<⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=⇒

==

=

Pair production (Text 2.8)

In matter, photons are absorbed by different mechanisms, depends on its energy.

At low energy: photoelectric effect

Intermediate energy: Compton scattering

High energy: pair production

Photoelectric effect

Compton scattering

Pair production

X-ray diffraction (photon is NOT absorbed)

Absorption of photons (In here we are talking about photons with energy higher than that of UV light)

Pair production (Text 2.8)Intensity = Energy transported per unit area per unit time

Because photons are absorbed as they pass through matter,

∴ dx I

dI- lossFraction ∝=

The proportional constant is called linear attenuation coefficient µ (a function of photon energy)

∴ x-0eI I dx

IdI- µµ =⇒=

As light penetrates matter, its intensity decay exponentially with distance,

What is light? (Text 2.4)

What is light? (Text 2.4)Light is both wave and particle. The wave theory and the quantum (particle) theory complement each other. One theory alone is not enough to explain every property of light.

It’s a string.It’s a rod.

I see particleI see wave

What is light? (Text 2.4)Depends on how you look at it (i.e. with what experiment) !

nose

Mouth

eyechin

neck

ear

De Broglie Waves (Text 3.1)

If a wave can be considered as a particle, can a particle be considered as a wave?

A moving particle behaves in a certain ways as though it has a wave nature.

From light, we know:

λν h c

h cE p ===

We can view this as a relationship between wave property (λ) and particle property (p), so it can be applied to moving particle also:

λν h c

h cE p === Now all moving particles

follow this equation, no matter it is a photon, or an electron!λ Is called the De Broglie wavelength of a

moving particle.

De Broglie Waves (Text 3.1)Yet the following is a better notation (easier to remember)

k 22h

2

2h

h p h==⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

==λπ

ππλπ

λ

Js10055.12

106.626 2h

Introduce

34-34-

×=×

==ππ

h

In general, for three dimensions:

p = h k

“h-bar”