Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in...

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Review of Special Review of Special Relativity Relativity S S and and S’ S’ system: system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect: The Doppler effect: x x' y z S y' z' S' S’ moves with velocity v in S along the x-axis. v x' x vt y' y z' z 2 v v t' x t c 1 2 1 x x x uv u' u v c 1 2 1 x y y v uv u' u c 1 2 1 x z z v uv u' u c 2 1 1 v v , c p u u m 1 2 2 1 u uc 2 u E mc 2 1 u KE mc proper v t t proper v L L u 2 2 2 2 4 E pc mc 1 cos source obs v f f When When θ =0, the course =0, the course is moving away from is moving away from the observer. the observer. v

Transcript of Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in...

Page 1: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Review of Special Review of Special RelativityRelativity

SS and and S’S’ system: system:

For a particle with velocity in S:For a particle with velocity in S:

The Doppler effect:The Doppler effect:

x

x'y

z

S

y'

z'

S '

S’ moves with velocity v in S along the x-axis.

vx' x vt

y' y

z' z

2v

vt' x t

c

1

21 xx x

u vu ' u vc

1

21 xy y v

u vu ' uc

1

21 xz z v

u vu ' uc

2

1

1v

v,

c

p uum

1

2 21u u c

2

uE mc 21uKE mc

propervt t

proper vL L

u

2 2 2 2 4E p c m c

1 cossource

obsv

ff

When When θ =0, the course is =0, the course is moving away from the moving away from the observer.observer.

v

Page 2: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Electromagnetic radiation Electromagnetic radiation behaves as particlesbehaves as particles

1.1. Discussion about homework: problem 33, Discussion about homework: problem 33, page 64.page 64.

2.2. Quiz 9.09 and a few comments on quiz Quiz 9.09 and a few comments on quiz 9.04.9.04.

3.3. Topics in EM waves as particles:Topics in EM waves as particles: Blackbody radiation and Planck’s constant, Blackbody radiation and Planck’s constant,

Planck’s Nobel Prize in physics.Planck’s Nobel Prize in physics. The Photoelectric Effect and Einstein's Nobel The Photoelectric Effect and Einstein's Nobel

Prize in physics.Prize in physics. The X-rays and Roentgen’s Nobel Prize in The X-rays and Roentgen’s Nobel Prize in

physics.physics. The Compton Effect and Compton’s Nobel Prize The Compton Effect and Compton’s Nobel Prize

in physics.in physics. Pair production, energy to mass conversion and Pair production, energy to mass conversion and

Anderson’s Nobel Prize in physics.Anderson’s Nobel Prize in physics. The wave-particle duality and the door to yet The wave-particle duality and the door to yet

another new world.another new world.4.4. The first of the many topics for our class The first of the many topics for our class

projects.projects.

today

Page 3: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Blackbody radiation Blackbody radiation and Planck’s constantand Planck’s constant

Blackbody radiation:Blackbody radiation:Blackbody: that radiates but not reflects.Blackbody: that radiates but not reflects.Blackbody is a good approximation of Blackbody is a good approximation of many objects that radiate, hence its many objects that radiate, hence its surface temperature measured.surface temperature measured.

Spectral energy density of a blackbody radiation:Spectral energy density of a blackbody radiation: Measurements:Measurements: Classical theory:Classical theory:

UV diverging problem.UV diverging problem. Planck’s proposal: Planck’s proposal:

The energy at a certain frequency isThe energy at a certain frequency isWhere Where nn is an integer (quantum) and is an integer (quantum) and hh is the Planck’s constant. is the Planck’s constant.

The Planck’s constant The Planck’s constant

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8B

dU Vk T f

df c

The lava’s surface temperature can be measured by the radiation it emits.

23

8

1Bhf k T

dU hf Vf

df e c

E nhf

346 63 10 J sh .

Page 4: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

The Photoelectric EffectThe Photoelectric Effect

The photoelectric effect:The photoelectric effect:There is a frequency threshold onThere is a frequency threshold onthe light to produce this effect.the light to produce this effect.the electron density proportional tothe electron density proportional toThe light density. The light density.

Einstein’s explanationEinstein’s explanationEinstein’s proposal: each photonEinstein’s proposal: each photonbehaves like a particle with energybehaves like a particle with energy

The electron’s maximum kinetic energy isThe electron’s maximum kinetic energy is

is the work function of the material with which an electron is the work function of the material with which an electron can be freed from its surface. See table 3.1.can be freed from its surface. See table 3.1.

Example 3.1, work on the blackboard in class.Example 3.1, work on the blackboard in class.

Example 3.2, work on the blackboard in class.Example 3.2, work on the blackboard in class.

E hf

maxKE hf

Page 5: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

The X-raysThe X-rays The X-rays: electromagnetic radiation from The X-rays: electromagnetic radiation from 33××10101616 to to 33××10101919 Hz. Hz. X-rays can be generated in many ways. One of them:X-rays can be generated in many ways. One of them:

High electrical potential is needed to accelerate electrons to High electrical potential is needed to accelerate electrons to hit the target.hit the target.

Photons produced by accelerating charges are called Photons produced by accelerating charges are called breamsstrahlungs. There is a cutoff wavelength associated breamsstrahlungs. There is a cutoff wavelength associated with the target material, indicating the quanta of the X-rays. with the target material, indicating the quanta of the X-rays.

Page 6: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Discussion and questionDiscussion and question

Photon energy is quantized to bePhoton energy is quantized to be

nn is an integer. is an integer. hh is Planck’s constant. is Planck’s constant. For a single photon: For a single photon:

Here energy is related to the Here energy is related to the electromagnetic wave’s frequency electromagnetic wave’s frequency ff, not , not its amplitude.its amplitude.

What is related to the wave amplitude? What is related to the wave amplitude? The light intensity.The light intensity.

E nhf

E hf

Page 7: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Review questionsReview questions In the text the spectral energy density of a In the text the spectral energy density of a

blackbody radiation is expressed as a function blackbody radiation is expressed as a function of the frequency: of the frequency:

WithWith , Can you change this formula to a , Can you change this formula to a function of wavelength? function of wavelength?

Einstein is famous for his theories of Special Einstein is famous for his theories of Special Relativity (1905) and General Relativity Relativity (1905) and General Relativity (1916), but he was award the Nobel Prize in (1916), but he was award the Nobel Prize in physics in 1921 for his work on photoelectric physics in 1921 for his work on photoelectric effect (1905). Do you know why? effect (1905). Do you know why?

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1Bhf k T

dU hf Vf

df e c

cf

Page 8: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Preview for the next Preview for the next classclass

Text to be read:Text to be read: In chapter 3:In chapter 3:

Section 3.4Section 3.4 Section 3.5Section 3.5 Section 3.6Section 3.6

Questions:Questions: Why the text claims that the Compton effect Why the text claims that the Compton effect

cannot be explained by classical EM theory?cannot be explained by classical EM theory? Who discovered positron? And What is a Who discovered positron? And What is a

positron? When an electron and a position positron? When an electron and a position meet, what happens? And what is a Positron meet, what happens? And what is a Positron Emission Tomography (PET)?Emission Tomography (PET)?

What is your opinion on this: a photon is an What is your opinion on this: a photon is an electromagnetic wave or a particle? electromagnetic wave or a particle?

Page 9: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Class project topic, 1Class project topic, 1

From X-ray to PET, Nobel Prize From X-ray to PET, Nobel Prize winning discovers in physics that winning discovers in physics that change people’s lives.change people’s lives.

Page 10: Review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect:

Homework 4, due by 9/23Homework 4, due by 9/23

1.1. Problem 12 on page 93.Problem 12 on page 93.

2.2. Problem 17 on page 93.Problem 17 on page 93.

3.3. Problem 21 on page 93.Problem 21 on page 93.

4.4. Problem 29 on page 94. (an Problem 29 on page 94. (an example for this problem can be example for this problem can be found on page 79, may not be found on page 79, may not be discussed in the classroom)discussed in the classroom)