physics 202 - university of virginia
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Physics 202Professor P. Q. Hung
311B, Physics Building
Physics 202 – p. 1/30
Quantum Physics
Blackbody Radiation
Blackbody: A perfect absorber of radiation ofall wavelengths.
A blackbody reradiates the energy that itabsorbs with a universal spectrum(wavelength or frequency)
The hotter the blackbody is the more energy itemits
Physics 202 – p. 2/30
Quantum Physics
Blackbody Radiation
Blackbody: A perfect absorber of radiation ofall wavelengths.
A blackbody reradiates the energy that itabsorbs with a universal spectrum(wavelength or frequency)
The hotter the blackbody is the more energy itemits
Physics 202 – p. 2/30
Quantum Physics
Blackbody Radiation
Blackbody: A perfect absorber of radiation ofall wavelengths.
A blackbody reradiates the energy that itabsorbs with a universal spectrum(wavelength or frequency)
The hotter the blackbody is the more energy itemits
Physics 202 – p. 2/30
Quantum Physics
Blackbody Radiation
Physics 202 – p. 3/30
Quantum Physics
Blackbody Radiation
Radiation with long wavelengths obey theWien’s displacement lawλmax T = 0.2898 × 10−2 m.K
Recall that f = cλ, compare the above
equation with the one in the book.λmax is the value of the wavelength where theradiation intensity versus wavelength reachesits maximum.
Physics 202 – p. 4/30
Quantum Physics
Blackbody Radiation
Radiation with long wavelengths obey theWien’s displacement lawλmax T = 0.2898 × 10−2 m.K
Recall that f = cλ, compare the above
equation with the one in the book.λmax is the value of the wavelength where theradiation intensity versus wavelength reachesits maximum.
Physics 202 – p. 4/30
Quantum Physics
Blackbody Radiation
Physics 202 – p. 5/30
Quantum Physics
Blackbody Radiation: Example 1Near what wavelength is the most energyradiated from an object at room temperature?
Room temperature: T ≈ 2930K.
λmax = 0.2898×10−2 m.KT
= 0.2898×10−2 m.K2930K
=
0.989× 10−5 m. This about in the middle of theinfrared range.
Physics 202 – p. 6/30
Quantum Physics
Blackbody Radiation: Example 1Near what wavelength is the most energyradiated from an object at room temperature?
Room temperature: T ≈ 2930K.
λmax = 0.2898×10−2 m.KT
= 0.2898×10−2 m.K2930K
=
0.989× 10−5 m. This about in the middle of theinfrared range.
Physics 202 – p. 6/30
Quantum Physics
Blackbody Radiation: Example 2The eye is most sensitive to a wavelength of500 nm. At what temperature would the intensityof an object be maximum at this wavelength?
T = 0.2898×10−2 m.Kλmax
= 0.2898×10−2 m.K500×10−9 m
= 5796 0K.
This is about the temperature on the surfaceof the sun.
Physics 202 – p. 7/30
Quantum Physics
Blackbody Radiation: Example 2The eye is most sensitive to a wavelength of500 nm. At what temperature would the intensityof an object be maximum at this wavelength?
T = 0.2898×10−2 m.Kλmax
= 0.2898×10−2 m.K500×10−9 m
= 5796 0K.
This is about the temperature on the surfaceof the sun.
Physics 202 – p. 7/30
Quantum Physics
Planck’s hypothesis
Classical model of blackbody radiation.: acavity filled with electromagnetic radiationwith a hole punched into it which then leaksthat radiation.
Rayleigh-Jeans ⇒ The energy density ofradiation (from which one can calculate theintensity) inside the cavity is inverselyproportional to the square of the wavelengthand proportional to the temperature.u(λ, T ) = 8π
c1λ2kT
Only good for long wavelength (fit the data)!
Physics 202 – p. 8/30
Quantum Physics
Planck’s hypothesis
Classical model of blackbody radiation.: acavity filled with electromagnetic radiationwith a hole punched into it which then leaksthat radiation.
Rayleigh-Jeans ⇒ The energy density ofradiation (from which one can calculate theintensity) inside the cavity is inverselyproportional to the square of the wavelengthand proportional to the temperature.u(λ, T ) = 8π
c1λ2kT
Only good for long wavelength (fit the data)! Physics 202 – p. 8/30
Quantum Physics
Planck’s hypothesis
The energy density blows up as λ → 0! Thisis called the ultraviolet catastrophe.
Experimentally, one finds u(λ, T ) → 0 asλ → 0.
Physics 202 – p. 9/30
Quantum Physics
Planck’s hypothesis
The energy density blows up as λ → 0! Thisis called the ultraviolet catastrophe.
Experimentally, one finds u(λ, T ) → 0 asλ → 0.
Physics 202 – p. 9/30
Quantum Physics
Planck’s hypothesis
Planck: In order to fit the data, he proposed tomodify the above formula.u(λ, T ) = (8π
chλ3 )
1
e( hc
λkT)−1
For large λ, e( hc
λkT)≈ 1 + hc
λkT⇒
Rayleigh-Jeans formula.
u(λ, T ) → 0 as λ → 0.This was a fit to the data. To derive it fromfirst principles, Planck had to assume that theenergy if blackbody radiation is quantized.
Physics 202 – p. 10/30
Quantum Physics
Planck’s hypothesis
Planck: In order to fit the data, he proposed tomodify the above formula.u(λ, T ) = (8π
chλ3 )
1
e( hc
λkT)−1
For large λ, e( hc
λkT)≈ 1 + hc
λkT⇒
Rayleigh-Jeans formula.
u(λ, T ) → 0 as λ → 0.This was a fit to the data. To derive it fromfirst principles, Planck had to assume that theenergy if blackbody radiation is quantized.
Physics 202 – p. 10/30
Quantum Physics
Planck’s hypothesis
Planck: In order to fit the data, he proposed tomodify the above formula.u(λ, T ) = (8π
chλ3 )
1
e( hc
λkT)−1
For large λ, e( hc
λkT)≈ 1 + hc
λkT⇒
Rayleigh-Jeans formula.
u(λ, T ) → 0 as λ → 0.This was a fit to the data. To derive it fromfirst principles, Planck had to assume that theenergy if blackbody radiation is quantized.
Physics 202 – p. 10/30
Quantum Physics
Planck’s hypothesis
Physics 202 – p. 11/30
Quantum Physics
Planck’s hypothesis
Planck’s Hypothesis:En = nh ff = c
λ.
Energy comes in bundles of hf and is notcontinuous. The above equation representswhat is known as Energy quantization.Energy comes in increment of fundamentalquanta of energy hf .
Physics 202 – p. 12/30
Quantum Physics
Planck’s hypothesis
Planck’s Hypothesis:En = nh ff = c
λ.
Energy comes in bundles of hf and is notcontinuous. The above equation representswhat is known as Energy quantization.Energy comes in increment of fundamentalquanta of energy hf .
Physics 202 – p. 12/30
Quantum Physics
Planck’s hypothesis
Fit to the data givesh = 6.63 × 10−34 J.s = 4.14 × 10−15eV.s
What is the physical meaning of the quantumhf?
Physics 202 – p. 13/30
Quantum Physics
Planck’s hypothesis
Fit to the data givesh = 6.63 × 10−34 J.s = 4.14 × 10−15eV.s
What is the physical meaning of the quantumhf?
Physics 202 – p. 13/30
Quantum Physics
Einstein and the Photoelectric effectWhat is the photoelectric effect?Set Up:
Two parallel plates, one called the cathodeand another called the anode. A potentialdifference can be applied to the 2 plates.
Light shines on the cathode.
If the anode is positive, it is observed thatelectrons that are ejected from the cathode,reach the anode and thus setting up acurrent.
Physics 202 – p. 14/30
Quantum Physics
Einstein and the Photoelectric effectWhat is the photoelectric effect?Set Up:
Two parallel plates, one called the cathodeand another called the anode. A potentialdifference can be applied to the 2 plates.
Light shines on the cathode.
If the anode is positive, it is observed thatelectrons that are ejected from the cathode,reach the anode and thus setting up acurrent.
Physics 202 – p. 14/30
Quantum Physics
Einstein and the Photoelectric effectWhat is the photoelectric effect?Set Up:
Two parallel plates, one called the cathodeand another called the anode. A potentialdifference can be applied to the 2 plates.
Light shines on the cathode.
If the anode is positive, it is observed thatelectrons that are ejected from the cathode,reach the anode and thus setting up acurrent.
Physics 202 – p. 14/30
Quantum Physics
Einstein and the Photoelectric effect
Physics 202 – p. 15/30
Quantum Physics
Einstein and the Photoelectric effect
If the cathode is made positive, it is observedthat there are still some electrons that haveenough kinetic energy to reach the anode.
There is a potential difference called the“stopping potential”, V0, at which and beyond,no electron can reach the anode.
The “stopping potential” V0 is found to beindependent of the intensity of light, and isfound to be dependent on the frequency.What is the explanation for this phenomenon?
Physics 202 – p. 16/30
Quantum Physics
Einstein and the Photoelectric effect
If the cathode is made positive, it is observedthat there are still some electrons that haveenough kinetic energy to reach the anode.
There is a potential difference called the“stopping potential”, V0, at which and beyond,no electron can reach the anode.
The “stopping potential” V0 is found to beindependent of the intensity of light, and isfound to be dependent on the frequency.What is the explanation for this phenomenon?
Physics 202 – p. 16/30
Quantum Physics
Einstein and the Photoelectric effect
If the cathode is made positive, it is observedthat there are still some electrons that haveenough kinetic energy to reach the anode.
There is a potential difference called the“stopping potential”, V0, at which and beyond,no electron can reach the anode.
The “stopping potential” V0 is found to beindependent of the intensity of light, and isfound to be dependent on the frequency.What is the explanation for this phenomenon?
Physics 202 – p. 16/30
Quantum Physics
Einstein and the Photoelectric effectEinstein:
Light is composed of quanta of energy hfcalled photons.
The photons penetrate the surface of thecathode and their energy is given completelyto the electrons.
φ: Energy necessary to remove an electronfrom the surface of the metal. It is called thework function and is characteristic of themetal.
Physics 202 – p. 17/30
Quantum Physics
Einstein and the Photoelectric effectEinstein:
Light is composed of quanta of energy hfcalled photons.
The photons penetrate the surface of thecathode and their energy is given completelyto the electrons.
φ: Energy necessary to remove an electronfrom the surface of the metal. It is called thework function and is characteristic of themetal.
Physics 202 – p. 17/30
Quantum Physics
Einstein and the Photoelectric effectEinstein:
Light is composed of quanta of energy hfcalled photons.
The photons penetrate the surface of thecathode and their energy is given completelyto the electrons.
φ: Energy necessary to remove an electronfrom the surface of the metal. It is called thework function and is characteristic of themetal.
Physics 202 – p. 17/30
Quantum Physics
Einstein and the Photoelectric effect
Physics 202 – p. 18/30
Quantum Physics
Einstein and the Photoelectric effect
The maximum kinetic energy isKmax = eV0 = hf − φ
One can plot V0 versus f . The slope is h/e.
Physics 202 – p. 19/30
Quantum Physics
Einstein and the Photoelectric effect
The maximum kinetic energy isKmax = eV0 = hf − φ
One can plot V0 versus f . The slope is h/e.
Physics 202 – p. 19/30
Quantum Physics
Einstein and the Photoelectric effect
Physics 202 – p. 20/30
Quantum Physics
Einstein and the Photoelectric effect
Threshold frequency and wavelength, f0 andλt:φ = hf0 = hc
λt
Useful number:hc = 1.24 × 104 eV.Å
Physics 202 – p. 21/30
Quantum Physics
Einstein and the Photoelectric effect
Threshold frequency and wavelength, f0 andλt:φ = hf0 = hc
λt
Useful number:hc = 1.24 × 104 eV.Å
Physics 202 – p. 21/30
Quantum Physics
Einstein and the Photoelectric effect: ExampleThe threshold wavelength for potassium is5, 640 Å. What is the work function for potassium?Solution:φ = hc
λt
= 1.24×104 eV.Å5,640 Å
= 2.2 eV
The work functions for metals are typically in afew of eV’s.
Physics 202 – p. 22/30
Quantum Physics
Mass and momentum of a photon
Recall: vc
= pcE
and E2 = p2c2 + (mc2)2
Photon travels with a speed of light ⇒ E = pc⇒ m = 0. The photon has zero mass.
E = hf ⇒ p = hf
c= h
λ
Physics 202 – p. 23/30
Quantum Physics
Mass and momentum of a photon
Recall: vc
= pcE
and E2 = p2c2 + (mc2)2
Photon travels with a speed of light ⇒ E = pc⇒ m = 0. The photon has zero mass.
E = hf ⇒ p = hf
c= h
λ
Physics 202 – p. 23/30
Quantum Physics
Mass and momentum of a photon
Recall: vc
= pcE
and E2 = p2c2 + (mc2)2
Photon travels with a speed of light ⇒ E = pc⇒ m = 0. The photon has zero mass.
E = hf ⇒ p = hf
c= h
λ
Physics 202 – p. 23/30
Quantum Physics
Compton EffectWhat happens when an electromagnetic wave isincident on a charged particle such as anelectron?
Physics 202 – p. 24/30
Quantum Physics
Compton Effect
Classical picture:When the charged particle is hit by an EMwave, it oscillates (due to the oscillatingelectric field). In turns, it gives off radiationbecause of the oscillation (acceleration). Thisradiation, according to the classical picture,would have the same frequency orwavelength as the incident EM wave.
Observation:The radiation has in general a differentwavelength.
Physics 202 – p. 25/30
Quantum Physics
Compton Effect
Classical picture:When the charged particle is hit by an EMwave, it oscillates (due to the oscillatingelectric field). In turns, it gives off radiationbecause of the oscillation (acceleration). Thisradiation, according to the classical picture,would have the same frequency orwavelength as the incident EM wave.
Observation:The radiation has in general a differentwavelength.
Physics 202 – p. 25/30
Quantum Physics
Compton EffectCompton:
Collision is considered to be between aphoton of energy hf and momentumhf/c = h/λ and an electron. Recall that for amassless particle, E = pc = hf ⇒
p = hf/c = h/λ.
The electron would absorb energy energydue to the recoil and the scattered photonwould have less energy and thus a lowerfrequency!
Physics 202 – p. 26/30
Quantum Physics
Compton EffectCompton:
Collision is considered to be between aphoton of energy hf and momentumhf/c = h/λ and an electron. Recall that for amassless particle, E = pc = hf ⇒
p = hf/c = h/λ.
The electron would absorb energy energy dueto the recoil and the scattered photon wouldhave less energy and thus a lower frequency!
Physics 202 – p. 26/30
Quantum Physics
Compton Effect
Let θ be the angle between the direction ofthe initial photon and the direction of thescattered photon. Let the initial wavelengthbe λ and that of the scattered photon be λ
′
.
Energy and momentum conservation givesλ
′
− λ = hmec
(1 − cos θ)h
mec= hc
mec2 = 0.0243 Å is called the Comptonwavelength of the electron.
Physics 202 – p. 27/30
Quantum Physics
Compton Effect
Let θ be the angle between the direction ofthe initial photon and the direction of thescattered photon. Let the initial wavelengthbe λ and that of the scattered photon be λ
′
.
Energy and momentum conservation givesλ
′
− λ = hmec
(1 − cos θ)h
mec= hc
mec2 = 0.0243 Å is called the Comptonwavelength of the electron.
Physics 202 – p. 27/30
Quantum Physics
Compton effect
Physics 202 – p. 28/30
Quantum Physics
Compton effect: ExampleX-rays of wavelength λ = 22 pm = 22 × 10−12 m(photon energy = 56 keV ) are scattered from acarbon target, and the scattered rays aredetected at 850 to the incident beam. What is theCompton shift of the scattered rays? Whatpercentage of the initial X-ray photon energy istransferred to an electron in such a scattering?
Physics 202 – p. 29/30
Quantum Physics
Compton effect: Example
∆λ = hmec
(1 − cos θ) = 0.0243 Å (1 − cos 850) =
0.2218 Å ≈ 2.2 × 10−12m = 2.2pm
Frac = E−E′
E= hf−hf
′
hf= λ
′
−λ
λ′ = ∆λ
λ+∆λ=
2.2pm22pm+2.2pm
≈ 9%
The photoelectric effect + the Compton effect⇒ a convincing support of the photonconcept of light. Since light also exhibits awave nature ⇒ duality: light has both waveand particle properties.
Physics 202 – p. 30/30
Quantum Physics
Compton effect: Example
∆λ = hmec
(1 − cos θ) = 0.0243 Å (1 − cos 850) =
0.2218 Å ≈ 2.2 × 10−12m = 2.2pm
Frac = E−E′
E= hf−hf
′
hf= λ
′
−λ
λ′ = ∆λ
λ+∆λ=
2.2pm22pm+2.2pm
≈ 9%
The photoelectric effect + the Compton effect⇒ a convincing support of the photonconcept of light. Since light also exhibits awave nature ⇒ duality: light has both waveand particle properties.
Physics 202 – p. 30/30
Quantum Physics
Compton effect: Example
∆λ = hmec
(1 − cos θ) = 0.0243 Å (1 − cos 850) =
0.2218 Å ≈ 2.2 × 10−12m = 2.2pm
Frac = E−E′
E= hf−hf
′
hf= λ
′
−λ
λ′ = ∆λ
λ+∆λ=
2.2pm22pm+2.2pm
≈ 9%
The photoelectric effect + the Compton effect⇒ a convincing support of the photonconcept of light. Since light also exhibits awave nature ⇒ duality: light has both waveand particle properties.
Physics 202 – p. 30/30