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Fundamentals of Physics by Eunil Won, Korea University 1
Eunil WonDepartment of Physics
Korea University
Ch 39 Photons and Matter Waves
Fundamentals of Physics by Eunil Won, Korea University 2
The Photon, the Quantum of LightIn 1905, Einstein proposed: electromagnetic radiation is quantized and exists in elementary amounts (quanta) called photons
h: Planck constant: h = 6.63 x 10-34 J s = 4.14 x 10-15 eV s
(energy of single photon)
The quantum of a light wave of frequency f has energy: E = hf f =
c
λ
ex) A lamp with 100 W power (wavelength=590 nm). How many photons are emitted per second?
# of photons per second = power / hf = power x c / h x wavelength
=(100 W )(590 × 10−9m)
(6.63 × 10−34J · s)(3.0 × 108m/s)
= 2.97 × 1020photons/s
Fundamentals of Physics by Eunil Won, Korea University 3
The Photoelectric Effect
First photoelectric experiment
1) incident light causes current
2) apply potential difference V : collector C is slightly negatively charged
3) At certain V, there will be no current V = Vstop (stopping potential)
Kmax : the kinetic energy of most energetic
electrons Kmax = eVstop
Kmax does not depend on the intensity of the
light source (inconsistent with wave nature)
If a beam of light is directed onto a clean metal surface, the light cause electrons to leave that surface
Fundamentals of Physics by Eunil Won, Korea University 4
The Photoelectric Effect
Photoelectric effect does not occur below a certain cutoff frequency f0
2nd Photoelectric Experiment: now we vary the frequency of the incident light and measure Vstop
λ0 =
c
f0
(cutoff wavelength)
To just escape from the target, e- must pick up a certain energy (properties of the target material: work function)
Φ
Einstein summed up the photoelectric experiments as:
hf = Kmax + Φ (photoelectric equation)
Vstop =Kmax
e=
h
cf −
Φ
eexplains the above plot
Fundamentals of Physics by Eunil Won, Korea University 5
Photons have MomentumIn 1916, Einstein extended his concept of light quanta: a quantum of light has linear momentum
(photon momentum)
Scattered x rays showed a shift in wavelength (Compton shift): a fraction of momentum is transfered
p =
hf
c=
h
λ
∆λ =h
mc(1 − cos φ)
Fundamentals of Physics by Eunil Won, Korea University 6
Light as a Probability WaveA fundamental mystery:
Light can be a wave in classical physicsIt is emitted and and absorbed as photons (in quantum physics)
Standard Version
: small photon detector tells us relative probability of single photon will be detected We take a concept of “probability wave”
Single-photon version
: A single-photon version of double-slit experiment (one photon at a time) -> Astonishingly interference fringes still build up,supporting the probability wave nature
Fundamentals of Physics by Eunil Won, Korea University 7
Electrons and Matter WavesMatter can behave wave?In 1924, Louis de Broglie suggested matter waves( A moving matter has wavelength)
λ =
h
p
ex) K=120 eV electron
p = mv, K =1
2mv2
= m
√2K
m=
√2mK
=√
2 × (9.11 × 10−31kg)(120eV )(1.6 × 10−19J/eV )
= 5.91 × 10−24kg · m/s
λ =h
p=
6.63 × 10−34J · s
5.91 × 10−24kg · m/s
= 1.12 × 10−10m = 112 pm
ex) Me running v=1m/s
λ =h
p=
6.63 × 10−34J · s
60kg × 1 m/s
10−35 m
X-ray and electron diffraction
Fundamentals of Physics by Eunil Won, Korea University 8
Wave and Particles
Schrodinger Equation : wave equation describes the matter wave
, i2 = -1
Ψ(x, y, z, t) = ψ(x, y, z)e−iωt
Matter wave: Ψ(x, y, z, t)
The probability (per unit time) of detecting a particle in a volume: |ψ|2
(space and time is separable in our case)
(one dimensional case)
For a free particle:
solution to this: ψ(x) = Aeikx + Be−ikx
Ψ(x, t) = Aei(kx−ωt) + Be−(ikx+ωt)
Choose B=0 to get a particle moving +x only
|ψ(x)|2 = constant
cannot predict the position of a free particle?
d2ψ
dx2+
8π2m
h2[1
2mv2]ψ = 0
d2ψ
dx2+
(2π
p
h
)2
ψ = 0
d2ψ
dx2+ k2ψ = 0
p
h=
1
λ,
2π
λ= k
d2ψ
dx2+
8π2m
h2[E − U0(x)]ψ = 0
Fundamentals of Physics by Eunil Won, Korea University 9
Heisenberg’s Uncertainty PrincipleThe position and the momentum of a particle cannot be measured simultaneously with unlimited precision
∆x · ∆px ≥ h̄
∆y · ∆py ≥ h̄
∆z · ∆pz ≥ h̄
h̄ =h
2π
Do not think that the particle really has a sharply defined position: I’m sure you are confused by now :-)
Fundamentals of Physics by Eunil Won, Korea University 10
Barrier Tunnelingelectron with energy E moving toward to a potential barrier (U0) when E<U0
classical physics: the electron is bounced off all the time
quantum physics: in some cases the electron penetrates the barrier
Transmission coefficient : the probability of tunneling of the electron(If T=0.020, 20 out of 1000 electrons will tunnel through)
T ≈ e−2kL
k =
√8π2m(U0 − E)
h2
Fundamentals of Physics by Eunil Won, Korea University 11
Crystalline quartz changes its dimension when an electric potential is applied (piezoelectricity): tip can be moved precisely
The Scanning Tunneling Microscope (STM)
Electrons from the sample can tunnel through to the tip : tunnel current can be measured and used as a microscope (STM)
Fundamentals of Physics by Eunil Won, Korea University 12
Summary
Light Quanta - PhotonsEnergy E = hf
Momentum p =
hf
c=
h
λ
Photoelectric Effect
Compton Shift
hf = Kmax + Φ
∆λ =h
mc(1 − cos φ)
Heisenberg’s Uncertainty Principle