SLIDE 1
Physics 2D Lecture Slides Feb 10
Vivek Sharma UCSD Physics
SLIDE 2 Bohr’s Explanation of Hydrogen like atoms
- Bohr’s Semiclassical theory explained some spectroscopic
data Nobel Prize : 1922
- The “hotch-potch” of clasical & quantum attributes left
many (Einstein) unconvinced
– “appeared to me to be a miracle – and appears to me to be a miracle today ...... One ought to be ashamed of the successes of the theory”
- Problems with Bohr’s theory:
– Failed to predict INTENSITY of spectral lines – Limited success in predicting spectra of Multi-electron atoms (He) – Failed to provide “time evolution ” of system from some initial state – Overemphasized Particle nature of matter-could not explain the wave- particle duality of light – No general scheme applicable to non-periodic motion in subatomic systems
- “Condemned” as a one trick pony ! Without fundamental
insight …raised the question : Why was Bohr successful?
SLIDE 3 Prince Louise de Broglie
- Key to Bohr atom was Angular momentum quantization
- Why Quantization mvr = |L| = nh/2π ?
- Invoking symmetry in nature the Prince deBroglie
postulated
– Because photons have wave and particle like nature particles must have wave like properties – Electrons have accompanying “pilot” wave (not EM) which guide particles thru spacetime.
– Pilot wave of Wavelength λ= h / p = h / (γmv) – frequency f = E / h
- If matter has wave like properties then there would be
interference (destructive & constructive)
- Use analogy of standing waves on a plucked string to
explain the quantization condition of Bohr orbits
SLIDE 4 Matter Waves : How big, how small
34 34
1.Wavelength of baseball, m=140g, v=27m/s h 6.63 10 . = p (.14 )(27 / ) size of nucleus Baseball "looks"
like a particle 1.75 10
baseball
h J s mv kg m s m λ λ
− −
× = <<< = ⇒ × = ⇒
1 2
19
3 2 4 4
p K= 2 2m = 2(9.11 10 )(120 )(1.6 10 ) =5.91 10 . / 6.63 10 Size . 5.91 10 . /
1
e e
p mK eV Kg m s J s kg m s h m p λ λ
− − − −
⇒ = × × × × = = × ⇒ = ×
SLIDE 5
Models of Vibrations on a Loop: Model of e in atom
Modes of vibration when a integral # of λ fit into loop ( Standing waves) vibrations continue Indefinitely Fractional # of waves in a loop can not persist due to destructive interference
SLIDE 6 De Broglie’s Explanation of Bohr’s Quantization Standing waves in H atom: s Constructive interference when n = 2 r Angular momentum Quantization condit ince h = p ...... io ! ( ) 2 n h m NR nh r m n mvr v v λ π λ π ⇒ ⇒ = = =
This is too intense ! Must verify such “loony tunes” with experiment
SLIDE 7
Reminder: Light as a Wave : Bragg Scattering Expt
Interference Path diff=2dsinϑ = nλ
Range of X-ray wavelengths scatter Off a crystal sample X-rays constructively interfere from Certain planes producing bright spot
SLIDE 8
Verification of Matter Waves: Davisson & Germer Expt If electrons have associated wave like properties expect interference pattern when incident on a layer of atoms (reflection diffraction grating) with inter-atomic separation d such that path diff AB= dsinϑ = nλ Layer of Nickel atoms Atomic lattice as diffraction grating
SLIDE 9
Electrons Diffract in Crystal, just like X-rays
Diffraction pattern produced by 600eV electrons incident on a Al foil target Notice the waxing and waning of scattered electron Intensity. What to expect if electron had no wave like attribute
SLIDE 10
Davisson-Germer Experiment: 54 eV electron Beam
Scattered Intensity Polar Plot Cartesian plot max Max scatter angle Polar graphs of DG expt with different electron accelerating potential when incident on same crystal (d = const)
Peak at Φ=50o when Vacc = 54 V
SLIDE 11 Analyzing Davisson-Germer Expt with de Broglie idea
10 acc acc 2 2
de Broglie for electron accelerated thru V =54V 1 2 ; 2 2 If you believe de Broglie h = 2 (de Br 2 V = 54 Volts 1.6
p 2 F lie) Exptal d 7 10
predict
p eV mv K eV v m m h h mv eV m m eV p mv m m h meV m λ λ λ λ
−
= = ⇒ = = = = = × = = ⇒ =
nickel m
ax
ata from Davisson-Germer Observation: Diffraction Rule : d sin = =2.15 10 (from Bragg Scattering) (observation from scattering intensity p n d =2.15 A 50 lo
F t r P
m θ φ λ = ⇒ ×
1.67 rincipal Maxima (n=1); = agreement (2.15 A)(sin =1 50 ) .65
meas
A Excellent A λ λ λ =
SLIDE 12 Davisson Germer Experiment: Matter Waves !
Excellent Agreeme 2 nt
predict
h meV λ =
SLIDE 13
Practical Application : Electron Microscope
SLIDE 14
Electron Micrograph Showing Bacteriophage Viruses in E. Coli bacterium The bacterium is ≅ 1µ size
Electron Microscope : Excellent Resolving Power
SLIDE 15 Just What is Waving in Matter Waves ?
- For waves in an ocean, it’s the
water that “waves”
- For sound waves, it’s the
molecules in medium
- For light it’s the E & B vectors
- What’s waving for matter
waves ?
– It’s the PROBABLILITY OF FINDING THE PARTICLE that waves ! – Particle can be represented by a wave packet in
- Space
- Time
- Made by superposition of
many sinusoidal waves of different λ
- It’s a “pulse” of probability
Imagine Wave pulse moving along a string: its localized in time and space (unlike a pure harmonic wave) Wave packet represents particle prob localized
