WHAT DOES THE ATOM REALLY LOOK LIKE? THE THOMSON MODEL

WHAT DOES THE ATOM REALLY LOOK LIKE? THE THOMSON MODEL

RUTHERFORD SCATTERING

RUTHERFORD SCATTERING: SOME DETAILS

RUTHERFORD SCATTERING: FINAL RESULTS N() = no. scattered into interval to +d N i = total no. of particles incident in area A n = density of scattering atoms t = thickness of target foil r = distance of detection K = particle kinetic energy = distance of closest approach

The Bohr Model of the Atom: A first step toward quantum mechanics Assumptions: Electrons move in stable circular orbits around the nucleus under Coulombic attraction: F C 2 Ze k Ze C 4 r r 0 Their angular momentum is quantized in units of h/2 ( h-bar ): L r x p r m v n, with n = 1, 2, 3,... e These orbits obey classical physics, but we do not know what is going on when an electron moves from one orbit to another 2 Radiation is emitted or absorbed only in transitions from one n value to another

The Bohr orbits and energy levels

Bohr s explanation of the spectra of hydrogen

Problems with the Bohr atom Only applies precisely to atom with single electron: +Ze Nucleus Doesn t explain the splitting seen in some spectra (e.g. sodium D lines ) Doesn t explain how atoms bind into molecules: A + B A-B Doesn t say anything about time it takes to make a transition not a dynamical theory Need the full quantum theory of wave motion:?

Incident wave Scattered wave

Dipole Antenna The Movies + - + - + - - + http://www.ee.iastate.edu/~hsiu/movies/dipole.mov link gone

Oscillating (Accelerating) Charge The Movies Dr. Rod Cole, UCD-- http://maxwell.ucdavis.edu/~electro/ Oscillating Charge

Two sets of atomic planes in a sodium chloride crystal Planes in a simple cubic crystal Many sets of planes to diffract from In any crystal, some stronger than others

Protein Structures from X-Ray Diffraction X-ray beam Diffracted x-rays Computer analysis The protein crystal X-ray diffraction pattern: Many spots Structure of protein/rna/dna Biology

Particles behaving as waves (de Broglie): = h/p Why a peak and not continuous as in Rutherford scattering?

The Davison-Germer Experiment: Details decreasing

I(z)= I(0)exp(-z/ e ): Strong inelastic scattering attenuation

A little demonstration of row diffraction with diffraction gratings Single diffraction grating -1 D 1 Double diffraction grating D -1,1-10 -1,-1 01 0,-1 10 11 1,-1 D/2

I(z)= I(0)exp(-z/ e ): Strong inelastic scattering attenuation

The experimental pattern from Ni(111) Top Second layer layer rows rows (attenuated)

The Davison-Germer Experiment: Details Explained

NEUTRONS (AND OTHER PARTICLES) DIFFRACT TOO: debroglie = h/p In reactors, use H 2 O and D 2 O (to avoid reaction n + p = d in H 2 O.

The American Physical Society looks back to this expt. LANDMARKS: ELECTRONS ACT LIKE WAVES APS has put the entire Physical Review archive online, back to 1893. Focus Landmarks feature important papers from the archive. A 1927 paper in the Physical Review demonstrated that particles of matter can act like waves, just as light waves sometimes behave like particles. Clinton Davisson and Lester Germer of the Bell Telephone Laboratories in New Jersey found that electrons scatter from a crystal in the same way that x rays do. The work began as a result of a laboratory accident and ultimately earned Davisson a Nobel Prize. (C. Davisson and L. H. Germer, Phys. Rev. 30, 705) Link to the paper: http://link.aps.org/abstract/pr/v30/p705 COMPLETE Focus story at http://focus.aps.org/story/v17/st17

Electron diffraction from a crystal Davisson & Germer-1925 A particular silicon surface (1980s)

ELECTRONS AS DE BROGLIE WAVES (CONTINUED)-- YOUNG S DOUBLE-SLIT EXPERIMENT: L >> D Maxima when: Dsin = n Constructive Interference or Superposition D

Maxima when: Dsin = Constructive Interference or Superposition http://www.walter-fendt.de/ph14e/doubleslit.htm

Repeated from prior lecture Don t know where individual bright spots will appear, but know probability, proportional to light wave intensity Wave 2 = 2, and finally, with many individual photon events, see detailed image.

Interference of electrons with a double slit Just like light on film, with final intensity Wave 2 = 2 But how do we calculate the function of the wave = wave function?

How well can we measure the electron position with a photon (or any scattering de Broglie wave) With = h/p? xsin /2 Destructive p 0 p Heisenberg s Gedanken (Thought) Experiment (Initially, he forgot the microscope resolution) A first Uncertainty Principle

Adding (superposing) stationary waves:

Superposition of traveling waves: Trig. identity : cos a cos b 1 2cos ( a b) 2 1 cos ( a b) 2 E.g.--Musical notes close together in frequency Movies at: http://galileo.ph ys.virginia.edu/ classes/109n/m ore_stuff/apple ts/sines/group Velocity.html

v v group phase k d dk http://www.colorado.edu/physics/2000/applets/fourier.html

Superposing waves Much more general method (See additional reading at website) k n+1,n = k n+1 k n = 2(n+1-n)/ = 2/ 2 Ex. Does this work?

a n FOURIER (CONT D..) Example determination of one of the coefficients a n : zero, unless m = n 2 a 2 m 2 m 2 n 0 [ am cos( x ') bm sin( x ')] cos( x ')dx ' 2 0 m1 m1? zero zero 2 2 2n 2an a cos ( x ')dx ' 2 2n cos ( x ')dx ' n 0 0 and with change of var iable : 2a n 2 n n 0 2 n 2 n 0 2 n 2 n 2 cos ( x ')d( x ') a 2 an cos ( x ") dx" n an, just what we want! n n Nice cosine and sine series at: http://www.falstad.com/fourier/index.html

Nice set of variable cosine series at: http://www.falstad.com/fourier/index.html http://www.physics.ucdavis.edu/classes/nonclassicalphysics/fouriertransform/index.html

0 n=1 2 x 1 b n 0 sines n=5-1 0 2 x 1 cosines 0 n=11 2 x a n 0-1 0 5 10 n

Example application: Capacitive reactance: Q(t) = C(t); (t)= max cos(t) dq/dt = I = - max Csin(t)I max = max C I max = max C= max /(C) -1 = max /X C, with X C =1/(C) 1.0 R C?

n+1,n = n+1 n = 2(n+1-n)/T = 2/T

Fourier Integrals Most General Let period (or T), then k n+1,n = 2/ (or n+1,n = 2/T) 0, and we can include all k n (or m ) values, sums become integrals and, in x: with Or in t: Or in both x and t, traveling waves: with v ph (k)= /k dispersion See supplementary reading from Serway et al.

THE RANGE OF TYPES OF WAVE SUPERPOSITION: Well-defined position All wavelengths present Well-defined wavelength All positions present wave is everywhere

A FINITE WAVE PACKET IN TIMEA SECOND UNCERTAINTY PRINCIPLE Heisenberg s Uncertainty Principles: p x x p y y p z z Et /2 /2 /2 /2 E.g., -Lifetimes of states E, -Frequency spread in short laser pulses