PHYS 202

Lecture 22 Professor Stephen Thornton April 18, 2005 Reading Quiz Which of the following is most correct?

1) Electrons act only as particles. 2) Electrons act only as waves. 3) Electrons act as particles sometimes and as waves other times. 4) It is not possible by any experiment to determine whether an electron acts as a particle or a wave. Answer: 3

In some cases we explain electron phenomena as a particle –for example, an electron hitting a TV screen. In other cases we explain it as a wave – in the case of a two slit diffraction experiment showing interference. Exam III Wednesday, April 20 Chapters 25-28

20 questions, bring single sheet of paper with anything written on it. Number of questions for each chapter will be proportional to lecture time spent on chapter. Last time

Blackbody radiation Max Planck and his hypothesis Photoelectric effect Photons Photon momentum Compton effect Worked Exam 3 problems Today de Broglie wavelengths Particles have wavelike properties Wave-particle duality Heisenberg uncertainty principle Tunneling Models of atoms Emission spectra Work problems Finish last year’s exam problems de Broglie wavelength

We saw that light, which we think of as a wave, can have particle properties. Can particles also have wavelike properties? A rule of nature says that if something is not forbidden, then it will probably happen.

h λ = all objects p How can we demonstrate these wavelike properties? Typical wavelengths Tennis ball, m = 57 g, v = 60 mph; λ ~ 10-34 m. NOT POSSIBLE to detect!!

50 eV electron; λ ~ 0.2 x 10-9 m or 0.2 nm

We need slits of the order of atomic dimensions. Scattering from a Crystal

X-rays or particles

2sdminθ = λ m=1,2,3,... Diffraction Patterns

Davisson and Germer showed in 1928 that electrons scattered from a Ni crystal also showed a diffraction pattern.

Clinton Davisson was Professor of Physics here at UVa from 1947-49. He died here in 1958. He won the Nobel Prize in physics in 1937. Do electron diffraction demo Neutron diffraction

This requires neutrons of very low momentum – low speeds. Called thermal neutrons. E ~ 0.03 eV Electron microscope

Visible light has wavelengths of 400-700 nm, but a 10 eV electron has a wavelength of 0.4 nm, some 1000 times smaller. Allows more detail to be observed. Colored scanning electron micrograph (SEM) of a T- lymphocyte blood cell (green) infected with HIV. Magnification 6,000 at 6 x 7cm size. Conceptual Quiz: If we double the kinetic energy of a neutron, by how much is its wavelength changed? Do this non-relativistically.

1) increased by 2 2) decreased by 2 3) increased by 2 4) decreased by 2 Answer: 4

If the kinetic energy is doubled (K = p2/2m), then p increases by 2 . Then because λ = h/p, then wavelength decreases by 2 .

hh λ == p 2mK Two slit experiment with electrons Interference Pattern by Electrons Passing Through Two Slits Wave-particle duality: sometimes objects act as waves, sometimes as particles, but never both at the same time. We cannot possibly know precisely where the next electron will strike the screen. We can only know the probability. Diffraction Pattern of Electrons

We only know probability distribution of electrons on screen. Uncertainty in Position and Note sizes of Momentum slit openings. ∆py∆yh∼ Heisenberg Uncertainty Principle Werner Heisenberg showed in 1927 by a careful analysis that it is not possible to know absolutely and precisely the momentum and position at the same time. Same is true for the energy and time at the same time. h ∆∆py≥ y 2π This occurs because of the wave h ∆∆px≥ properties of matter. x 2π h ∆∆Et≥ 2π Both slits open Cover one slit Try to determine which slit the electron goes through Example – tennis ball Consider tennis ball of mass 57 g moving at 56 mph (25 m/s). Let’s consider we know speed to 5%. How accurately do we know where to swing at the tennis ball? pm==v(0.057 kg)(25 m/s) = 1.4 kg ⋅m/s ∆=pp5% =0.07 kg ⋅m/s h 6.63×⋅10−34 J s ∆=x = =1.6×10−33 m 2(ππ∆⋅px 2)(0.07 kgm/s) This is not a problem!! Optical Tunneling Alpha decay in nucleus

Alpha particle tunnels Operation of a Scanning Tunneling Microscope Schematic diagram of scanning tunneling microscope STM Picture The Plum-Pudding Model of an Atom

J. J. Thomson – discoverer of electron The Solar System Model of an Atom Difficulties: 1) Electron is accelerating and radiates energy. 2) Electromagnetic theory says radiation frequency would be that of orbiting electron, so it would continuously decrease. Rutherford inspired experiment Alpha particle scattering

Plum pudding model can’t be correct.

Alpha particle The Line Spectrum of an Atom The Line Spectrum of Hydrogen

Emission

Absorption Hydrogen energy levels

Emission Name n = 1, to E1 Lyman n = 2, to E2 Balmer n = 3, to E3 Paschen n = 4, to E4 Brackett Do emission spectra demo Conceptual Quiz: Which of the following statements is not true?

1) Rutherford is given credit for discovering the nucleus concept. 2) J.J. Thomson’s plum pudding model doesn’t work. 3) Alpha particles can’t scatter backwards from heavy atoms. 4) The planetary model looks good, but can’t work because of radiation from accelerating electrons. Answer: 3

The experiment performed by Geiger and Marsden (for Rutherford) indeed did find alpha particles scattered backwards from heavy atoms. Work Problems 30-59, 30-66