Physics 3 for Electrical Engineering

Ben Gurion University of the Negev www.bgu.ac.il/atomchip,www.bgu.ac.il/nanocenter Physics 3 for Electrical Engineering Lecturers: Daniel Rohrlich, Ron Folman Teaching Assistants: Daniel Ariad, Barukh Dolgin Week 4. Towards quantum mechanics – photoelectric effect • Compton effect • electron and neutron diffraction • electron interference • Heisenberg’s uncertainty principle • wave packets Sources: Tipler and Llewellyn, Chap. 3 Sects. 3-4 and Chap. 5 Sects. 5-7; פרקים בפיסיקה מודרנית, יחידה 2

Einstein’s relativity theories (Special Relativity in 1905 and General Relativity in 1915) were a revolution in modern physics, and in how we think about space, time and motion at high speeds.

Einstein’s relativity theories (Special Relativity in 1905 and General Relativity in 1915) were a revolution in modern physics, and in how we think about space, time and motion at high speeds. Meanwhile, a second revolution in modern physics, and in how we think about small energies, small distances, measurement and causality, was underway.

Einstein’s relativity theories (Special Relativity in 1905 and General Relativity in 1915) were a revolution in modern physics, and in how we think about space, time and motion at high speeds. Meanwhile, a second revolution in modern physics, and in how we think about small energies, small distances, measurement and causality, was underway. quantum mechanics

Crucial experiments on the way to quantum theory: Blackbody spectrum (1859-1900) quantum mechanics

Crucial experiments on the way to quantum theory: Spectroscopy (1885-1912) Blackbody spectrum (1859-1900) quantum mechanics X-rays (1895)

Crucial experiments on the way to quantum theory: Spectroscopy (1885-1912) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) X-rays (1895)

Crucial experiments on the way to quantum theory: Spectroscopy (1885-1912) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) X-rays (1895) Radium (1898) Discovery of the electron (1897)

Crucial experiments on the way to quantum theory: Spectroscopy (1885-1912) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) X-rays (1895) Radium (1898) γ-rays (1900) Specific heat anomalies (1900-10) Discovery of the electron (1897)

Crucial experiments on the way to quantum theory: Spectroscopy (1885-1912) Superconductivity (1911) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) X-rays (1895) Radium (1898) Rutherford scattering (1911) γ-rays (1900) Specific heat anomalies (1900-10) Discovery of the electron (1897) X-ray interference (1911)

Crucial experiments on the way to quantum theory: Paschen-Back effect (1912) Spectroscopy (1885-1912) Superconductivity (1911) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) X-rays (1895) Radium (1898) X-ray diffraction (1912) Rutherford scattering (1911) γ-rays (1900) Specific heat anomalies (1900-10) Discovery of the electron (1897) X-ray interference (1911)

Crucial experiments on the way to quantum theory: Franck-Hertz experiment (1914) Paschen-Back effect (1912) Spectroscopy (1885-1912) Superconductivity (1911) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) X-rays (1895) Radium (1898) X-ray diffraction (1912) Rutherford scattering (1911) γ-rays (1900) Specific heat anomalies (1900-10) Discovery of the electron (1897) X-ray interference (1911) Stern-Gerlach (1921-23)

Crucial experiments on the way to quantum theory: Franck-Hertz experiment (1914) Paschen-Back effect (1912) Spectroscopy (1885-1912) electron diffraction (1927) Superconductivity (1911) Radioactivity (1896) Blackbody spectrum (1859-1900) quantum mechanics Photoelectric effect (1887-1915) Compton effect (1923) X-rays (1895) Radium (1898) X-ray diffraction (1912) Rutherford scattering (1911) γ-rays (1900) Specific heat anomalies (1900-10) Discovery of the electron (1897) X-ray interference (1911) Stern-Gerlach (1921-23)

The photoelectric effect An irony in the history of physics: Heinrich Hertz, who was the first (in 1886) to verify Maxwell’s prediction of electromagnetic waves travelling at the speed of light, was also the first to discover (in the course of the same investigation) the photoelectric effect! Receiver Spark Gap Transmitter

Receiver Spark Gap Transmitter

Receiver Spark Gap Transmitter Hertz discovered that under ultraviolet radiation, sparks jump across wider gaps!

Hallwachs (1888): Ultraviolet light on a neutral metal leaves it positively charged. Hertz died in 1894 at the age of 36, one year before the establishment of the Nobel prize. His assistant, P. Lenard, extended Hertz’s research on the photoelectric effect and discovered (1902) that the energy of the sparking electrons does not depend on the intensity of the applied radiation; but the energy rises with the frequency of the radiation. photoelectric

Vacuum tube Ammeter

V With an applied potential V, the saturation current is proportional to the light intensity… …but the stopping potential V0 does not depend on the light intensity.

Einstein’s prediction (based on his “heuristic principle”): • Emax is the maximum energy of an ejected electron. • V0 is the stopping potential. • h is Planck’s constant, h = 6.6260693 × 10−34 J · sec. • νis the frequency of the applied radiation. • Φ is the “work function” – the work required to bring an electron in a metal to the surface – a constant that depends on the metal.

Measurements by Millikan (1914) showed that the coefficient of ν is indeed the h discovered by Planck. V0 = Emax/e ν0 = Φ/h ν

Can we understand the physics? Consider a light source, producing 1 J/sec = 1 W of power, shining on metal at a distance of 1 meter. If the metal has ionization energy (work function) Φ = 1 eV, how long will it take to eject electrons from the metal?

Can we understand the physics? Consider a light source, producing 1 J/sec = 1 W of power, shining on metal at a distance of 1 meter. A simple calculation: 1 J/sec of power is distributed (at 1 m) over an area Ssphere = 4p(1 m)2. The cross-section of an atom is Satom = p(10−10 m)2. The atom absorbs (1 J/sec) (Satom /Ssphere). So the time required for 1 eV to build up at the atom is

Can we understand the physics? Consider a light source, producing 1 J/sec = 1 W of power, shining on metal at a distance of 1 meter. In fact the light ejects electrons from the metal as soon as it arrives!

The Compton effect For almost two decades, no one believed in Einstein’s “quanta ” of light. Then came Compton’s experiment (1923):

If the energy of a “light quantum” of frequency ν is hν, what is its momentum? Theorem: the velocity v of a particle of relativistic energy E and momentum p is v = pc2/E. Hence Thus plight = Elight/c = hv/c. Since 0 = (Elight)2 – (plight)2c2 = m2c4, it follows that a “quantum of light” has zero mass.

Consider light of frequency ν scattering from an electron at rest: ν′ θ ν φ e– Energy conservation: hν–hν′ = me(γ–1)c2, where . Forward momentum conservation: Transverse momentum conservation:

Compton’s data: λ′ θ

Compton’s data finally convinced most physicists that light of frequency ν indeed behaves like particles – “quanta” or “photons” – with energy E = hνand momentum p=E/c = hν/c orp=h/λ.

Compton’s data finally convinced most physicists that light of frequency ν indeed behaves like particles – “quanta” or “photons” – with energy E = hνand momentum p=E/c = hν/c orp=h/λ. Soon (1924) Louis de Broglie conjectured that, just as an electromagnetic wave could behave like a particle, an electron – indeed, any particle – of momentum p could behave like a wave of wavelength p=h/λ.

Compton’s data finally convinced most physicists that light of frequency ν indeed behaves like particles – “quanta” or “photons” – with energy E = hνand momentum p=E/c = hν/c orp=h/λ. Soon (1924) Louis de Broglie conjectured that, just as an electromagnetic wave could behave like a particle, an electron – indeed, any particle – of momentum p could behave like a wave of wavelength p=h/λ. Confirmation of de Broglie’s conjecture came in 1927 with the experiments of C. Davisson and L. Germer, and of G. P. Thompson, who showed that a beam of electrons falling on a thin layer of metal or crystal produces interference rings just like a beam of X-rays.

Electron diffraction Electrons on gold X-rays on zirconium oxide electrons

Neutron diffraction Diffraction of neutrons on a single NaCl crystal Diffraction of X-rays on a single NaCl crystal

Electron interference Bohr (1927): thought-experiment Heiblum (1994): real experiment

Electron interference λ=6 nm at T=300K λ=600 nm at T=30 mK

A world in which electromagnetic waves interact like particles, and particles diffract and interfere like waves, is very different from the world we know on a larger scale. It forces us to search for a new mechanics – “quantum mechanics”.

A world in which electromagnetic waves interact like particles, and particles diffract and interfere like waves, is very different from the world we know on a larger scale. It forces us to search for a new mechanics – “quantum mechanics”. But already we can anticipate a strange, far-reaching and disturbing implication of the new mechanics: It limits what we can measure.

A world in which electromagnetic waves interact like particles, and particles diffract and interfere like waves, is very different from the world we know on a larger scale. It forces us to search for a new mechanics – “quantum mechanics”. But already we can anticipate a strange, far-reaching and disturbing implication of the new mechanics: It limits what we can measure. Heisenberg (1926) stated this limit as an “uncertainty relation”: (Δx) (Δp) ≥ h

Heisenberg’s uncertainty principle Any optical device resolves objects in its focal plane with a limited precision Δx. According to Rayleigh’s criterion, Δx is defined by the first zeros of the image.

Heisenberg’s uncertainty principle Any optical device resolves objects in its focal plane with a limited precision Δx. According to Rayleigh’s criterion, Δx is defined by the first zeros of the image. By the way, how did Heisenberg know about Rayleigh’s criterion?

p = h/λ. Heisenberg’s uncertainty principle 1. If a lens with aperture θfocuses light of wavelength λ, Rayleigh’s criterion implies Δx ≈ λ/2sinθ.

p = h/λ. Heisenberg’s uncertainty principle 1. If a lens with aperture θfocuses light of wavelength λ, Rayleigh’s criterion implies Δx ≈ λ/2sinθ. 2. A wave of wavelength λ has momentum p = h/λ.

Heisenberg’s uncertainty principle 1. If a lens with aperture θfocuses light of wavelength λ, Rayleigh’s criterion implies Δx ≈ λ/2sinθ. 2. A wave of wavelength λ has momentum p = h/λ. 3. From geometry we see here that Δp ≥ 2p sinθ. θ p = h/λ.

Physics 3 for Electrical Engineering