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Lecture 20b The Birth of Mechanics

The Origins of the Quantum Theory Announcements Planck (1900) • Schedule: • Today: The beginnings of Planck, Einstein & Bohr E = h ν March Chapt. 15 o Data • Next Time: Particles act like ! Theory Prince DeBroglie and the equation Bohr March Chpt. 16 Einstein lightman, Chpt. 4 (1911) (1905) o Data • Report/Essay • Outline due MONDAY, November 17 max

E Slope = h

Introduction Blackbody • The true beginnings of the quantum theory lie in a strange • Last time: , , Nuclei place: the spectrum emitted by a solid when it is • Evidence for atoms heated (“blackbody” radiation). • Discovery of the • Experimental : the frequency spectrum was well determined.. a continuous spectrum with a shape that • “Planetary model” with electrons around a small heavy depended only on the temperature (light bulb, … ) nucleus • Theoretical prediction: Classical kinetic theory predicts the radiated to increase as the square of the frequency • Today: Origins of Quantum Theory (Completely Wrong! - “”). • Blackbody radiation: (1900) • : (1905) • Atomic Model: (1912)

frequency

Planck’s Solution E = h ν • Max Planck (1901): In order to describe the data Planck made the bold assumption that light is • The two most important formulas in modern physics emitted in packets or quanta, each with energy E = mc2 (Einstein – special relativity - 1905) E = h ν, where ν is the frequency of the light. E = h ν (Planck – quantum mechanics - 1901) • The factor h is now called Planck’s constant, h = 6.626 (10-27) erg-sec. • Planck initially called his theory “an act of desperation”. • “I knew that the problem is of fundamental significance for physics; I knew the formula that reproduces the energy distribution in the normal spectrum; a theoretical interpretation had to be found , no matter how high.” • Leads to the consequence that light comes only in certain packets or “quanta”

o Data Theory • A complete break with where all physical quantities are always continuous

1 Lecture 20b The Birth of Quantum Mechanics

Photoelectric Effect: The Phenomena Photoelectric Effect: The Theory • Einstein took Planck’s hypothesis • Einstein’s explanation: Suppose the energy in the seriously in order to explain the light is concentrated in particle-like objects (now we photoelectric effect. call them ) whose energy depend on the (Nobel Prize) frequency of the light according to Planck’s equation: E = hν. • Effect: Shining light on a metal can liberate electrons from its surface. • Prediction: Maximum energy of electrons liberated = • Experimental facts: energy of - binding energy of electron. • Easy for ultraviolet light (high frequency) and difficult for red Emax = hν -hν0 light (low frequency). • Energy of the electrons liberated depends on frequency of • Experiment: done accurately by Millikan in 1916: light o Data • Increasing of light increases number of electrons emitted, but not the energy of each electron max Slope = h • If light is generated then quantized units, Einstein E reasoned that it would also arrive at the metal with quantized amounts of energy Frequency ν

What is the Significance of h? The Problem of the • The fact that the slope in Millikan’s experiment was • Last time we saw that experiments supported the equal numerically to Planck’s constant establishes picture that an atom is composed of light electrons the importance of incorporating h into physics in a around a heavy nucleus fundamental way. But how? • Problem: if the electrons orbit the nucleus, classical • Usual approach: Try to understand h in terms of physics predicts they should emit electromagnetic previous theory (classical physics) applied to waves and loose energy. atoms. If this happens, the electrons • Revolutionary approach: Planck’s constant h is will spiral into the nucleus! fundamental - more fundamental than our previous classical conceptions. • The atom would not be stable!

• What are the tests? • What is the solution to • Niels Bohr (1911): atomic spectra: obvious quantum effect this problem? (lines, not continuous spectra). • Question: how can h explain these spectral lines?

Bohr’s Revolutionary Idea Planck’s Constant h and the atom • Bohr (and others) noted that the combination a = (h/2π)2/ me2 • Can the new quantum 0 theory explain the stability has the units of length about the of atoms of the atom? • If the can take on • Bohr postulated that it was not the atom that only certain discrete determined h, but h that determined the properties values, I.e., it is quantized, of atoms! there would be a lowest energy orbit, and the electron is not allowed to • Since the electron is bound to the nucleus by fall to a lower energy! electrical forces, classical physics says that the energy should be • What is the role of E = - (1/2) e2/a Planck’s Constant h? 0

• If the radii are restricted to certain values, the the energy can only have certain values

2 Lecture 20b The Birth of Quantum Mechanics

The Bohr Atom (NOT Correct in detail!) Ideas agree with Experiment • The allowed orbits are labeled by the • Bohr’s picture: integers: n = 1, 2, 3, 4. 4 • The only stable orbits of the electrons occur at definite 3 radii. • The radii of these orbits can be 2 determined from the quantization 1 • When in these orbits, contrary to classical E&M, the condition: electrons do not radiate. 2 2 2 2 radius = n a0 = n (h/2π) / me • The radiation we see corresponds to electrons moving from one stable orbit to another. • The energy can only have the values • Experiments (already known before 1912) E = E /n2,E = - (1/2)(e2 / a )/n2 n 1 1 0 • Experiment: Balmer had previously noticed a regularity in the emitted from hydrogen: • The spectra are the result of 2 2 transitions between these orbits, ν = ν 0 ( (1/n ) - (1/m )) where n and m are integers. with a single photon (ν = E/h) • Bohr’s Theory: Fits exactly using the value of h determined carrying off the difference in energy from other experiments E between the two orbits. Photon carries energy (=hν) = difference of stable orbits.

Hydrogen Spectrum: Balmer series Demonstration: 6.171 7.314 Spectra of different atoms • Observe spectra of different gases frequency (1014 Hz) • Individual grating for each student 4.571 6.912 7.557 • Using interference - wave nature of light - to separate the different frequencies (colors)

2 2 6.171 7.314 Balmer Formula: ν = ν0 ( (1/n ) - (1/m )) Hydrogen 32.91 ( 1/4 - 1/9 ) = 4.571 frequency (1014 Hz) 32.91 ( 1/4 - 1/16 ) = 6.171 32.91 ( 1/4 - 1/25 ) = 6.911 4.571 6.912 7.557 32.91 ( 1/4 - 1/36 ) = 7.313 Neon - strong line in Red 32.91 ( 1/4 - 1/49 ) = 7.556 Sodium - strong line in yellow (street lights) IT WORKS! Mercury - strong lines in red, blue (street lights)

Summary • A hot body emits light with frequencies that defy the laws of classical physics. • Max Planck (1900) had the idea that this could be explained if light was emitted in quanta with E=hν • Einstein (1905) reasoned that this would also explain the photoelectric effect (light transfers quanta of energy to emitted electrons) • Niels Bohr (1912) realized the significance that the quantization could explain the stability of the atom • But at what price? • Must give up classical physics - physical properties that are quantized and not continuous is completely different from the ideas of continuous space and time in classical physics • Also completely different from Einstein’s relativity • Two most important Eqs in physics: E = mc2 E=hν

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