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# Early quantum theory

PowerPoint: Early Quantum Theory Chap 27 Giancoli

## 27.1: Discovery of the electron

### Discovered in 1896 by British physicist J. J. Thomson

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## 27.2: Blackbody Radiation; Planck’s Quantum Hypothesis

### The spectrum of this radiation is determined by the object’s temperature alone, not by the body’s shape or composition. This is called Planck’s law.

A black body in thermal equilibrium has two notable properties:

• It is an ideal emitter: at every frequency, it emits as much energy as – or more energy than – any other body at the same temperature.
• It is a diffuse emitter: the energy is radiated isotropically, independent of direction.

An approximate realization of a black surface is a hole in the wall of a large enclosure (see below). Any light entering the hole is reflected indefinitely or absorbed inside and is unlikely to re-emerge, making the hole a nearly perfect absorber.

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## The ultraviolet catastrophe

### In the early 1900s, scientists calculated how much energy should be emitted from a blackbody, at varying wavelengths. It was reasonably assumed that atoms (and e- ) were classical objects; they were modeled as harmonic oscillators.

As a natural vibrator, the string will oscillate with specific modes dependent on the length of the string. In classical physics, a radiator of energy will act as a natural vibrator. And, since each mode will have the same energy, most of the energy in a natural vibrator will be in the smaller wavelengths and higher frequencies, where most of the modes are.
According to classical electromagnetism, the number of electromagnetic modes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the Rayleigh–Jeans law, and be proportional to frequency squared.

Thus, both the power at a given frequency and the total radiated power is unlimited as higher and higher frequencies are considered: this is clearly unphysical as the total radiated power of a cavity is not observed to be infinite, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in 1905.

– Wikipedia, Ultraviolet catastrophe

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### Einstein solved the problem by postulating that Planck’s quanta were real physical particles—what we now call photons, not just a mathematical fiction.

* Wikipedia

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### Planck also noticed another fatal flaw in our physics by demonstrating that the electron in orbit around the nucleus accelerates. Acceleration means a changing E-field (the electron has charge), which means that photons should be emitted. But, then the electron would lose energy and fall into the nucleus. Therefore, atoms shouldn’t exist!

To resolve this problem, Planck made a wild assumption:

energy, at the sub-atomic level, can only be transferred in small units, called quanta.

Due to his insight, we call this unit Planck’s constant (h).

The word quantum derives from quantity

It refers to a small packet of action or process, the smallest unit of either that can be associated with a single event in the microscopic world.

Light, for example, appearing in some respects as a continuous electromagnetic wave, on the submicroscopic level is emitted and absorbed in discrete amounts, or quanta.

For light of a given wavelength, the magnitude of all the quanta emitted or absorbed is the same in both energy and momentum.

These particle-like packets of light are called photons

All phenomena exhibit quantization: observable quantities are restricted to a natural set of discrete values.

Changes of energy, such as the transition of an electron from one orbit to another around the nucleus of an atom, is done in discrete quanta.

Quanta are not divisible.

The term quantum leap refers to the abrupt movement from one discrete energy level to another, with no smooth transition. There is no “in-between”.

This differs sharply from classical physics – which represented motion as smooth, continuous change.

Quantization limits the energy to be transfered to photons and resolves the UV catastrophe problem.

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec12.html

## 27.3: Photon Theory of Light and the Photoelectric Effect

### E = h·f   or E = h·ν

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## The Photoelectric Effect

The following is excerpted from from Prof. James Schombert, HC 209: 21st Century Science

An unusual phenomenon was discovered in the early 1900’s. If a beam of light is pointed at the negative end of a pair of charged plates, a current flow is measured. A current is simply a flow of electrons in a metal, such as a wire. Thus, the beam of light must be liberating electrons from one metal plate, which are attracted to the other plate by electrostatic forces. This results in a current flow.

In classical physics, one would expect the current flow to be proportional to the strength of the beam of light (more light = more electrons liberated = more current). However, the observed phenomenon was that the current flow was basically constant with light strength, yet varied strong with the wavelength of light such that there was a sharp cutoff and no current flow for long wavelengths.

Einstein successful explained the photoelectric effect within the context of the new physics of the time, quantum physics. In his scientific paper, he showed that light was made of packets of energy quantum called photons. Each photon carries a specific energy related to its wavelength, such that photons of short wavelength (blue light) carry more energy than long wavelength (red light) photons. To release an electron from a metal plate required a minimal energy which could only be transfered by a photon of energy equal or greater than that minimal threshold energy (i.e. the wavelength of the light had to be a sufficiently short). Each photon of blue light released an electron. But all red photons were too weak. The result is no matter how much red light was shown on the metal plate, there was no current.

The photoelectric earned Einstein the Nobel Prize, and introduced the term “photon” of light into our terminology.

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec12.html

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The following text is excerpted from The Photoelectric Effect, Michael Fowler, University of Virginia

In 1902, Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light, and could increase the intensity a thousand-fold.

Ejected e- hit a metal plate, the collector, which was connected to the cathode by a wire with an ammeter

To measure the energy of the ejected e-, Lenard charged the collector plate negatively, to repel the e- coming towards it.

Thus, only e- ejected with enough KE to overcome that would contribute to the current.

Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, Vstop.

To his surprise, Vstop did not depend on the intensity of the light

Doubling the light intensity only doubled the # of e- emitted, but did not affect their energy

A more powerful field ejected more e-, but the max individual energy of the ejected e- was the same as for the weaker field.

Lenard found that the max energy of the ejected e- depended on the light’s color

Shorter wavelength, higher frequency light caused e- to be ejected with more energy.

more text

In 1905 Einstein assumed that the incoming radiation should be thought of as quanta of frequency h·f

In photoemission, one quantum is absorbed by one e-.

If the e- is some distance into the material of the cathode, some energy will be lost as it moves towards the surface.

There will always be some cost as the e- leaves the surface, this is called the work function, W.

The most energetic e- emitted will be those very close to the surface

They leave the cathode with kinetic energy E = hf – W

On cranking up the negative voltage on the collector plate until the current just stops, that is, to Vstop, the highest kinetic energy electrons must have had energy eVstop on leaving the cathode. Thus,

eVstop = hf – W

This makes a quantitative prediction: if frequency of the incident light is varied, and Vstop is plotted as a function of frequency, then the slope of the line should be h/e.

It is also clear that there is a minimum light frequency for a given metal, that for which the quantum of energy is equal to the work function. Light below that frequency , no matter how bright, will not cause photoemission.

Summary graphic from the ESA

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## 27.4: Energy, Mass, and Momentum of a Photon

We must use a relativistic formula for dealing with a photon’s mass, energy and momentum

## 27.5: Compton Effect

Compton scattered short wavelength light – X-rays – from various materials

The scattered light had a slightly longer wavelength than did the incident light, and therefore a slightly lower frequency, indicating a loss of energy…

## 27.6: Photon Interactions; Pair Production

When a photon passes through matter, it interacts with atoms and electrons. There are four important types of interactions that a photon can undergo:

## 27.7: Wave-Particle Duality; the Principle of Complementarity

Some experiments indicate that light behaves like a particle

Some experiments indicate that light behaves like a wave

These two different ideas seem to be contradictory, yet both have experimental evidence in support of them.

Niels Bohr (1885-1962) proposed the principle of complimentary

There is no visualization of this principle

## 27.8: Wave Nature of Matter

Louis de Broglie (1892-1987) extended the idea of wave-particle duality

wavelength of a particle = h / p

Philosophical or physical question: what is an electron?

## 27.9: Electron Microscopes

Unlike conventional light microscopes, electron microscopes use an accelerated beam of electrons as the source of illumination. Because the wavelength of an electron is up to 100,000x shorter than that of a visible light photon, electron microscopes can resolve much smaller objects.

While most conventional light microscopes are limited to around 2,000x magnification and ~200nm resolution, transmission electron microscopes can achieve up to 10,000,000x magnification and resolve objects as small as 50 picometers!

A scanning electron microscope was used to image the interaction of a vinyl LP with the needle of a record player. The irregularities in each groove of the vinyl represents the audio waveform for both the left and right channels of stereo audio.

As the needle moves down the path, the minor deflections are converted into electrical signals and output to a speaker. Each groove is roughly 80µm wide and ranges between 35-40µm in depth.

Colin Sullender: Electron Microscope Imagery of Vinyl LP

## 27.10: Early Models of the Atom

Ernest Rutherford – Planetary model

also see:

https://scienceconceptions.wikispaces.com/Orbiting+Electrons

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## 27.12: The Bohr Model

text

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec12.html

## 27.13: de Broglie’s Hypothesis Applied to Atoms

Neils Bohr developed a new model of the atom The data he had revealed that atoms simply were not classical objects.

de Broglie Matter Waves

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec12.html

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## Atomic physics is often associated with nuclear power and nuclear weapons. However, physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and nuclear physics, which considers atomic nuclei alone.

text above loosely adapted by RK from https://en.wikipedia.org/wiki/Atomic_physics

Here’s the question students always ask: What do atoms really look like?

Really advanced stuff best left for college, but here you go: Are there any differences between wavefunctions (physics) and atomic orbitals (chemistry)?
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Chapter 27: Early Quantum Theory and Models of the Atom

27.1: Discovery and Properties of the Electron (3)
27.2: Blackbody Radiation; Planck’s Quantum Hypothesis (5)
27.3: Photon Theory of Light and the Photoelectric Effect
27.4: Energy, Mass, and Momentum of a Photon (16)
27.5: Compton Effect (1)
27.6: Photon Interactions; Pair Production (4)
27.7: Wave-Particle Duality; the Principle of Complementarity
27.8: Wave Nature of Matter (7)
27.9: Electron Microscopes (2)
27.10: Early Models of the Atom
27.11: Atomic Spectra: Key to the Structure of the Atom
27.12: The Bohr Model (4)
27.13: de Broglie’s Hypothesis Applied to Atoms

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

## Learning Standards

SAT Subject Test: Physics

Quantum phenomena, such as photons and photoelectric effect
Atomic, such as the Rutherford and Bohr models, atomic energy levels, and atomic spectra
Nuclear and particle physics, such as radioactivity, nuclear reactions, and fundamental particles
Relativity, such as time dilation, length contraction, and mass-energy equivalence

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies.

AP Physics Curriculum Framework
Essential Knowledge 1.D.1: Objects classically thought of as particles can exhibit properties of waves.
a. This wavelike behavior of particles has been observed, e.g., in a double-slit experiment using elementary particles.
b. The classical models of objects do not describe their wave nature. These models break down when observing objects in small dimensions.

Learning Objective 1.D.1.1:
The student is able to explain why classical mechanics cannot describe all properties of objects by articulating the reasons that classical mechanics must be refined and an alternative explanation developed when classical particles display wave properties.

Essential Knowledge 1.D.2: Certain phenomena classically thought of as waves can exhibit properties of particles.
a. The classical models of waves do not describe the nature of a photon.
b. Momentum and energy of a photon can be related to its frequency and wavelength.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.