Quantum Theory

Classical physics failed to explain certain events which led to the development of the field known as quantum mechanics.

Explains particle behavior at the microscopic level

These effects of this particle behavior is easily observed

Ex: Neon signs, chemical flame tests, fireworks, why stars shine, MRI’s, northern lights

History

Maxwell’s wave theory (1860) explained how electric and magnetic fields combine to form an electromagnetic wave.

Maxwell also determined that the speed at which waves move is the speed of light.

Hertz (1887) demonstrated experimentally that Maxwell’s theory was correct.

Unexplained Phenomena

Two unexplained events in the study of optics led to the creation of quantum theory.

Why does molten metal emit light? (hotbody or blackbody radiation)

Why does UV light discharge electrically charged metal plates? (photoelectric effect)

Blackbody Radiation

All objects emit EM radiation Continuous distribution of wavelengths

from infrared to UV (low T to high T) Coolest flame is __________ Hottest flame is __________ A blackbody is an ideal system that

absorbs all incoming radiation (they do not exist in nature)

EM Spectrum

Data collected experimentally for the radiation given off by an object at three different temperatures could not be explained by Maxwell’s wave theory

Blackbody Radiation

Although it is not truly a blackbody nor ideal, it allows for study of the phenomena. A small hole leading to a cavity inside a block of material. Only a tiny fraction of the radiation can make its way back out of the hole.

Approximated Blackbody

Classical physics predicted that as the wavelength approaches zero, the amt of E radiated should become infinite

Experimentally it was shown that as the wavelength approaches zero, the amount of energy radiated also approaches zero

Classical Theory - Ultraviolet Catastrophe

Quantization of Energy

The failure of classical electromagnetic theory led Max Planck to introduce the idea that energy is not continuous

Planck’s work was based on the idea that thermal energies can be discrete rather than continuous

Energy of vibration E = nhf n = an integer (0,1,2) f = frequency of the vibration of the atom h = 6.63 x 10-34 J•s (Planck’s constant)

hf is called a quantum of energy The energy of an atom can change only by the

absorption or emission of energy in discrete or quantum amounts

Quanta of Light

Einstein introduced the idea that light was quantized in 1905

He proposed that the atom must emit a specific amount (quantum) of light energy which he named the photon

Each photon has a definite amount of energy that depends on the frequency of light according to E=hf

This idea suggests that light can behave as discrete quanta or “particles” of energy rather than as a wave.

We are able to calculate the energy of each photon using the mathematical equation E = hc/λ

Photoelectric effect

Einstein used the photon concept to explain the photoelectric effect.

Certain metallic materials are photosensitive, meaning that when light strikes their surface, electrons may be emitted.

Released electrons are called photoelectrons. Negatively charged zinc plates will discharge in the

presence of UV radiation, but not visible light or if the plate is positively charged

Led to further investigation where it was discovered that electrons are only ejected if the frequency of radiation is above a certain minimum value called the threshold frequency (ft)

The threshold varies with the metal involved Ex: Cs – all wavelengths of visible light except red

Zn – no wavelength of visible light

Demonstration Videos

Simple Photoelectric Effect Demo - YouTube

photoelectric - YouTube

Characteristics of the Photoelectric Effect

1. The photocurrent is proportional to the intensity of the light.

2. The maximum kinetic energy of the emitted electrons depends on the frequency of the light, but not on its intensity.

3. No photoemission occurs for light with a frequency below a certain cutoff frequency fο, regardless of the light intensity.

4. A photocurrent is observed immediately when the light frequency is greater than fο, even if the light intensity is extremely low.

Only #1 is predicted by wave theory.Einstein’s quantum theory of light and his photon model

of light explain ALL experimental results of the photoelectric effect.

Applications of the photoelectric effect

Photography light meters Photocells Electric eye – garage door safety

mechanism

Compton Effect

1923 Arthur Compton conducted experiments with X-rays and graphite and explained the observed results (the scattering of X-rays from a graphite block) by assuming the radiation to be composed of quanta

His explanation of the observed effect provided additional convincing evidence that light energy is carried by photons.

Idea was that if light is a particle, when it interacts with other particles, the two should act like pool balls

Results showed scattered rays with less energy (momentum) and longer wavelengths than incoming rays; and electrons gained energy (momentum) and had shorter wavelengths

The changes in the two particles were exactly equivalent Only significant for X-rays and gamma-ray scattering

The blue ball is the recoiling electron with increased energy and shorter wavelength

The blue squiggle is the scattered ray with decreased energy and longer wavelength

The energy of the two combined is equivalent to the incident ray

Compton Shift

Dueling theories

Classical wave theory says that light is a traveling wave, and this satisfies such phenomena as interference and diffraction.

Quantum theory, with says light can be a particle is necessary to explain the photoelectric and Compton effects.

The two were combined to produce a description of the dual nature of light.

Wave Particle Duality

To explain all electromagnetic phenomena, light has to be considered sometimes as a wave and other times as a beam of photons. When it interacts with small (quantized systems), such as atoms, nuclei, and molecules, the photon (quantized energy) picture must be used. In everyday-sized systems – for example, slit systems causing diffraction and interference – the wave model is applicable.

Contributors to Wave-Particle Duality

deBroglie proposed in 1923 that particles have wave properties

This led to changes in the atomic model of the atom b/c electrons were no longer thought to be in specific orbit around the nucleus, they were moving with a wave-motion instead

This led directly to Heisenberg developing the uncertainty principle (can’t know both the _____________ & ___________ ) why?

Momentum of photons

The photoelectric effect demonstrated that photons have no mass – just energy

Einstein (1916) predicted that the photon should have another property of particles: momentum

The Compton effect verified that photons have momentum

Formula for photon momentum is p = hf = h c

Light emission and absorption

Differences between incandescent light and gas-discharge tubes became apparent

Incandescent = continuous spectrum (all wavelengths are present)

Gas-discharge tubes = emission spectrum – (which means discrete spectra with only specific wavelengths were observed)

Atoms can absorb light as well – which produces a dark-line spectrum or absorption spectrum.

Atomic Emission Spectrum

Absorption Spectrum

Emission Spectrum

Early 1900’s, it was observed that certain elements emitted visible light from the sun, microwaves and x-rays

Analysis revealed that an element’s chemical behavior is related to the arrangement of it’s electrons

Each element has its own unique emission spectrum, which allows for identification of elements using spectroscopic analysis

The Bohr Theory of the Hydrogen Atom

Niels Bohr provided an explanation of the spectral lines in 1913.

He proposed that the attractive force between the protons in the nucleus and the electrons outside supplied the necessary centripetal force for the electron to stay in orbit around the nucleus.

The flaw in this initial explanation was that classical theory indicates the electron should be emitting light due to acceleration, which it was not doing.

The Bohr Theory of the Hydrogen Atom

Bohr further postulated that the electrons do not emit light when in a stable discrete orbit, only when they change energy levels.

When electrons make a downward transition to an orbit of lower energy level, light is emitted.

When electrons make an upward transition to an orbit of higher energy level, light is absorbed.

Energy Levels

Orbits of electrons are commonly referred to by their energy level.

Ground state is the lowest allowable energy level (principal quantum number 1)

Excited states are those levels above ground state.

Electrons are normally located in the ground state, but when excited, they move up energy levels by absorbing discrete quantities of energy (ladder rungs)

Every jump from one energy level to another corresponds to a specific spectral line (either emission or absorption)

Energy Level Diagram of Hydrogen

The Bohr Theory of the Hydrogen Atom

The Bohr model worked well for hydrogen and an other atoms that had only one electron (ionized helium), but could not successfully describe multi-electron atoms.

His theory produced fragments of quantum theory into a basically classical framework

LASER

Light Amplification by Stimulated Emission of Radiation

Based on electrons being excited Normally electrons have very short

lifetimes in their excited state Some materials have relatively long

lifetimes (called a metastable state) and are phosphorescent (glow in the dark materials) and can emit light for lengthy periods of time.

Stimulated Emission (Einstein…again)

When a photon with energy equal to an allowed transition (from ground state to an excited state or b/w 1st and 2nd excited state…) strikes an atom already in a metastable state, it may stimulate that atom to make a transition to a lower energy level, which is called stimulated emission.

This transition yields a photon identical to the original photon, thus two photons are able to go in the next round (1 in and 2 out each time) allows the reaction to be amplified.

Uses of Lasers

Helium-Neon lasers: characteristic red light Check-out scanners CD/DVD

Other lasers Varicose veins Tattoo removal Holographic images