Chapter 27: Quantum Theory
OBJECTIVES:
The main purpose of this chapter is to understand the spectrum emitted by a hot body and
the basics of the theory that explains this spectrum. The other objective is to define
the photoelectric effect; recognize that the quantum theory can explain it while the wave
theory can't; solve problems involving the photoelectric equation. The main focus is to
also define the compton effect and explain in terms of the momentum and energy of
the photon. lastly, describe experiments that demonstrate the particle-like properties of
electromagnetic radiation.
KEY TERMS:
PHOTOELECTRIC EFFECT:
The emission of electrons when electromagnetic radiation falls on an object.
The photoelectric effect can be studied in a photocell.
Photocells are used to turn lights on automatically at dusk.
THRESHOLD FREQUENCY (f0):,
This varies with the metal. It depends on the cathode material.
Not all radiation results in current flow. Electrons are ejected only if the
frequency of the radiation is above a certain minimum value, called the threshold frequency.
PHOTONS:
According to Einstein, light and other forms of radiation consist of discrete bundles of energy, which were later called photons.
The energy of each photon depends on the frequency of the light.
WORK FUNCTION:
The threshold frequency is related to the energy needed to free the most weakly-bound electron from a metal, called the work function of the metal.
The work function is thus measured by hf0.
COMPTON EFFECT:
is the shift in energy of scattered photons.
de Broglie wavelength of a particle:
is given by ^=h/p=h/mv.
HEISENBERG UNCERTAINTY PRINICIPLE:
after the German Physicist werner Heisenberg is when the position and momentum of a
particle cannot both be precisely known at the same time.
SUMMARY:
WAVES BEHAVE LIKES PARTICLES
The development of the quantum theory and its experimental confirmation is one of the highlights
of the history of the twentieth century. Objects hot enough to be incandescent emit light because of
the vibrations of the charged particles inside their atoms. The spectrum of incandescent objects covers
a wide range of wavelengths. The spectrum depends on their temperature. Planck explained the spectrum
of an incandescent object by supposing that a particle can have only certain energies that are multiples
of a small constant now called Planck's constant. In 1900, the German Physicist Max Planck(1858-1947)
found that he could calculate the spectrum only if he introduce a revolutionary hypothesis. Planck assumed
that the energy of vibration of the atoms in a solid could have only the specific frequencies given by
the equation, E=nhf. Further Planck proposed that atoms did not radiate electromagnetic waves as predicted by
Maxwell. Instead, they could emit radiation only when their vibration energy changed. Planck found that
the constant h was extremely small, about 7 x 10-34j/Hz. It was the first hint that the physics of
Newton and Maxwell might be valid only under certain conditions. The second troubling experimental result unexplained
by Maxwell was the photoelectric effect.
The photoelectric effect is the emission of electrons when certain metals are exposed to light.
The photoelectric effect can be studied in a photocell. Einstein explained the photoelectric effect by
postulating that light came in bundles of energy called photons. The photoelectric effect allows the
measurement of Planck's constant,h. Planck's constant,h is the slope of the graph of maximum kinetic energy
of ejected electrons versus light frequency. The work function, the
energy with which electrons are held inside metals, is measured by the threshold frequency in the
photoelectric effect. The compton effect demonstrates the momentum of photons, first predicted by Einstein.
Photons, or light quanta, are massless and travel at the speed of light. Yet they have energy, hf, and
momentum, p=h/^.
PARTICLES BEHAVE LIKE WAVES
The wave nature of material particles was suggested by de Broglie and verified
experimentally by diffracting electrons off crystals. The particle and wave aspects are complementary
parts of the complete nature of both matter and light. The Heisenberg uncertainty principle states
that the position and momentum of a particle(light or matter) cannot both be known precisely at
the same time. The photoelectric effect and compton scattering showed that
electromagnetic waves had particle properties. The French
Physicist Louis Victor de Broglie(1892-1987) suggested in 1923
that material particles have wave properties. His suggestions
were ignored by other scientists until Einstein read his papers
and supported his ideas.
EQUATIONS:
E=hf, where h is PLanck's constant 6.626x10-34J/Hz.
KE=hf-hfo
KE=-qVo
h= DeltaKE Change in maximum KE of ejected electrons
-------- = -----------------------------------------------
Delta f Change in frequency of incident radiation
p= hf h
-- = ---
c ^
E= hc
--
^
p=mv=h
-
^
^=h h
- = -
p mv
qV = 1/2mv2
^ = h/mv
IMPORTANT THEORIES IN THIS CHAPTER
Planck's theory states that spectrum of an incandescent object
by assuming atoms could vibrate only at specific frequencies.
The German Physicist Max Planck found that he could calculate
the spectrum only if he introduce revolutionary hypothesis.
Planck proposed that atoms did not radiate electromagnetic waves
all the time they were vibrating, as predicted by Maxwell.
Instead, they could emit radiation only when their vibration
energy changed. For example, when energy changed from 3hf to 2hf,
the atom emitted radiation. The energy radiated was equal to the
change in energy of the atom, hf.
Einstein's photon theory states that light and
other forms of electromagnetic radiation consists of
particles. Einstein's theory of the photon reinterpreted
and extended Planck's theory of hot bodies.
Einstein's photoelectric-effect theory explains
the existence of a threshold frequency.
CONNECTIONS OF THIS CHAPTER TO SOCIETY
LIGHT POLLUTION AND OBSERVATORIES
Light pollution is a general glow in the night sky
caused by thousands of unshielded lights along highways and
in cities to make them safer for travelers. Most of these
lights emit light over virtually the entire visible spectrum.
Observatories must attempt to filter out skyglow from star light.
Today, there is almost no observatory on earth where illumination
from distant cities has not or will not become a problem.
Earth's atmosphere causes problems of his own for astronomers.
The atmosphere also blocks almost all ultraviolet light, which
due to its shorter wavelength, could be focused into much sharper
images than visible light. The hubble space telescope, orbiting
370 miles above Earth's surface, is designed to receive light of
all wavelengths. The goal is for astronomers to be able to see
five to ten times farther and more clearly than ever before.
SOCIOLOGY CONNECTION
Many public buildings have doors that open automatically
as people approach. These doors are often operated
by so called "electric eyes". A light beam shines across
the door opening onto a photovoltaic cell, causing
electrons to be given off and a current to flow in a circuit.
When the beam is broken, the current stops, and a mechanism is
triggered that opens the door. These devices have allowed easier
access to many people who would otherwise find door opening mechanisms
difficult to use.
PHYSICS LABORATORY: photoelectric Steel Balls
PURPOSE:
To simulate the photoelectric effect.
MATERIALS
4 2-cm steel balls
grooved channel(U Channel or shelf bracket)
red, orange, yellow, green, blue, violet colored
marking pens or colored stickers
PROCEDURE
Shape the grooved channel as shown in the diagram.
Mark a point 4cm above the table, on the channel, as "R" for red.
Mark a point 14cm above the table, on the channel
with a "V" for violet. Place marks for B, G, y, and O
uniformly between them.
Place two steel balls at the lowest point on the channel.
These steel balls represent valence electrons in the atom.
Place a steel ball on the channel at the red mark.
This represents a photon of red light.
Release the photon and see if the electrons
are removed from the atom. See if either steel ball
escapes from the channel.
Remove the steel ball that represents the photon from
the lower part of the channel.
Repeat steps 4-6 for each color mark on the channel.
Note: Always start with two electrons at the low point in the channel.
OBSERVATIONS AND DATA
WHICH COLOR PHOTONS WERE ABLE TO REMOVE THE ELECTRONS?
ANSWER:
The color photons that were able to remove the electrons were
green, yellow, orange, and red.
DID ONE PHOTON EVER REMOVE MORE THAN ONE ELECTRON?
ANSWER:
Yes, the red photon was the one photon that ever remove
more than one electron.
ANALYSIS
PREDICT WHAT WOULD HAPPEN IF TWO RED PHOTONS COULD HIT THE
ELECTRONS AT THE SAME TIME.
ANSWER
The electrons would be removed from the atom if
the two red photons could hit the electrons at the same time.
START TWO STEEL BALLS(PHOTONS) AT THE RED MARK ON
THE CHANNEL AND SEE WHAT HAPPENS. DESCRIBE THE RESULTS.
ANSWER
The red two photons would move faster than before
and would escape from the channel speedily.
APPLICATIONS
PHOTOGRAPHERS OFTEN HAVE A RED LIGHT IN THEIR DARKROOMS.
EXPLAIN WHY A RED LIGHT IS SAFE, BUT A BLUE LIGHT IS NOT SAFE.
ANSWER
A red light in safe because it produces more
photoelectric effect more than the blue light.
A red light is a very powerful transmission of electrons
from one point to another.
LINKS TO OTHER SOURCES
WEBSITES:
enclycopedia
wikipedia
newsscientist.com
theory.uwinnipeg.ca
quantum_field_theory.wikiverse
PERIODICALS
1. DISCOVER: Loops of space. (a possible theory of quantum gravity)
April 1, 1993; Bartusaik, Marcia
2. SCIENCE: Quantum Mechanics: Quantum Computing makes solid progress
April 30, 1999; Service, Robert F
3. SCIENCE: Quantum information theory: A general surrenders the field,
but black hole battle rages on
August 13, 2004; Seise, Charles
4. DISCOVER: Faster than a speeding photon
August 1, 1998; Freedman, David H
5. POPULAR MECHANICS: Quantum Theory
October 1, 1997; Wilson, Jim
REFERENCES USE IN THIS PROJECT
A Glencoe/McGraw-Hill Program
Merill Physics: Priniciples & Problems
Author: Paul W. Zitzewitz,Robert F. Neff,Mark Davids
Content Consultants: Robert B. Clark, Ph.D.,Patrick Kenealy, Ph.D.