Download Physics 12 Notes Modern Physics Learning Outcomes (Students will

Physics 12 Notes
Modern Physics
Learning Outcomes (Students will be able to…):
 explain how quantum physics evolved as new evidence came to light and as laws and theories were tested and
subsequently restricted, revised, or replaced
 describe how the quantum energy concept explains both black-body radiation and the photoelectric effect
 explain qualitatively and apply the formula for the photoelectric effect
 explain how a photon momentum revolutionized thinking in the scientific community
 explain quantitatively the Compton effect and the de Broglie hypothesis, using the laws of mechanics, the
conservation of momentum, and the nature of light
 summarize the evidence for the wave and particle models of light
 explain quantitatively the Bohr atomic model as a synthesis of classical and quantum concepts
 explain the relationship among the energy levels in Bohr’s model, the energy difference between levels, and the
energy of the emitted photons
 use the quantum-mechanical model to explain naturally luminous phenomena
 compare and contrast fission and fusion
DEFINITIONS
Electromagnetic Radiation – radiation that is produced by oscillating electric and magnetic fields; includes radio,
microwaves, infrared, visible light, ultraviolet, x-rays and gamma rays. The electromagnetic (EM) spectrum is shown
below:
James Clerk Maxwell developed classical electromagnetic theory, synthesizing all previously unrelated observations,
experiments and equations of electricity, magnetism and even optics into a consistent theory. His set of equations—
Maxwell's equations—demonstrated that electricity, magnetism and even light are all manifestations of the same
phenomenon: the electromagnetic field. From that moment on, all other classic laws or equations of these disciplines
became simplified cases of Maxwell's equations. Maxwell's work in electromagnetism has been called the "second great
unification in physics", after the first one carried out by Isaac Newton.
Maxwell demonstrated that electric and magnetic fields travel through space in the form of waves, and at the constant
speed of light or c (approx. 3.00 x 108 m/s). Finally, in 1864 Maxwell wrote "A Dynamical Theory of the Electromagnetic
Field", where he first proposed that light was in fact oscillations in the same medium that is the cause of electric and
magnetic phenomena. His work in producing a unified model of electromagnetism is considered to be one of the greatest
advances in physics.
Blackbody – an object that absorbs all radiation that is incident upon it. (The Sun is a good approximation to a blackbody
since most radiation incident upon the Sun will be absorbed by it – little will be reflected)
Blackbody radiation – the electromagnetic radiation emitted by a blackbody. (Blackbodies that are ‘cool’ will tend to emit
most of their radiation at long wavelengths, in the microwave and infrared regions of the spectrum. ‘Hot’ blackbodies will
emit most of their radiation at shorter wavelengths, in the visible and ultraviolet (UV) regions of the spectrum.)
Planck’s quantum hypothesis – vibrating molecules in a heated material can only vibrate with discrete amounts of
energy. The minimum amount of energy, Emin, of vibration of a vibrating molecule is proportional to the natural frequency
of oscillation. Defining equation Emin = hf, where h is the constant of proportionality and is called Planck’s constant (h =
6.626 x 10-34 Js). The above implies that for a vibrating system: E = nhf, where n must be a whole number (n = 1, 2, 3,
…). The last equation is Planck’s quantum hypothesis.
Quantum – means ‘fixed amount’
Quantized – a quantity is said to be ‘quantized’ if it can only exist is discrete amounts as opposed to being ‘continuous’.
(Note: the concept that certain physical quantities were ‘quantized’ was well known at the end of the nineteenth century –
e.g. matter is quantized – it comes in “packets” called atoms. What was revolutionary was the hypothesis that quantities
such as energy were similarly quantized).
Photon – a particle of light. (Einstein proposed that if energy of a molecular system is quantized then by the law of
conservation of energy that light emitted by vibrating molecular systems must also be quantized. He called the ‘packet’ of
light energy, the particle of light, a “photon” (or “quanta”). Each photon has energy: E = hf = hc/, where c is the speed
of light, f is the frequency and  is the wavelength.
Universal wave equation – the relation between the speed of a wave, its frequency and its wavelength. Defining
equation: v = f. For light, the speed is c.
Photoelectric effect – the emission of electrons from the surface of a metal when light is incident on the metal’s surface.
(Einstein proposed the photoelectric effect experiment as a critical test of the theory that light consists of particles called
‘photons’ in contrast to the accepted theory that light was a vibrating electromagnetic wave. The photoelectric effect
experiment was carried out by Millikan.
Work function (Wo) – the minimum amount of energy that binds an electron to a metal. Measured in joules or electron
volts (eV). Different metals have different work functions. Photons incident upon the surface of a metal must have energy
equal to or greater than the work function of the metal to eject electrons from the metal’s surface. Defining equation:
Ek(max) = hf – Wo. Note that most photoelectrons ejected from the surface of a metal will have a kinetic energy less than
the amount given by the above equation. Only those at the surface of the metal will have the maximum amount of kinetic
energy.
Threshold or cut-off frequency (fo) – the minimum frequency of the light which will cause the electrons to be ejected
from the surface of a metal. (Since the ejected electrons have 0 J of kinetic energy when the incident radiation ahs a
frequency equal to the cut-off frequency; the work function of a metal can be determined by: Wo = hfo)
Wave-particle duality – the principle that light must have both particle-like properties (as demonstrated by the
photoelectric effect) and wave-like properties (as determined by Young’s double slit experiment).
Principle of Complementary – states that to understand any particular experiment using light scientists must see either
the wave theory or the particle theory of light but not both. Light has both wave and particle like properties but only one of
the properties will be evidenced in a given experiment. Since light has both wave and particle-like properties, these two
aspects of light complement each other.
Compton effect – a phenomenon involving the scattering of an X-ray photon with a “free” electron, in which, through
conservation of energy and momentum, some of the photon’s energy is transferred to the electron.
de Broglie’s hypothesis – the hypothesis that since light has both wave and particle-like characteristics, then matter also
has wave and particle-like characteristics. (de Broglie presented this hypothesis on the basis of ‘symmetry’ in nature – i.e.
if light that had traditionally been thought of as a wave has particle-like properties, then things traditionally thought of as
having only particle-like properties must also have wave-like properties. The wavelength (sometimes called the de Broglie
wavelength), , of a particle is given by the equation:  = h/p, where p is the momentum of the particle. Note that the
wave associated with those objects that have ordinarily been thought of as particles (i.e. electrons, atoms) is not an
electromagnetic wave. Instead the amplitude of the wave is to be interpreted as being a measure of the probability of
finding a particle in a given volume of space.
Blackbody Radiation
On the graph above, the blue curves show the measured intensity of electromagnetic radiation vs. the wavelength of the
radiation for three different blackbodies – one ‘cold’, one ‘warm’ and one ‘hot’. Note that as the temperature of a
blackbody increases, the intensity of the radiation at all wavelengths increases and the wavelength at which the maximum
intensity of the radiation occurs decreases; temperature is measured in Kelvin or K (0 K = -273oC). The black curve show
the predicted intensity vs. wavelength based on classical theories (namely Maxwell’s equations). Note that classical
physics predicts what is called the ultraviolet catastrophe – that is, the electrons in motion around the nucleus of an atom
should spiral into the nucleus, travelling faster and faster as they do so, because of their increasing centripetal
acceleration; the electromagnetic radiation they emit should move to higher and higher frequencies until at the point when
the electron collides with the nucleus; this radiation is in the ultraviolet region of the spectrum. Obviously, if electrons
actually did spiral into the nucleus as predicted by classical physics, atoms –and thus the universe- would not exist as it
does currently. Planck was able to show that his hypothesis that the energy of vibrating molecules is quantized, predicts
an intensity vs. frequency distribution graph identical with the
experimental values.
Photoelectric Effect
Classical physics’ explanation of light as an electromagnetic wave and Einstein’s hypothesis that light consists of particles
called photons and that the energy carried by each photon is proportional to the frequency of the light leads to different
predictions for the maximum kinetic energy of electrons emitted from the surface of a metal when light is incident upon the
surface.
The predictions of classical physics are as follows:
 if the intensity of the incident light is increased, the number of electrons ejected and their maximum kinetic energy
should increase.
 the maximum kinetic energy of the ejected electrons should be independent of the frequency of the light.
The predictions of Einstein’s photon theory are as follows:
 if the intensity of the incident light is increased, the number of electrons ejected should increase, but their
maximum kinetic energy should remain the same. (The energy of the photons is determined by the frequency and
not the number of photons.)
 the maximum kinetic energy of the ejected electrons should increase linearly with increasing frequency of the
light. The predicted equation is Ek(max) = hf – Wo . This equation predicts a graph of Ek(max) vs. frequency should
be a straight line with a slope equal to Planck’s constant and the intercept on the frequency axis is the threshold
or cut-off frequency and the absolute value of the intercept on the E k(max) axis is the work function of the metal.

There should be a certain frequency, called the threshold frequency, below which no electrons are ejected from
the metal’s surface regardless of the light’s intensity.
Millikan performed the experiment that proved Einstein’s predictions were correct.
Example #1: Calculate the energy of a photon of light with a wavelength of 525 nm (x10 -9 m) in units of joules and
electron-volts.
Example #2: The work function of a certain metal is 1.45 eV. What is the maximum kinetic energy and speed of the
electrons ejected from this metal when light of wavelength 525 nm is incident upon it? Also determine the threshold
frequency for this metal.
Compton Scattering Effect
Arthur H. Compton observed the scattering of x-rays from electrons in a carbon target and found scattered x-rays with
a longer wavelength than those incident upon the target. Compton explained and modeled the data by assuming a
particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision
between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength
according to the Planck relationship. At a time (early 1920's) when the particle (photon) nature of light suggested by
the photoelectric effect was still being debated, the Compton experiment gave clear and independent evidence of
particle-like behavior.
Compton sought to confirm the Law of Conservation of Momentum but he knew a photon has no mass. So, he turned
to Einstein’s E = mc2 to find a mass equivalence. He calculated that the momentum of photon is p = h/. Therefore,
momentum is not a quantity solely associated with mass.
Example #3: Calculate the momentum of a photon with a frequency of 5.09 x 14 Hz.
de Broglie’s Hypothesis
As a young student at the University of Paris, Louis DeBroglie had been impacted by relativity and the photoelectric effect, both of
which had been introduced in his lifetime. The photoelectric effect pointed to the particle properties of light, which had been
considered to be a wave phenomenon. He wondered if electons and other "particles" might exhibit wave properties. The
application of these two new ideas to light pointed to an interesting possibility:  = h/p = h/(mv) de Broglie introduced the
idea of wave-particle duality.
Example #4: What is the de Broglie wavelength of an electron moving at 15% of the speed of light?
Example #5: What is the wavelength of an alpha particle that is accelerated from rest through a potential difference of
250 000 V? (Note: the mass of an alpha particle is approx. 6.70 x 10-27 kg and a charge twice that of a proton, or
3.20 x 10-19 C).
Wave-Particle Duality
Historical Models of Light
Three historical models of light that were proposed around the same time in the latter part of the seventeenth century:
Newton Particle Model, Huygen’s Wave Model & Electromagnetic Theory.
Newton Particle Model
In the latter part of the seventeenth century, a group of scientists proposed a particle model of light. The most
prominent of these scientists was Isaac Newton.This model proposed that light was madeup of extremely small particles
that travelled extremely fast. It was reasoned that the particles must be extremely small, since two beams of light could be
observed to pass through one another without any interference; the particles must be moving very fast, since beams of
light appear to travel in straight lines (just as the curvature of a projectile’s path is reduced as the particle’s speed is
increased). This model gained acceptance because it could be used to explain various properties of light, namely:
• Reflection – Light was observed to be reflected at the same angle as the angle of incidence; this was also
observed when a particle collided with a surface (for example, a ball thrown against a wall).
• Refraction – Light appeared to bend when going from one medium to another; for example, going from air to
water the light was observed to bend toward the normal. Newton theorized that the light particles are attracted to
the individual molecules of the medium in which it is travelling. In a uniform medium, the pull would be the same in
all directions and the light would travel in a straight line. As the light gets closer to the water, the water molecules
attract the light particles with more force than the air molecules. This causes the light to change direction as it
speeds up toward the water. It also implies that the light would be going faster in water than in air.
• Dispersion – Newton proposed that different colors of light were actually different sized particles. As these
particles passed through a prism, the smaller particles were deflected more than the larger particles which
resulted in the white light being split up into the entire spectrum of colors. Each color consisted of similarly sized
particles that had been lined up.
This particle model of light was the dominant model of light for almost two centuries.
Huygens Wave Model
Around the same time as Newton and others were proposing the particle model of light, another group of scientists, led by
Christian Huygens, was putting forward a wave model of light. They proposed that light actually consists of waves; since
all waves at this time required a medium, these scientists also proposed that all of space was filled with an ether that
provided the medium for these light waves. As with Newton’s particle model, Huygen’s wave model could be used to
explain various properties of light:
• Reflection – By observing water waves, it can be observed that they follow the same law of reflection as light –
the angle of incidence is the same as the angle of reflection.
• Refraction – Again by observing water waves, it could be seen that waves bend toward the normal when going
from deep water to shallow water, just as light bends toward the normal going from air to water; however, waves
travel slower in shallow water than deep water. This would imply that light travels slower in water than in air,
which contradicts Newton’s theory.
• Diffraction – When light goes through a very small pinhole or slit, the resulting image is slightly blurred,
indicating a spreading out of the light. Similarly, water waves exhibit this effect of bending and
spreading out when going through a small opening.
Huygen’s wave model was not as well accepted as Newton’s particle model, mainly due to Newton’s reputation; however,
by the early to mid 1800’s it began to gain more acceptance for the following reasons. Around the beginning of the
nineteenth century, Young performed his double slit experiment to show that light passing through two slits
demonstrated the same interference pattern as two sources of water waves; a wave theory of light began to make more
sense now as this alone could explain the interference pattern. Also, in 1850, the speed of light was shown to be lower in
water than in air; this supported Huygen’s theory of refraction and contradicted Newton’s theory of refraction. By the
middle of the nineteenth century, the
wave model of light became the more widely accepted model of light. This model was not, however, without its problems.
For example, there was no evidence of the ether that was supposedly required for the transmission of waves.
Electromagnetic Theory
In the latter part of the nineteenth century, James Clerk Maxwell improved upon Huygen’s wave model. Maxwell predicted
that an accelerating electric charge will emit interacting electric and magnetic waves (electromagnetic waves) that require
no medium (just as electric and magnetic fields require no medium). He further calculated that in order for these waves to
continue to travel and interact together, they must be travelling at a speed of 3.0 × 10 8 m/s — the same speed as the
speed of light!! The logical conclusion was that light is a type of electromagnetic wave. The existence of electromagnetic
waves was demonstrated a few years later by Hertz. According to Maxwell’s theory, light waves are just a very narrow
band of frequencies of this electromagnetic wave spectrum.
Comparing the Wave and Particle Models of Light
Phenomenon
Transmission through a
vacuum
(i.e. starlight)
Speed
(c = 3.0 x 108 m/s)
Rectilinear Propagation
(i.e. laser beam)
Waves
Particles
Notes
“Ether” was a physical
medium used to transmit
electromagnetic waves.
No particle having mass has
ever been accelerated to “c”.
The path of a light ray bends
in a gravitational field; mass
also affected by gravitational
field
Reflection
Both waves and particles
obey the Law of Reflection.
Refraction
Both waves and particles
refract and obey Snell’s Law
(a.k.a. Law of Refraction).
Partial Transmission
Reflection
Waves naturally do this;
particles do not.
Color
(R-O-Y-G-B-I-V)
Difficult to explain using
particles.
Interference
Waves naturally do this;
particles do not.
Diffraction
Waves naturally do this;
particles do not.
Polarization
Difficult to explain using
particles.
Dispersion
Waves naturally do this;
particles do not.
Photoelectric effect
Particles naturally do this;
waves do not.
Modern Theory of Light
Experiments demonstrating the photoelectric effect and the Compton effect have brought credibility back to Newton’s
particle model of the seventeenth century; however, the wave theory of light can also explain some aspects of light such
as diffraction, refraction, and interference where the particle theory fails. The two theories, which appear to be
incompatible, each explain certain aspects of the behaviour of light. Neither theory by itself can be used to explain light.
Scientists have come to accept this and have called it the wave – particle duality of light.
Neils Bohr has proposed the principle of complementarity to summarize this situation. It states that to understand any
given experiment, we must use either the wave or particle theory of light; but to understand light fully, we must refer to
both theories. The two aspects of light complement one another. The equation for the energy of a photon itself (E = hf)
demonstrates the integration of the two theories. The equation represents the energy of a particle on the left side, but on
the right side is the frequency of the corresponding wave.
We cannot try to visualize this duality as a particle vibrating, or as a wave that has a mass; we cannot picture a
combination wave and particle. The two aspects of light are different “faces” that light shows, depending on which
property of light is being measured. In general, when light passes through space or a medium, its behavior imitates that of
a wave; when light interacts with matter, its behaviour is more like that of a particle. When we try to visualize light, we try
to think of it in terms of what we observe in the everyday, macroscopic world. We think of waves as the water waves that
we can easily see, or a particle as a baseball moving through the air, because these are things that we have
observed to transfer energy from one point to another. We instinctively want to describe light in these terms; however,
there is no reason that light should fit our narrow view of the world around us. Science simply uses abstractions of the
human mind to try to explain and predict the world around us. In terms of everyday language and images, light reveals
both wave and particle properties. This does not mean that light is either a wave or a particle, or even a combination of
the two. It simply means that in different situations, light behaves similarly to things (particles and waves) with which we
have experience.
Atomic Models
While the concept of the atom was developed by the Greeks, John Dalton (1810) is considered
to be the first modern scientist to propose that the smallest constituents of matter are solid
“billiard ball like” particles which he called atoms. With the discovery of electricity later in the
nineteenth century, this model was modified by Thompson who proposed that atoms, although
overall electrically neutral, were in fact composed of small solid positively charged structures with negatively charged
electrons embedded in the solid material. This led to the “plum pudding” model of the atom (with the electrons being the
plums – see diagram to the right). This model was satisfactory for some time because it explained all of the electrical
properties of matter known to that time and also explained the existence of cathode rays (cathode rays were a form of
radiation that was later discovered to be a beam of electrons).
In 1911, two German students, Geiger and Marsden, working under the direction of
Rutherford performed a series of experiments where alpha particles were allowed to collide
with very thin sheets of gold foil. They measured the number of particles scattered off the
gold foil (atoms) at various angles. They observed that most of the alpha particles passed
through the gold foil either undeflected or deflected through a very small angle. A few,
however, were deflected through a much larger angle and in some cases even fewer
particles were deflected through a straight angle back to the source of the alpha particles.
These observations can not be explained by Thompson’s model. Rutherford suggested that
atoms were mostly empty space with a very small solid central core which he called the
nucleus. Revolving around the nucleus in orbits very much like planets around the Sun,
were to be found the negatively charged particles called electrons. Thus the name “solar system” model was used. The
force that held the electrons in orbit around the nucleus was provided by the attractive electrical force between the
positively charged nucleus and the electrons. In 1920, Rutherford gave the name “proton” to the single positively charged
nucleus of a hydrogen atom. He proposed that other atoms had a greater number of protons. In 1932, Chadwick
discovered the neutron and Rutherford’s model was modified to include the neutron: the nucleus consisted of two
particles, the proton and the neutron.
Gold Foil Experiment
While Rutherford’s model explained the results of the gold foil experiment, it did not explain two important observations:
 The line spectra of the elements
 The stability of atoms
Maxwell’s electromagnetic theory predicted the “ultraviolet catastrophe”. Intensity-frequency curves experimentally
contradicted the classical prediction of Maxwell. Bohr attempted to overcome these inconsistencies by modifying
Rutherford’s model. Bohr postulated:
 Electrons move in certain allowed circular orbits or stationary states and while in one of these orbits, they do not
radiate or lose energy.
 The orbit closest to the nucleus has the least amount of energy. Each orbit is assigned a number, n, which starts
with n = 1 for the orbit closest to the nucleus.
 Electrons in a given orbit have a specific amount of energy and that electromagnetic radiation is emitted only
when an electron falls from a higher energy orbit into a lower energy orbit. At the moment of transition from one


orbit to another, a photon is created and it carries energy equal to the difference between the enrgy in the upper
orbit, Ef, and the lower orbit, Ei or:
Energy of a photon = hf = Ef - Ei
This postulate explains line spectra.
The angular momentum, L, of electrons in each orbit must be n = h/2π = ћ (pronounced h-bar), where n is the
principal quantum number. This postulate was not defined theoretically but made the theory agree with the line
spectra. Later, de Broglie showed that electrons have wave-like behaviour and that this postulate must be valid if
a whole number of electron wavelengths are to fit around an electron’s orbit (producing constructive interference).
Each orbit can contain a certain maximum number of electrons.
Overall, the model predicts that the total energy of an electron in the nth level of a hydrogen atom is given by:
Line Spectrum of Hydrogen
The Energy Transitions for Hydrogen
The Bohr model successfully predicts:
 Line spectra of elements
 Accurate wavelengths of emitted light of hydrogen
 Absorption spectra
 Stability of atoms
 Energy required to ionize a hydrogen atom
The Bohr model does not successfully:
 Predict line spectra of multi-electron atoms
 Explain quantization of angular momenta
 Explain the lack of electromagnetic radiation when electrons are in fixed orbits about the nucleus
 Explain how an electron makes a transition from one energy level to another
 Explain why certain lines in the spectra of elements are brighter than others
 Explain the ‘splitting’ of spectral lines when exposed to a magnetic field (called the Zeeman Effect)
 Explain the bonding of atoms to form molecules of solids and liquids
Example #6: How much energy is required to ionize a hydrogen atom in the n = 3 state?
Example #7: Calculate the wavelength of all of the possible photons released when an electron drops from the n = 4 to
the n = 2 energy levels in a hydrogen atom.
Quantum Mechanics
Bohr’s model of the atom, while very useful, had some serious defects. In addition, while it was a blend of classical
physics and early quantum mechanical ideas, it was unable to include the wave-particle duality of matter satisfactorily. In
the 1920’s, a new theory of the atom was developed, called quantum mechanics, and it included the duality of matter.
Actually, two theories were developed independently – one by Schrödinger and the other by Heisenberg – which were
quickly shown mathematically equivalent to one another. The wave-like nature of matter was included in the theory of
quantum mechanics by including a wave function, Ψ (pronounced psi). The Schrödinger Wave Equation can be solved
to find the amplitude of the wave associated with a particle. The wave is not an electromagnetic wave but a probability
wave. More precisely, the square of the wave function, Ψ2, is interpreted to mean the probability of finding an electron at
a certain point in space and time. Quantum mechanics successfully overcomes all of the problems associated with Bohr’s
model.
In 1927, Heisenberg developed his uncertainty principle, which states that there are pairs of variables, both of which
cannot be measured precisely at the same time. Classical physics had always assumed that variables (e.g. position,
momentum, time, energy) could be measured in principle to any degree of precision. Heisenberg showed that the very
act of measuring one variable would disturb the value of the other in a completely unpredictable way. The more precisely
one of the variables was measured, the less precisely was the value of the other variable known. This principle pairs the
variable’s position (x) and momentum (p) and also the variable’s energy (E) and time (t). More precisely, Heisenberg
showed that the product of the uncertainties in these sets of paired variables is equal to or greater than the ratio h/2π or
ћ.
x  p 
h
2
and
E  t 
h
2
Example #8: According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the energy of an
electron during a time interval of 2.5 x 10-8 s?
Example #9: If the uncertainty in an electron’s speed is 6.5 x 105 m/s, what is the minimum uncertainty in the electron’s
position?
Artificial Radioactivity: Nuclear Fission & Fusion
Nuclear Fission
Radioactive isotopes can be formed from stable isotopes by bombarding them with alpha particles, protons, neutrons,
electrons, or gamma rays. A nuclear reaction is said to occur when a nucleus is bombarded by another particle, resulting
in a transmutation. Nuclear reactions can be human-made (in a laboratory), but they
can also occur in nature. Enrico Fermi discovered in the 1930’s that neutrons are most effective at causing nuclear
reactions, since they are not repelled by the positively charged nuclei. Fermi began bombarding the heaviest known
element (uranium). It was discovered in 1938, following Fermi’swork, that uranium actually splits in tworoughly equal
particles when bombarded by aneutron. This was called nuclear fission, because
it resembled cell division. A typical fissionreaction is given by
although there are many other possibilities.
A tremendous amount of energy is released because the U-235 nucleus has a much greater
mass than that of the fission fragments, Ba-141 and Kr-92. The fission fragments are much more tightly bound than the
uranium nucleus. It was observed that extra neutrons wereproduced in these fission reactions, and a single neutron was
required to start a fission reaction. It was reasoned that these extra neutrons could be used to start other reactions,
resulting in a sustained chain reaction. This would provide enormous amounts of energy. The first nuclear reactor
(research) based on this concept was constructed at the University
of Chicago in 1942.
The first use of nuclear fission was the atomic bomb used in World War II. President Roosevelt authorized the Manhattan
Project to research and attempt to build an atomic bomb. Under the direction of Robert Oppenheimer, the top scientists in
Europe and the U.S. developed the first nuclear bomb.This bomb consisted of two masses of uranium, each less than the
critical mass required for the bomb. To detonate the bomb, the two masses would be brought together quickly. A chain
reaction would begin and a tremendous amount of energy would be released. A bomb using uranium was dropped on
Hiroshima, and one using plutonium was dropped on Nagasaki. This ended the war. When a fission bomb explodes,
radioactive fission fragments are released into the atmosphere; this is known as radioactive fallout. This fallout is a
concern with nuclear testing. If these fission fragments enter our food chain, they can be much more dangerous than the
fallout itself. Alpha and beta particles can usually be prevented from entering our bodies by clothing and skin; however, if
the radioactive source enters our body through our food, these particles are in direct contact with our cells.
Nuclear Reactors
There are some problems associated with the practical use of fission in nuclear reactors:
1. The neutrons emitted during the reaction are moving too fast; they must be slowed down to be absorbed by the
uranium-235. This is accomplished with a moderator, often deuterium (heavy water) or graphite (carbon-12). A moderator
is most effective if the atoms are close to the mass of the neutrons.
2. Naturally occurring uranium is 99.3% U-238 and only 0.7 % of the fissionable U-235; to sustain a chain reaction, the
uranium must be enriched so that is is 2-5% U-235. Without enough fissionable uranium, too many of the neutrons will be
absorbed by the nonfissionable materials. There is also only a limited supply of uranium.
3. Some neutrons may escape before having a chance to cause further fissions; some minimum critical mass is needed
(usuallya few kg). Most people are aware of the dangers of nuclear reactions. The fission fragments from these reactions
have many more neutrons than protons and are unstable (they are radioactive). There is a danger associated with the
disposal of these materials, particularly since they usually have large half-lives. In a nuclear reactor that is being used to
produce electrical energy, the heat from the fission reaction is used to boil water; this produces steam which is then used
to turn a generator. The core of the reactor consists of fuel to sustain the nuclear reaction (sealed in metal rods) and a
moderator, which was discussed earlier. Also present are control rods, usually containing cadmium or boron; these control
the rate of the reaction. To slow the reaction down, the control rods are fully inserted into the reactor
so that they can absorb the neutrons. Because of the high temperatures reached in the reactor, a coolant is also
necessary to take away some of the excess heat.
Breeder reactors are a particular type of reactor that actually creates more fissionable fuel than was there originally. One
of the by-products is Pu-239, which is created when U-2238 absorbs neutrons. This Pu-239 is fissionable, and can be
separated to be used as fuel; however, this plutonium has an extremely long half-life of 24 000 years and is very toxic. It
can also easily be used to construct a nuclear bomb.
CANDU Reactor
This reactor has been developed for use by Atomic Energy Canada Limited (AECL). The major difference between the
CANDU reactor and other reactors is that it uses heavy water as a moderator andcoolant. Since heavy water is a better
moderator than natural water, the reactor can use natural uranium instead of enriched uranium, which is very expensive. It
has a simplified design, so it can be built where technology is limited. Because of its design, it has a higher lifetime
capacity and has longer operating cycles than other types of nuclear reactors. There are presently CANDU reactors in
Ontario, Quebec, and New Brunswick.
Nuclear Fusion
In nuclear fusion, nuclei with smaller masses combine to give a nucleus with a larger mass (this is the process that occurs
in the stars). As long as this larger mass is more tightly bound than the smaller masses, energy will be released. For
example, helium is extremely tightly bound; any reaction resulting in the formation of helium will very likely release energy.
The series of reactions that occur in the sun involves the following steps:
The first two reactions would have to occur twice. The net result is that 4 protons produce one alpha particle (He), 2
positrons and 2 neutrinos. Nuclear fusion has many features which make it more attractive than nuclear fission. Some of
the benefits of nuclear fusion include:
1. The energy released is greater (for a given mass of fuel) than that released in fission.
2. There is less of a radioactive waste problem than there is associated with nuclear fission (the products are mainly
hydrogen and helium).
3. The fuel is plentiful (such as deuterium, which is available in the oceans)
We do not presently have any practical nuclear reactors, so obviously there are some problems with controlled fusion
reactions. Some of the problems associated with nuclear fusion are:
1. Fusion reactions require extremely high temperatures (108 K). This is higher than any known material can stand. These
temperatures are needed to make positive nuclei travel fast enough to get close to one another (in order to overcome the
strong nuclear force). For this reason, fusion reactions are often referred to as thermonuclear reactions.
2. Once this high temperature is achieved, it is very difficult to control the reaction (or to even contain it) to obtain usable
energy. Controlled fusion has not yet been attained. This is not necessarily a problem when designing a bomb, but it is
a problem with a nuclear reactor. Attempts have been made to use magnetic fields to confine reaction, but as of now this
requires more energy than is produced in the fusion reaction, and all of the particles can still not be contained in the field.
Example #10: Calculate the energy released in the fission reaction:
Example #11: The first atomic bomb released 1.0 ×1014 J of energy. What was the mass of the uranium-235 that was
fissioned to produce this energy?