Modern Physics

Modern Physics

• Scientists are exploring the atom, space, and matter using quantum theory and relativity.

• This field impacts our lives through the control and use of high-energy radiation.

• The sun is a readily available source of high-energy radiation (ultraviolet light).

• UV light can damage chemical bonds and rearrange molecules, similar to X-rays.

Radiation-Damaged Paper Experiment

• Expose colored construction paper to direct sunlight with opaque objects on top.

• Do not use glass, as it absorbs UV light and slows the process.

• Exposed paper will lighten as the sun's UV radiation destroys dye molecules.

• Experiment with different papers and colors to see which fade fastest.

• Observe if the fading seems to have a half-life.

Optical Bleaching

• Sunlight causes optical bleaching on items in shop windows and outdoor furniture.

• Historically, sunlight was used to whiten fabrics.

• Sunburn is radiation damage from the sun's ultraviolet radiation, not thermal damage.

• UV light can't penetrate far into your body.

Nuclear Weapons

• Nuclear weapons involve more penetrating forms of radiation.

• Exploring the structure of atomic nuclei and how they release energy through disassembly or joining.

Nuclear Reactors

• Nuclear reactors extract nuclear energy and convert it into electric energy.

• Safety and health issues related to nuclear energy are explored.

Medical Imaging and Radiation

• High-energy radiation can be used for beneficial purposes.

• X-rays and gamma rays are produced and interact with atoms and molecules in a patient.

• Particle accelerators produce high-energy particles for radiation therapy.

Computed Tomography (CT) and Magnetic Resonance Imaging (MRI)

• CT and MRI create detailed maps of patients’ insides without physical contact.

Atomic Bomb Development

• Atomic bomb development was propelled by fear, curiosity, and temptation during World War II.

• Scientists discovered the principles behind nuclear energy in the late 1930s.

• The world has lived in the shadow of nuclear weapons since their creation.

*Where is nuclear energy stored in the atoms?
*From where did this nuclear energy come?
*How do nuclear weapons release nuclear energy?
*Why are nuclear weapons so difficult to build?
*Why do we associate uranium and plutonium with nuclear weapons?
*How much uranium or plutonium does it take to build a bomb?

Dominoes Experiment

• Use dominoes to understand chain reactions.

• Dominoes standing on end have gravitational potential energy.

• If spread out, dominoes tip over one by one when the table is shaken.

• If packed tightly, one falling domino can knock over others, creating a chain reaction.

• Chain reactions occur when a single event triggers an increasing number of subsequent events.

*What characteristics of the dominoes and their arrangement determine whether or not such a chain reaction occurs?
*Can you envision a scenario in which a single tipping domino could trigger the release of an enormous amount of stored energy?

• Another chain reaction, this time in the decay of atomic nuclei, is what makes nuclear weapons possible.

Classical Physics

• Classical physics includes rules of motion, gravitation (Galileo, Newton, Kepler), electricity, and magnetism (Ampère, Coulomb, Faraday, Maxwell).

• By the end of the nineteenth century, physicists thought most of physics was understood.

• Specific difficulties like the spectrum of light emitted by a blackbody, the photoelectric effect, and the absence of an ether remained unexplained.

• Classical physics collapsed under these difficulties at the beginning of the twentieth century.

Quantum Physics and Relativity

• Quantum physics and relativity emerged as major advances from 1901 to 1926.

• Confirmed countless times and have enormous predictive power.

• These theories are carefully constructed and codified rules that model the behavior of the physical universe.

• These theories made the discovery of nuclear forces and nuclear energy unavoidable.

• They also made nuclear weapons inevitable.

Theory

• A theory's truth depends on the theory and its comparison to the real world.

• Many theories have been formulated to explain the world.

• Theories must be tested to determine their validity.

• Theories of relativity and quantum physics have long since been proven true, although there is always the possibility that they may be only parts of a more complete theory.

The Nucleus and Radioactive Decay

• Nuclear weapons release energy from atomic nuclei, not atoms.

• Atoms are tiny: a grain of salt magnified to the size of Colorado would appear as an orderly arrangement of grapefruit-sized atoms.

• Table salt crystal (Sodium chloride)

  • Chlorine negative ion Diameter: 1.81 \times 10^{-10} meter

  • Sodium positive ion Diameter: 0.97 \times 10^{-10} meter

Electrons and Chemistry

• Electrons dominate the chemistry of atoms and molecules.

• Sodium is a reactive metal, and chlorine is a reactive gas because of their electrons.

• Mixing sodium and chlorine results in a violent reaction, forming table salt and releasing light and heat.

Nuclear Energy

• Nuclear bombs tap into energy deep within atoms.

• Einstein's equation, E = mc^2, expresses the equivalence of matter and energy.

• Mass can become energy, and energy can become mass.

• Objects can reduce mass by transferring energy.

Because of this equivalence, mass and changes in mass can be used to locate energy that’s hidden within normal matter.

• When sodium and chlorine react, their combined mass decreases slightly as chemical potential energy is released.

Atomic Nucleus

• Electrons are the lightest part of an atom, with little mass to release as energy.

• Most of an atom's mass is in the nucleus, which is extremely small (~10^{-15} m in diameter).

• The nucleus of a sodium ion contains 11 protons and 12 neutrons (nucleons).

• Nucleons have about 2000 times the mass of an electron, making up 99.975% of the ion's mass.

• The ion is mostly empty space, with electrons and a tiny nuclear lump.

Sodium nucleus (11 protons, 12 neutrons) Neutron Diameter: 1 \times 10^{-15} meter Proton Diameter: 1 \times 10^{-15} meter The center of a sodium ion is a tiny nucleus containing about 99.975% of the ion's mass. It consists of 11 positively charged protons and 12 uncharged neutrons. The protons repel one another at any distance, but the protons and neutrons are bound together by the highly attractive nuclear force as long as they touch one another.

Forces in the Nucleus

• Competing forces within the nucleus: electrostatic repulsion between protons and the attractive nuclear force.

• The nuclear force dominates at short distances when nucleons are touching.

• Analogy: a hopping toy with a spring and suction cup, where the spring separates and the suction cup holds.

• The suction cup leaks, eventually releasing the stored energy in the spring.

• Similarly, nuclei need energy to release energy, like pushing a cork out of a champagne bottle.

Energy Barrier

• The attractive nuclear force prevents the nucleus from coming apart, creating an energy barrier.

• Classical physics predicts the nucleus will remain together forever unless energy is added.

Quantum Physics and the Nucleus

• Quantum physics introduces uncertainty in an object's location (Heisenberg uncertainty principle).

• This fuzziness results from the wave-particle nature of objects.

• There is a tiny chance that nucleons will temporarily separate beyond the reach of the nuclear force.

• Electrostatic repulsion will then push them apart in radioactive decay.

Quantum Tunneling

• Quantum tunneling allows nucleons to escape the nuclear force without surmounting the energy barrier.

• Radioactive decay is a random process characterized by a half-life, the time for half the nuclei to decay.

• After one half-life, half the original nuclei remain; after two, a quarter, and so on.

This halving of the population with each additional half-life is a type of exponential decay.

Exponential Decay

• The fraction of nuclei remaining after a given time is fraction remaining = (\frac{1}{2})^{\frac{elapsed \, time}{half-life}}. This is expressed as N/N0 = (\frac{1}{2})^{t/T{1/2}}.

• Long-lived radioactive nuclei (uranium and thorium) have survived since Earth's formation and are abundant in nature and essential to nuclear weapons.

Who Hid the Energy?When a large nucleus breaks apart into fragments, it releases a great deal of energy. In what form was that energy stored in the intact nucleus?

• It was stored as electrostatic potential energy in the repulsion between protons
  
  Why: Although it is routinely called nuclear energy, much of the energy stored in radioactive nuclei is actually electrostatic potential energy. Assembling a giant nucleus out of positively charged particles requires a considerable amount of work against electrostatic forces, and it is that stored work that’s released when the nucleus decays.

Carbon-14 Dating

• A small fraction of carbon is carbon-14, a radioactive form with a half-life of 5730 years.

• Living organisms incorporate carbon-14; after death, the fraction of carbon-14 decreases due to decay.

• To find the fraction of carbon-14 remaining after 1001 years: fraction \, remaining = (\frac{1}{2})^{\frac{1001 \, years}{5730 \, years}} = (\frac{1}{2})^{0.1747} \approx 0.886

• Approx 0.886 of the original carbon-14 should remain

If you find that fraction of carbon 14 when you test the garment, that indicates that the fibers in the garment come from plants or animals that died approximately 1001 years ago, although you can’t tell exactly when the fabric itself was woven. If you find a larger fraction, that proves that the garment is less than 1001 years old.

Fission and Fusion

• The more protons in a nucleus, the greater the repulsive force, increasing the likelihood of radioactive decay.

• Additional neutrons can reduce proton repulsion by increasing the size without adding positive charge.

• A stable nucleus construction is a balancing act.

Nuclear Stability

• Small nuclei have a strong attractive nuclear force and stick like crazy. These nuclei resemble hopping toys with weak springs and big suction cups; once brought together, the pieces never come apart.

• Nuclei with many protons decay rapidly. They resemble hopping toys with strong springs and small suction cups.

• Nuclei with roughly 26 protons are extremely stable.

• Smaller nuclei can release potential energy by growing, while larger nuclei release potential energy by shrinking toward this intermediate size.

Nuclear Fusion

• For a small nucleus to grow, something must push more nucleons toward it.

• Electrostatic repulsion will initially oppose this growth, but once everything touches, the nuclear force will bind the particles together and release a large amount of potential energy.

• This coalescence process is called nuclear fusion.

Nuclear Fission

• For a large nucleus to shrink, something must separate its pieces beyond the reach of the nuclear force.

• Electrostatic repulsion will then push the fragments apart and release a large amount of potential energy.

• This fragmentation process is called nuclear fission.

Energy Comparison

• The energies released when small nuclei undergo fusion or when large nuclei undergo fission are enormous compared to chemical energies.

• Uranium converts about 0.1% of its mass into energy when it breaks apart.

• Kilogram for kilogram, nuclear reactions release about 10 million times more energy than chemical reactions.

Discovery Timeline

• 1896: Antoine-Henri Becquerel discovered natural radioactive decay.

• Marie and Pierre Curie discovered polonium and radium.

• 1911: Ernest Rutherford discovered that atoms have nuclei.

• 1932: James Chadwick discovered the neutron.

• 1934: Enrico Fermi and colleagues added neutrons to nuclei, thinking they had formed ultraheavy nuclei.

• Lise Meitner, Otto Frisch, Otto Hahn, and Fritz Strassmann collectively showed that uranium was fragmented into lighter nuclei.

When a neutron strikes a uranium nucleus, there’s a good chance that the nucleus will fall apart into fragments. This process is called induced fission. Among the fragments of induced fission are other neutrons.

Incoming neutron + ^{235}U -> Fission fragments + Free neutrons

Nuclear Problems

If you take two intermediate-size nuclei and combine them to make a single uranium nucleus, will the process release or consume energy?

• It will consume energy.
  
  Why: To merge two smaller nuclei and form a uranium nucleus, you will have to push the two together with considerable force because they contain many protons. You will have to do considerable work to bring these nuclei close enough for the nuclear force to bind them. The energy you invested in this new nucleus is the same energy that is released when it undergoes fission.

Chain Reaction

• A chain reaction occurs when the fission of one uranium nucleus induces fission in two nearby uranium nuclei, and so on.

Atomic Bomb Requirementes

• Four conditions had to be satisfied for an atomic or fission bomb to be possible:

  • A source of neutrons to trigger the explosion

  • Fissionable nuclei in the bomb

  • Each fission must produce more neutrons than it consumes

  • Efficient use of released neutrons to induce further fission

Uranium Isotopes

• Uranium nuclei must contain 92 protons but can have varying numbers of neutrons (isotopes).

• Natural uranium consists of ^{235}U (92 protons, 143 neutrons) and ^{238}U (92 protons, 146 neutrons).

• Only ^{235}U is suitable for a bomb due to its marginal stability and immediate shattering upon neutron impact, releasing ~2.5 neutrons.

• ^{235}U has a radioactive half-life of 710 million years.

• ^{238}U slows a chain reaction. Most neutrons are absorbed without fission. It becomes ^{239}Pu, plutonium, through complicated changes. Has a half-life of 4.51 billion years.

Therefore it must first be seperated.

Isotope Seperation Requirements

• ^{235}U is rare, making up only 0.72% of natural uranium.

• Separating ^{235}U from ^{238}U is extremely difficult due to their chemical similarity.

• Requires comparing their masses which requires Heroic measures to extract ^{235}U from natural uranium were developed by the U.S. government during World War II and the Cold War.

Critical Mass

• For a chain reaction, the bomb must efficiently use neutrons without wasteful absorption or excessive escape.

• A large enough lump of relatively pure ^{235}U is needed.

• Must also be a sphere to have a minimal surface.

• Neutrons can travel several centimeters through uranium without hitting a nucleus.

• For bare sphere of ^{235}U, critical mass required to intiate is about 52 kg (115 lbm), a ball about 17 cm (7 in) in diameter. At that point, each fission will induce an average of one subsequent fission.For an explosive chain reaction, in which each fission induces an average of much more than one fission, additional 235U is needed—a supercritical mass.
  About 60 kg (132 lbm) will do it

Little Boy

• To prevent premature explosion, had to be assembled quickly.

• In pure ^{235}U, inducing time is about 10 ns (10 nanoseconds or 10 billionths of a second).

• In a supercritical mass, each generation of fissions is much larger than the previous generation, so it takes only a few dozen generations to shatter a significant fraction of the uranium nuclei.

• Whole explosive chain reaction over in less than a millionth of a second, with energy released during the last few generations (about 30 ns).

Bomb Assembly

• A cannon fired a cylinder of ^{235}U through a hole in a sphere of ^{235}U to assemble a 60-kg mass.

• It released the energy of about 15,000 tons of TNT

Testing

• Little Boy was dropped without testing due to its foolproof concept and precious ^{235}U.

• Developed plutonium which could use a sophisticated method.

Manhattan Project

• Synthesized plutonium from ^{238}U in nuclear reactors

• A nuclear reactor carries out a controlled chain reaction, and neutrons from this chain reaction can convert ^{238}U into ^{239}Pu

Plutonium and 239Pu

• ^{239}Pu releases an average of three neutrons, so could be used in a chain reaction.

• Critical mass: ~10 kg (22 lbm)—a ball about 10 cm (4 in) in diameter for bare 239Pu sphere.

Cannon Assembly Issues

• So radioactive and releases many neutrons that a chain reaction develops almost instantly.

• Cannon assembly method won’t work.

• Gadget required crushing sphere of plutonium which was surrounded by a tamper of ^{238}U

Implosion and Compression

• Compression scheme worked. The chain reaction was quick, reached super critical mass instantly.

• Succeeded in getting a chain reaction to occur (more than 1.

Fat Man

• Nearly identical to gadget. Was dropped over Nagasaki Japan and killed 140,000 people.

The longer a supercritical mass could be held together before it overheated and exploded, the larger would be the fraction of its nuclei that would fission and the greater the explosive yield.