The Physics of Nuclear Weaponry

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The Physics of Nuclear Weaponry By

Matthew Agdanowski &

Roberto Gonzalez

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Table Of Contents:

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 History: World War II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Mass-‐Energy Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Strong Nuclear Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Nuclear Fission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Types of Nuclear Bomb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Nuclear Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Blast Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 Weak Nuclear Force & Particle Decay . . . . . . . . . . . . . . . . . . . . . 22 Health Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Works Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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Science has no biases, no agendas; its only ulterior motive is that of the truth. This knowledge can be used for good and evil, but is not inherently either one. We are the ones who decide how to use this knowledge. It is us humans that give science both its positive and negative connotations. Over the course of its evolution, from primates beginning to classify objects in their environment to the nanotechnology of today, science has been used for both the betterment of mankind and responsible for some of its darkest moments.

In 1918, Fritz Haber earned the Nobel Prize in Chemistry for the Haber-‐Bosch process for Synthetic Nitrogen Fixation. His process was originally researched to create ammonia, a precursor to nitric acid used in the explosive munitions that were crucial to Germany in World War I. Today 453 billion kilograms of fertilizer is manufactured for food production each year by this process, boosting the world’s population.

A parallel can be drawn for the case with Nuclear Technology in the fact that the ideas it encompasses were also accelerated by the drive of all out world war. While the early beginnings of nuclear physics began with the discovery of radioactive elements in the early 20th century, it was not until the late 1930’s when nuclear fission was discovered. It was around this time that physicists around the world petitioned to their respective governments to invest and support nuclear fission research just on the brink of World War II. In 1945 “Trinity,” code name of the first nuclear test was tested with unknown repercussions. Later in the 1950’s, yielded the nuclear power era, as many countries including Russia and the United States committed to the field in order to sustain their growing power grids.

Living in the age of nuclear technology has its advantages and its disadvantages. After the conclusion of World War II, the Soviet Union and the United States engaged in a 40-‐year arms race know as the Cold War. Over the course the war, thousands of nuclear weapons were stockpiled, and citizens of each country lived in constant fear of world destruction; nuclear war, power-‐plant meltdowns and deadly fallout lasting decades to just name a few. These dangers also have their counterparts however, nuclear technology has given us a potential of never-‐ending energy source, as well as life-‐saving cures through nuclear medicine.

The culmination of humanities hopes and dreams for nuclear technology can all be traced back to a group of men, working under total secrecy to try to bring an end to the bloodiest war in history. These men would become superstars, not only among the scientific community, but to ordinary citizens as well. This project would become know as The Manhattan Project.

In January of the year 1939, two German chemists, Otto Hahn and Fritz Strassman

in the peer-‐reviewed scientific journal, Naturwissenschaften, proposed the process of nuclear fission. This publication furthered the research of Physicist, Enrico Fermi and his team, started in 1934. Over the course of their research, atoms of Uranium-‐235 were bombarded with streams of neutrons, creating Barium atoms with roughly half of the atomic mass that Uranium had, showing how an atom’s nucleus can be split in half. These revelations set off frenzy around the scientific community. As a result of this discovery, Germany launched the Uranverein, or the “Uranium Club.” This project was disbanded in

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August of 1939 as Germany prepared for World War II with the invasion of Poland in September of the same year. The project was renewed on the very day that war broke out, when German Army Ordnance established the program headed by army physicist Kurt Diebner. The goal for this revitalization in German nuclear research was to investigate military applications for fission.

Not all scientists were enthusiastic by the discovery of nuclear fission with some fearing the worst. Among these scientists were the likes of Albert Einstein, Leó Szilárd and Eugene Wigner. On August 2, 1939 Dr. Leó Szilárd, with the aid of fellow Hungarian physicists Edward Teller, and Eugene Wigner, along with supervision from Albert Einstein, wrote what would become known as the Einstein-‐Szilárd letter. Addressed to President Franklin Delano Roosevelt, the letter urged that because of the potentially catastrophic power of atomic weaponry, the United States should begin its own nuclear research program. The letter went on to say that:

It may become possible to set up a nuclear chain reaction in a large mass of uranium, by which vast amounts of power and large quantities of new radium-‐like elements would be generated. Now it appears almost certain that this could be achieved in the immediate future. This new phenomenon would also lead to the construction of bombs, and it is conceivable — though much less certain — that extremely powerful bombs of a new type may thus be constructed (The Letter from Albert Einstein).

This letter presented President Roosevelt with a difficult decision. The implications of German nuclear capability were dire; if they were able to develop this technology first, the world would most certainly fall under its fascist rule.

In a quick, but cautious response to these scientists’ call to arms, Roosevelt “appointed Lyman J. Briggs, of the National Bureau of Standards to head the new Advisory Committee on Uranium, which first met on October 21, 1939” (The Manhattan Project). This committee included both civilian and military personal working together cohesively to determine the United States’ stand on Uranium research. The committee’s first course of action was a recommendation for limited funding on Uranium Isotope research along with funding Enrico Fermi’s and Leo Szilard’s research on nuclear chain reactions being conducted at Columbia University.

The research towards this nuclear chain reaction was slow at first; it was not until the Kaiser Wilhelm Institute in Germany began the undertaking of an extensive research program involving uranium that the United State’s research really gained momentum. The first meeting of the Advisory Committee on Uranium was held on October 21, 1939 and a little over one week later, on November 1, the committee released a statement that said that “If the reaction turns out to be explosive in character, it would provide a possible source of bombs with a destructiveness vastly greater than anything now known [and] we recommend adequate support for a thorough investigation” (Atomic Heritage Foundation).

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In June of 1940, the National Defense Research Committee, with Bush as its head, reorganized the Uranium Committee into a scientific body and eliminated military membership. Not dependent on the military for funds, as the Uranium Committee had been, the National Defense Research Committee had more influence and more direct access to money for nuclear research. The Uranium Committee was renamed and given the codename: S-‐1, holding its first meeting on December 18, 1941, less than two weeks after the Japanese attacked the United States naval base at Pearl Harbor, Hawaii. This meeting pulled together the nations brightest minds; include the likes of Harold Urey and Ernest Lawrence. The goal was to explore several techniques for extracting the uranium, as well as work toward several designs for the reactors.

Over the course of their research, it became evident that in order to continue, the project would require several large facilities. Working alongside the US Army Corps of Engineers, several sites were established in the locations of Hanford, Washington Los Alamos, New Mexico. The workhorse of the again newly named “Manhattan Project” was its principle facility in Oak Ridge, Tennessee, where 59,000 acres of farmland was purchased and within a matter of several months, it became the states 5th largest city; but it was a secret city.

The research was divided up between each of the locations, enabling the project to

excel rapidly. “Oak Ridge and Hanford focused on uranium enrichment and plutonium

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production” while locations such as Los Alamos, headed by project leader Robert Oppenheimer, focused more on bomb development (World War II). As a result, on December 2, 1942 at the University of Chicago, Enrico Fermi and his team constructed the world’s first nuclear reactor, which successfully sustained an artificial nuclear chain reaction. The research continued progressing under total secrecy as, Oppenheimer and his team finished up the designed for the atomic bomb:

Early work focused "gun-‐type" designs, which fired one piece of uranium into another to create a nuclear chain reaction. While this approach proved promising for uranium-‐based bombs, it was less so for those utilizing plutonium. As a result, the scientists at Los Alamos began developing an implosion design for a plutonium-‐based bomb, as this material was relatively more plentiful (World War II).

By July 1944, the uranium gun-‐type bomb was less of a priority the bulk of the research was dedicated to plutonium designs.

Because the implosion-‐type device produced was more complex than the uranium gun-‐type, Oppenheimer believed that a test was needed before the bomb could be approved. Thus, on July 16, 1945 at 5:30am, codenamed “Trinity,” a test bomb nicknamed “The Gadget” was dropped from a 100ft-‐tall constructed tower in the middle of New Mexico’s Jornada del Muerto desert and humanity entered the nuclear age.

The bomb exploded with the power equivalent of 20 kilotons of TNT, or 84

terajoules of energy, releasing a shockwave felt over 100 miles away and producing a mushroom cloud stretching almost eight miles into the sky. Following the explosion, after the euphoria had faded, Oppenheimer was famously reciting a verse from the scripture Bhagavad Gita, saying “Now I am become death, the destroyer of worlds”.

Following the death of President Roosevelt, his successor, Harry S Truman was left with a hard decision to make. After long consideration, taking into the time needed and potential casualties as a result of a US invasion of Japan he agreed to the use of atomic weapons on the Japanese mainland. Tow weeks after the Trinity test, on August 6th and 9th of 1945, two bombs, Fat Man and Little Man were dropped on Japan, marking the end of World War II. Little Boy, a Uranium gun-‐type bomb developed at the Los Alamos facility

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with his brother, the Plutonium bomb Fat Man, was dropped on Hiroshima, Japan by the US B-‐29 bomber, the Enola Gay; Fat Man was dropped on Nagasaki, Japan, forcing the Japanese to surrender. The total casualties could not be fully calculated, but was estimated at between 150 and 250 thousand, lower than the 250 to 500 thousand estimated for a non-‐nuclear conflict.

Over the course of ten years, and numerous name changes, the Manhattan project cost an estimated $2 billion US dollars and employing over 130,000 people, making it the United States largest endeavor. It was not until 1949, when the USSR detonated their first nuclear weapon that the project closed, making room for a new world of atomic possibilities.

All this talk of nuclear technology and splitting atoms would not have been

possible if it were not for the work of thousands of scientists who contributed immense bodies of knowledge to the scientific communities. One of these important discoveries was the idea that the mass and energy of an object could be related to each other by a factor of the speed of light squared, E=MC2. This mass-‐energy equivalence theorem would become not only crucial for the all future nuclear ventures, but also has become perhaps the most famous physics equation in the world.

For centuries, the concept mass and energy equivalence had puzzled the world’s greatest minds. Starting with his work Opticks, published in 1704, Isaac Newton speculated that light particles and matter particles were inter-‐convertible. Building upon Newton’s work, Swedish scientist Emanuel Swedenborg, in 1734, postulated that all matter is ultimately composed of dimensionless points of “pure and total motion” (E. Swedenborg). With each new generation of physicists working toward fully explaining the universe, much scientific knowledge was accumulated over the span of a few hundred years.

It took an Einstein however to unify this mass-‐energy equivalence theory; actually it took the Albert Einstein. The work of James Clerk Maxwell in the 1850’s, that unified the seemly-‐unrelated phenomena and equations from electricity, magnetism and optics into one single theory, was crucial to Einstein’s derivations. From Maxwell we have learned that photons, particles of light, have momentum yet no mass. We know from classical physics, that momentum, illustrated by the letter “p” is equal to an objects mass, “m” times its velocity, “v” according to the expression:

This left Einstein with a quandary; how can a photon have momentum, yet no

mass. To reconcile this, Einstein believed that “the energy of a photon must be equivalent to a quantity of mass” and therefor could be related (The Derivation).

To test this hypothesis, Albert Einstein set up a thought experiment that involved a stationary box, sitting inside a vacuum. At a given moment, a photon of light is emitted

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from inside the box. Due to the conservation of momentum, as the photon moves across the box, from left to right, the box must also move from right to left. Eventually the photon hits the opposite side of the box, transferring all its momentum to the box, therefore stopping the box from further moving to the left, and the total momentum of the system if conserved. This only lead to further complications; because there was no external forces acting on the box, its center of mass must remain unchanged, yet the box has clearly moved. To resolve this, Einstein proposed that there must be a “mass equivalent” to energy of the photon, which is the same as the mass moving from left to right inside the box. Furthermore, the mass must be large enough that its center of mass remains stationary.

From these parameters, Einstein was able to successfully derive the theorem using Maxwell equations for light. If the energy of a photon, “E” and the speed of light is “c,” using the electrostatic wave, we get:

The box from which the photon is contained has a mass of “M” and it moves in the

opposite direction of the photon with some velocity, “v,” then the boxes momentum is given by:

If the photon moves a distance, x, or dt in an amount of time dt, then the boxes

velocity can be rewritten as:

To this we can apply the conservation of momentum, equating the

momentum of the box and that of the photon into a single equation that can be manipulated to solve for wanted variables:

If the box has a mass of “L,” the photon thus travels “L” distance in “t” amount of

time. If we substitute this into our previous equation and rearrange our variables we get: In order to effectively take into account the center of mass of an object not

moving, we have to imagine that hypothetically the photon has a mass of “m.” This allows us to calculate the center of mass for the entire system assuming that the box starts at

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position x1 and the photon as the position x2. To accommodate for the center of mass not moving, we can equate the center of mass at the start to the center of mass at the end:

The original starting position of the photon can be written as zero, and by

substituting in for M(dx), we get: As you can thus see, the length’s of the box cross out and a simple rearrangement

bring us to our final answer:

This theory was very controversial at first. In fact, it took a few decades and many variations of this derivation, both by Einstein and by his peers, until this theory became fully recognized. Even today people are coming up with odd derivations in special cases. University of Pittsburg professor, Dr. John D. Norton came up his own, quick method. In this

he uses just two equations and a little bit of manipulation. If we input equation two into equation one for force, we get:

The first equation is: Energy gained = Force x Distance through which force acts.

The energy gained is labeled E. Since the body moves very close to c, the distance it moves in unit time is c or near enough. The first equation is now:

E = Force x c

The second equation is:

Momentum gained = Force x Time during which force acts The unit time during which the force acts, the mass increases by an amount labeled m and the velocity stays constant at very close to c. Since momentum = mass x velocity, the momentum gained is m x c. The second equation is now:

Force = m x c

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E = Force x c = (m x c) x c

Simplified, this becomes:

E = mc2 Now, Dr. Norton acknowledges his critics by going on to say that this derivation is

a very special case and a further argument is needed to show this is true for all cases. It has been roughly 100 years since the publication of Einstein’s papers on Special

Relativity, where he outlined this important derivation in a different way than described, which involved using Lorentz transforms. This is because he had used Maxwell’s Equations in the prior derivation, which relied on implicit assumptions. Through this new derivation, Einstein showed this equation “suggested a new way of describing the origins of chemical energy and suggested another source of energy that at that point was unknown in history – nuclear energy” (Energy Tribune).

After proving that is it possible relate energy to mass, the next step for the nuclear

research team was to turn their attention to the internuclear forces that would have to be overcome in order to unlock all this stored energy; they first turned to the strong force. Of all the fundamental forces of physics, the Strong Force is the strongest, hence its name. While it may not be something that you interact with on a daily basis, it is the force that is holding every atom in the entire universe together. The Strong Force is complicated because it does this in two ways: It holds the atoms nucleus together as well as the protons and neutrons together as well.

The term “Nucleons” is commonly used when referring to protons and neutrons because those two subatomic particles are what make up an atoms nucleus. Protons and Neutrons are both classified as a type of particle known as a Hadron. A certain

type of hadron, which protons and neutrons fall under, are composed of three quarks, which are a fundamental constituent of matter; they cannot be broken down further into smaller particles.

Among their many traits, quarks have a property that physicists call “color.” This is not the type of color that most people associate with that word

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because we are not able to see quarks. To illustrate how small quarks are, they have an order of magnitude of 10-‐15m, and our strongest microscope can only make out atoms or molecules which have an average diameter in the magnitude of 10-‐12m. Instead, we refer to the individual quantum states that a quark can exist in. We call these states the colors: Red, Blue, and Green. “The property can be considered something like a "color charge" with three distinct values, with only color neutral particles allowed” (Color Force).

Now the color force is by no means an arbitrary invention, there has even been experimental evidence for the existence of color. “Both the rate at which [pi]0 decays into two photons and the probability that electrons and positrons will create hadrons when they collide indicate that there are three times as many quarks as would be expected if color did not exist” (The Color Force).

Another important characteristic of quarks is that they have something that we call “flavors.” Again, it is not the flavor in a typical sense, rather descriptions of the type of quark they are. The flavors are as follows, from smallest mass to largest: Up, Down, Charm, Strange, Top, and Bottom.

The most common types are the Up and Down quarks. This is because the rarer,

heavier quarks quickly decay into Up and Down quarks. Quarks also the property of charge, where “an 'up' quark has a charge of +2/3 and a 'down' quark has a charge of -‐1/3” (Jefferson Lab). A proton is made up of two Up quarks and one Down quark. When we do the math, we see that get when we multiple the fractional charge of an up quark by two and add it to the fractional charge of the down quark we get a total unit charge of one. This charge is equal to 1.6x10-‐19 Coulombs. The same can be done for the charge of a neutron, which consists of one up quark and two down quarks. This, when added up gives us the neutral charge that neutrons hold.

The tie between these two seemingly unrelated characteristics of quarks comes from the need for color in order for any calculation to occur; without color, we would not be able talk about the composition of protons and neutrons, even atoms would be defeated.

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It all stems from a postulate made by Austrian physicist Wolfgang Pauli known as the Pauli Exclusion Principle. This principle states:

No two electrons can have the same four quantum numbers. We are aware that in one orbital a maximum of two electrons can be found and the two electrons must have opposing spins. That means one would spin up ( +1/2) and the other would spin down (-‐1/2). (UC Davis).

This can be tied into color force by relating the spins of electrons inside orbitals to the color of quarks inside a hadron. Since there are two up quarks, as well as a down quark, inside a proton, those quarks need to have different colors in order to not violate this principle.

The Strong Force is able to bind these hadrons together by a process we call Color Force. I will be using the example of a proton to illustrate this color interaction. Inside of a proton, there are two up quarks and one down quark, each with a different color as explained above. What makes this force special is that each quark inside the hadron is changing its color constantly. The process that allows the quarks to do that is also the process that holds the quarks together.

The process occurs by the exchange of the Strong Force carriers known as Gluons. Force carriers are exchanged between particles that are controlled by that force. Gluons have no mass and no charge, but they do have color, which is how quarks are able to change their color. This whole thing happens as the gluons pass from quark to quark inside this hadron. As they leave a quark, they change its color, and as they come in contact with a new one, they change that quarks color as well; always the colors add up to white, or neutral color.

You can imagine this gluon movement as a rubber band that has been wrapped around all the quarks. Quarks are allowed to move around inside the hadron but are unable to leave. If the quark strays too far away, the color attraction due to gluon exchange pulls the quark back into the hadron. This explains why we quarks are not observed floating around on their own; the only way to isolate quarks or other particles is to smash atoms together at immense speeds. These collisions, like the ones preformed at the Large Hadron Collider operated by CERN National Laboratories in Geneva, Switzerland send these fundamental constituents of matter in all directions and are measured by supercomputers and extremely calibrated machinery.

A residual effect of this color interaction is the ability to hold the atom’s nucleus together. This force is most commonly referred to as the Nuclear Force, and is probably the one most people are familiar with. An atom’s nucleus is composed of protons and neutrons, but the most important thing to remember is that protons are identical and positively changed. Because like charges repel and opposite charges attract, the like-‐charged protons want to be as far away from each other as possible; but for some reason they are jammed into the smallest place imaginable. This reason is the immense strength of the nuclear force.

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This nuclear force is the second form of the Strong Force with the other being the Color Force, responsible for holding hadrons together. The nuclear force is important for two main reasons:

1. The nuclear force is repulsive at extremely small distances, roughly about 0.7fm from center to center.

This keeps the protons and neutrons away from each other, which helps give atomic nuclei their size. This force occurs even though neutrons are electronically neutral and “do not care” who they are next to, be it a proton or another neutron.

2. The nuclear force is attracted at slightly larger distances, between 0.7fm to 0.9fm from center to center

If the protons and neutrons exceed a distance of 0.7fm from each other, the nuclear force pulls them back together. If however, the distances exceed 0.9fm, the force of attraction drops off exponentially until at a distance of 2.0fm apart, the force is so small that is becomes negligible.

During the color interaction, where gluons exchange color between three different color quarks, pions, made of two quarks are out side the proton on neutron. These pions are exchanged from hadron to hadron. Since there is color force being exerted between quarks inside the pion, and the pions are being exchanged between protons and neutrons, then the pions essentially make it possible for color force to be exerted across hadrons. This color force they exert however, can be described as a “watered down” version.

There is so much energy involved in the strong force, using Einstein’s Mass-‐Energy Equivalence theorem, we see that the energy release by one atom of Uranium-‐235 can potentially produce roughly 2.12x1019 joules of energy. That is just a single atom; imagine an entire uranium bomb’s worth of energy. This potential is what drew scientists to nuclear technology. Thanks to Einstein’s famous equation and the Strong Force, a new horizon for science had become very realistic.

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Nuclear bombs involve the strong force, which, as previously stated is integral to holding an atom together. These weapons are particular in which type of atoms work best for the release of high amounts of energy; atoms with unstable nuclei, specifically atoms from isotopes are the most efficient for this process. Both Fission and Fusion reactions release large amounts of energy from relatively small amounts of matter. For example the first nuclear fission bomb test released an amount of energy equivalent to twenty thousand tons of trinitrotoluene, better known as TNT. This is attributed to the properties of the particular isotope being used. For instance Uranium 238 is one of very few materials that can undergo induced fission and is used as the primary fuel in fission weapons rather than Uranium 235 because of its nuclear properties more specifically it’s higher probability of capturing a neutron as it passes by.

Nuclear fission is the process by which a nucleus of an atom is split into smaller fragments. The key to this reaction is using isotopes of uranium specifically U-‐238 as stated above. The reason for this is because the binding energy of this isotope is so low that when a neutron is absorbed the energy that is released during rearrangement exceeds it (Sublette). It takes about 7 to 8 million electron volts (MeV) to overcome the strong force, which is holding the nucleus of a U-‐238 atom together. This amount of input energy is supplied by the binding of an extra neutron to the heavy nucleus of the isotope. This relatively small amount of input energy is converted to output energy immediately after the fission process is complete. All of this output energy is released to the environment in the form of kinetic energy making it an exothermic process. Below is a statistical breakdown of the amount of energy released (output energy) during fission.

MeV Kinetic energy of fission fragments 165 +/- 5 Instantaneous gamma rays 7 +/- 1 Kinetic energy of neutrons 5 +/- 0.5 Beta particles from product decay 7 +/- 1 Gamma rays from product decay 6 +/- 1 Neutrinos from product decay 10 TOTAL 200 +/- 6 The release of approximately 200 million electron volts (MeV) is incredibly large in

comparison to the amount of energy it actually took to break apart the atom. Some of the fission products release their decay energy immediately while other unstable products take longer to decay and their energy shows up over time as nuclear fallout (Sublette).

On the following page the figure shows the fission process along with a step-‐by-‐step interpretation. What the figure doesn’t show are the electrons that were not absorbed by the neighboring atoms. The sum of the neutrons and the new fission fragments is not equal to the original mass of the original nucleus. They are slightly less heavy than the original nucleus because some of the original mass is converted into energy.

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Step1: When a U-‐235 atom is struck by and absorbs the moving neutron, that

neutron splits the atom into two lighter atoms and knocks off 2-‐3 neutrons. Step 2: The two lighter atoms then settle into their new states while emitting

gamma radiation. Step3: After the first collision, the three now free-‐moving neutrons ignite a chain

reaction which is set off in the nucleus of the surrounding U-‐235 atoms, as they also absorb these free-‐moving neutrons then become unstable and split immediately.

The design of a fission bomb is critical in the functionality of the weapon itself. Designers involved in production of the first bomb had a handful of issues that they had to overcome. One big issue was how they were going to house the nuclear fuel itself. The resolution to the problem was a rather simple one, which will be further discussed. There are two types of fusion bombs, first a gun-‐triggered assembly and second an implosion triggered assembly.

Within a gun-‐triggered fission bomb the nuclear fuel must be stored in what is known as “separate subcritical masses.” Subcritical mass is the smallest amount of nuclear matter that will not support fission. This is important because it prevents premature detonation. The next step is bringing these subcritical masses together to form a supercritical mass, which provides enough neutrons to support a fission reaction. This is accomplished by making a small bullet made of Uranium-‐235, which is then shot at a sphere also made of Uranium-‐235 bringing together the masses. The third step is producing free neutrons using a neutron generator which is composed of polonium and beryllium separated by foil. Once the subcritical masses join to form the supercritical mass the foil breaks causing polonium to produce alpha particle emissions. These alpha particles

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then collide with beryllium-‐9 then producing beryllium-‐8 neutrons that initiate the fission reaction.

Sequence of Events

1. Small explosives launch the Uranium bullet down the barrel towards the Uranium sphere.

2. The bullet strikes the sphere initiating the fission reaction within the sphere itself.

3. Fission reaction begins and the bomb explodes.

This type of assembly is

simple but the drawbacks are the weight and length of the barrel and that only U-‐235 can be used (Sublette).

Implosion triggered fission bombs utilize a different method when combining the two critical masses. In this method an implosion compresses the subcritical masses together in a sphere. The problem with this method is controlling the shockwave within the sphere so that it is dispersed evenly throughout. Scientists who were involved with the Manhattan Project attacked this problem by refining early prototypes. They

also improved the design by utilizing a concept known as Boosting. Boosting is the process by which fusion is used to create neutrons, which are used to trigger chain reactions faster (Sublette). In this type of design the nuclear fuel that is favored is Plutonium-‐239 because of its molecular stability. Although Pu-‐239 is an excellent type of nuclear fuel it is harder to ignite in comparison to U-‐235 (Nuclear Weapons). On the next page is an image of an early design of this weapon.

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This design is composed of a tamper surrounding a Pu-‐239 core. This is all

engulfed by a combination of fast and slow explosives which controls the internal shockwave as stated before. The most essential component in this device is the detonation sequence. First the explosives ignite creating a shockwave that thrusts pieces of plutonium into the neutron initiator. The neutron initiator then releases neutrons, which then begin their collision course with Pu-‐239 atoms to “initiate” fission (Fission Weapon).

Both of these fission designs have theoretical yield limits to how much energy is released to the surrounding environment. The largest amount of energy ever released by a fission weapon had a yield of about 500 kilotons (kt). Fusion weapons on the other hand have no such limits, as fusion can provide unlimited amounts of energy.

Fusion is a thermonuclear reaction between two isotopes of light elements. Fusion

occurs when the nuclei of two atoms combine to form a heavier atom. In order for the two nuclei to form they must collide with sufficient amount of energy, which is dependent on the surrounding temperature.

“Nuclei from different isotopes inherit different likelihoods of collision at a particular temperature. The rates of all fusion reactions are affected by both the temperature and density. The hotter and denser the fusion fuel the faster the fusion” (Sublette). For example, the heat in a bomb provides the heat needed to ensure that the

collision between nuclei occurs. For these light nuclei, energy is produced while mass is destroyed after the collision. A connection can be made to Einstein’s equivalence equation where mass is related to energy. Another connection can be made to the conservation of energy and momentum where the two nuclei (M₁ and M₂) collide at some initial velocity (V₁ and V₂) of each mass to form a heavier nucleus (M₃) and a lighter particle (M₄) (Atzeni). . This is a perfectly inelastic collision where the two nuclei converge into one heavier nucleus.

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PBefore=PAfter

M₁V₁+M₂V₂→M₃V₃+M₄V₄

After the collision the final velocities of the two products are equal to the velocity of the center of mass respectively for each product. The maximum energy loss occurs during a total inelastic collision.

Where M=mass and V=velocity for all equations shown According to the conservation laws the energy released by the reaction/collision is

distributed among the two fusion products.

EBefore=EAfter

There are many important and relevant fusion reactions, but the most effective one for a fusion weapon is the reaction between Deuterium and Tritium both of which are isotopes of hydrogen (the lightest element on the periodic table).

The first line in the figure above is the fusion equation involving Deuterium and

Tritium. When these two isotopes combine they form a helium atom composed of two protons and two neutrons. Energy is released in the formation of helium along with a free neutron, which is then captured (as seen in the second line) by a Lithium atom. Lithium and the neutron undergo fission and produce another helium atom, Tritium and release more energy. The Tritium atom produced then fuses with another Deuterium atom (as shown by the green arrow). The overall significance of the third line is that it shows how Lithium and Deuterium can be used as the fuel for fission (Nuclear Weapons).

The design of a fusion weapon is rather complicated in that it had to overcome many different obstacles. The first problem was that Tritium and Deuterium were hard to

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store because of their gaseous state. This problem was resolved by using a solid compound called lithium-‐deuterate, which doesn’t decay under normal temperature as the nuclear fuel. The second problem was Tritium and its short supply and half-‐life. Scientists resolved this issue by using a fission reaction as stated earlier between Lithium and a neutron to replenish the Tritium supply. This fission reaction also solved another problem in which Deuterium and Tritium had to be highly compressed at high temperatures in order to initiate the fusion reaction. Designers of the weapon configured a two-‐stage design, which involved a boosted fission part first and fusion component second.

The above diagram is a simple depiction of the detonation process. The primary

fission reaction in this figure is gun-‐triggered but can be implosion triggered. First an explosive launches a U-‐235 bullet down the barrel to combine with the other mass of U-‐235 achieving supercriticality and begins the fission reaction. During fission X-‐rays are emitted which reflect within the warhead and heat the interior. This turns the polystyrene foam, which is encasing the fusion fuel, into plasma that heats up and compresses deuterium and Tritium to begin the fusion reaction. The end result of this sequence is the release of enormous amounts of energy. As stated earlier there is no limit to the theoretical yield of a fusion reaction. The largest fusion weapon ever tested yielded approximately 50 megatons.

Although more complex; fusion weapons have much larger yields than fission

bombs. One significant similarity between these two weapons is the effect of the nuclear explosions that follow the reactions. These effects are immediate and delayed. The immediate effects are nuclear blast waves, thermal energy and ionizing radiation. The most prominent delayed effect is radioactive fallout. Below is a statistical analysis of the distribution of energy within the first minute after detonation. Fallout attributes an additional 5-‐10% over time.

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Low Yield (<100 kt) High Yield(>1 Mt) Blast Wave 60% 50% Thermal Radiation 35% 45% Ionizing Radiation 5% 5%

(80% gamma, 20% neutrons) Immediately after the reaction takes place the majority of the energy is held within

the nuclear fuels. According to Carey Sublette author of Nuclear Weapons Frequently Asked Questions,

The energy is stored as (in order of importance): thermal radiation or photons; as kinetic energy of the ionized atoms and the electrons (mostly as electron kinetic energy since free electrons outnumber the atoms); and as excited atoms, which are partially or completely stripped of electrons (partially for heavy elements, completely for light ones). Thermal radiation in the form of photons make up about 80% of the energy

released from the reaction. Powerful gamma rays produced by the reaction are the first type of energy released moving at the speed of light. These rays ionize the ozone molecules in the air creating smog around the epicenter of the explosion. X-‐rays are also emitted carrying heat and energy away from the epicenter. Prior to the formation of the smog a fireball of ionized gas expands from the epicenter. The uniform temperature of the fireball is a result of the x-‐rays, which are moving much faster than the fireball itself. The heat itself is potentially dangerous to the human body as it causes flash burns. The severity of the burns is dependent on the amount of thermal radiation absorbed by the skin. The table below shows the minimum amount of thermal radiation needed to cause the different degrees of burn in gram-‐calories. Also in the columns of table are the different yields of three bombs and their maximum ranges of thermal radiation emissions.

SEVERITY 20 Kilotons 1 Megaton

20 Megatons 1st Degree 2.5 cal/cm^2 (4.3 km) 3.2 cal/cm^2 (18 km) 5

cal/cm^2 (52 km) 2nd Degree 5 cal/cm^2 (3.2 km) 6 cal/cm^2 (14.4 km)

8.5 cal/cm^2 (45 km) 3rd Degree 8 cal/cm^2 (2.7 km) 10 cal/cm^2 (12 km)

12 cal/cm^2 (39 km) What is not shown on the table above is the possibility of fourth and fifth degree

burns, which completely kill all affected tissue and prevent regeneration. Anything above a third degree burn requires immediate medical attention as shock sets in because the pain is excruciating. The thermal damage is the first harmful effect felt by surrounding bodies and structures; what follows is a shockwave only seconds after.

The fireball being a uniform sphere emits brightness from long distances and also produces a spherically expanding blast and shock wave. As the fireball expands its rate of

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expansion decreases due to the energy drop in the wavelengths of the photons; causing the photons to be absorbed faster. The initial shockwave is moving at 30 km/sec and with the decrease in expansion of the fireball it surpasses the outer surface of the fireball in a matter of seconds (Sublette). At its peak speed the shockwave may exceed several hundred kilometers per hour.

This extremely fast moving shockwave causes destruction as objects within its path are hit with severe increases in atmospheric pressure. Keep in mind that the average building cannot withstand overpressures of 35.5 kPa without some type of damage. One thing disguised, as good news for the surrounding structures is the shockwave expands its speed decreases. Just like any other type of wave there is a wave of incidence and a secondary wave. Unfortunately for structures or individuals in the vicinity, they may feel both waves as they are within the region where the two waves are separate. Those outside the region feel the combination of the two as the waves combine into one. The secondary wave catches up to the wave of incidence because the secondary wave is traveling through higher temperature air (high temperature air was created by the first wave). Due to constructive interference the height of the blast is increased and delivers horizontal damage to anything in its path. In the following figure the images show how high static overpressures and blast wind pressures affect buildings in both the positive and negative phases.

The table above presents the various measurements of overpressure and slant

range in which different structures fail. According to the figure, the length of the compression phase damages the buildings enough so that when the negative phase hits it creates such suction that it destroys the building. In this case the drag force and compression force combine creating an even stronger force (Nuclear Weapon Blast Effects.)

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The human body is resilient towards this shockwave and can withstand pressures of over 40 psi. Non-‐life threatening injuries such as shattered eardrums are common. The real concerns for human safety, regarding the blast wave are collapsed buildings and the debris being flung around. The shockwave described creates a powerful force that we can physically see coming, but what we can’t physically see are the effects of radiation until it’s too late. The deadly radiation released from the blast is a direct result of the weak nuclear forces acting inside the atoms.

The weak force is by far the least observed of all the fundamental forces. The

strong force holds the entire universe together; electromagnetism is being used as this paper is being written. Every day you feel the force of gravity pulling down on you, as expressed by Isaac Newton’s famous Second Law: Force = Mass x Acceleration, but is commonly expressed:

Where in the case of gravity, acceleration, or dv/dt, is the acceleration due to

gravity, and on earth is calculated to be equal to 9.8 m/s2. Called the weak force because “it's range of interaction occurs over a very

small distance (0.0000000000000001 m or 1 x 10-‐16 m) inside atoms” (Weak Force!), and is so unfamiliar to most because it deals with particle decay. The weak force affects all Fermions, which is a classification that contains electrons, protons and neutrons, as well as muons and lambda particles. This is crucial to the framework of the universe because the weak interaction changes quark flavor, causing this decay. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton -‐ the so-‐called "flavor changes" (The Weak Force). When just a single quark inside a hadron is changed, it in turn not only changes the particle, but all of its intrinsic properties as well. Because of these transformations, Deuterium can be formed inside the sun by the process of deuterium fusion, as described previously. A second crucial consequence is that the weak nuclear force allows the build up of heavier atoms and isotopes due to neutron accumulation.

Every force has its own specific force carried; the strong force has gluons and the gravitational force has gravitons, although gravitons are hypothetical and have never been observed in nature. There are two force carriers for the weak force, W-‐Bosons, which can have either a positive or negative charge, and Z-‐Bosons, which are electronically neutral. These particles were first discovered 1983, the unified the weak and electromagnetic interactions, through a process know as Electroweak Unification, and were hailed by scientists through out the world:

“With masses around 80 and 90 Gev, respectively, the W and Z were the most massive particles seen at the time of discovery while the photon is massless.

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The difference in masses is attributed to spontaneous symmetry breaking as the hot universe cooled. (Electroweak Unification).

With masses about 100 times that of a proton, it is their heaviness that defines the extremely short-‐range nature of the weak force and that makes the weak force appear weak at the low energies associated with radioactivity. A good example of the weak force in action is the interaction in which a neutron decays into a proton.

The interaction begins with a neutrino, a fundamental particle that is similar to an electron, only carries no charge. Because neutrinos have no charge, they are not affected by the same electromagnetic forces that effect electrons, and are able to pass through great distances without being effected by it (What is a Neutrino). The neutrino, when it passes close enough to a neutron for weak interaction to take place, transfers a positively charged W-‐Boson to the neutron. Neutrons are composed of two down quarks, each with a -‐1/3rd charge, and one up quark that has a +2/3rd’s charge.

As the W-‐Boson leaves the neutrino, which has a zero charge, it loses the boson’s

+1 charge and thus becomes a negatively charged electron. When the W-‐Boson makes contact with negatively charged down quark, it changes the quark from -‐1/3 to +2/3, making it an up quark. This new particle now has two up quarks and one down quark, making it a proton. Protons have a charge of +1, and since the neutrino became an electron with a -‐1 charge, the new atom remains electronically neutral, obeying conservation of charge. The number of protons an atom has inside its nucleus defines what that atom will be; carbon will always six protons or it is not carbon. Through the weak force, the atoms nucleus has changed, thus making it a completely new element.

There are many types of decay or emission a nucleus can undergo, but the three most important ones are alpha decay, beta decay and gamma decay. In alpha decay, denoted α, the atomic nucleus emits an alpha particle and transforms into an atom with an atomic number of two less than the starting atom and a mass number that is four amu’s less massive. The diagram below shows how a Uranium-‐238 atom will decay into a Thorium-‐234 atom by releasing an alpha particle:

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The second type of decay is called beta decay, denoted β, and is the type of decay

used to illustrate the weak force previously; that process is known as negative beta decay, β-‐. The neutron decay “results in a daughter nucleus, the proton number (atomic number) of which is one more than its parent but the mass number (total number of neutrons and protons) of which is the same” (“Beta Decay”). Below is an equation showing the process outlined previously in our description of the weak force:

Through negative beta decay, a Carbon-‐14 atom decays into a Nitrogen-‐14 atom

and releases an electron and electron antineutrino, which is the corresponding antiparticle to the electron neutrino described below. The other type of beta decay is positive beta decay, denoted β+. In β-‐positive decay, also know as “positron emission,” the nucleus converts into a nucleus of the next element lower on the periodic table by releasing a

positron, e+, and an electron antineutrino, denoted ν e: This occurs whenever a W-‐ boson is absorbed or a W+ boson is emitted from a

proton. This loss of positive charge or increase of negative charge turns one of the up quarks inside a proton into a down quark, creating a neutron. The positron emitted, is similar to an electron because it has the same mass as an electron, but has the opposite charge. An electron neutrino, is an electronically neutral subatomic particle. They were first hypothesized in 1930 to account for the missing energy and momentum in beta decay, and confirmed 1956 by a team of scientists headed by Clyde Cowan and Frederick Reines.

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The third type of weak force-‐driven decay is called gamma decay, abbreviated by the lowercase Greek letter γ. Most commonly known as gamma rays, or gamma radiation, they can originate from both nuclear and non-‐nuclear sources. In the case of nuclear sources, they are produced alongside α and β particles when “nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation in the form of photons” (Gamma Decay). Unlike alpha and beta particles, which have characteristics of matter: having definite masses and occupying space, gamma emission is referred to as radiation because there is no mass change associated with it. A good example of gamma decay occurs when Cobalt-‐60 undergoes beta decay, changing into Nickle-‐60 releasing an electron:

Following this, the Ni-‐60, which is still excited, drops down into a lower energy

state by releasing a gamma ray. The Ni-‐60 then drops to its resting ground state by releasing a second gamma ray. The unit of gamma particles in the Gray, abbreviated Gy, and is an SI unit defined as the absorption of one joule of such energy by one kilogram of matter:

All of the decays described above fall under the category of ionizing radiation,

which is consists of individual particles with enough kinetic energy to excite and dislodge an electron off of other atoms, creating ions. These ions intern react with other atoms creating more ions. In cells, ions can strip away electrons from important parts of DNA, causing the damage that could lead to mutations or cell death. In humans, exposure to high amounts of ionizing radiation causes Acute Radiation Syndrome (ARS), which becomes present within 24 hours. Small doses usually results in nausea, bleeding and vomiting, but the longer one is exposed, the effects become amplified. Severe neurological effects and rapid death typically follow a large dose of radiation. While treatment is available for minor cases, typically exposure at anything over exposure of 0.7-‐10 Gy the survival rate drops off exponentially. The best method for preventing exposure to oneself is to gain distance from the source of radiation. The strength of the ionizing radiation is inversely proportional to the distance. If movement is not an option, attempting to create a shield might be the only option.

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Alpha particles are the least penetrating of the three. Consisting of two protons, making it a Helium atom, alpha particles carry large velocities. Due to their size however, alpha particles are stopped easily, requiring only the thickness of a sheet of paper. Beta particles are slightly more penetrating, but can be shielded by just a few millimeters of aluminum foil. Gamma particles are the most penetrating of the three, yet still can be effectively blocked by several centimeters of lead. This is important because atoms with heavy nuclei best absorb gamma radiation like that in the human body. There is a fourth type of radiation, neutron radiation, which comes from the nuclear fission process that was described earlier. This type of radiation is a secondary effect of nuclear explosions but is the most penetrating and hazardous.

When it comes to nuclear blasts there are two sources of radiation emitted from

the weapon. The first source is prompt radiation, which is a brief burst of gamma rays and neutrons immediately after the explosion. The second is delayed radiation, which involves radioactive decay (fallout) being the source of alpha and beta particles. Gamma rays are short wavelength photons with lots of energy. Alpha and beta particles are both energetic but are different in that an alpha particle is a helium nucleus and a beta particle is an energized electron. Gamma rays and Neutrons are some of the most harmful as they penetrate all types of shielding as they can travel through large amounts of air and thick walls. Alpha and beta particles are less harmful as they can only travel through small distances. What they all share is the way they affect the human body. When these energetic radiation particles and rays touch living tissues in organisms they break the tissue into what is known as free radicals. These free radicals are dangerous because they are extremely reactive and disrupt Mother Nature’s natural chemical processes within the living organism. Neutrons do something similar in that they can react with nuclei of regular atoms and produce radioactive isotopes within the body which results in further ionizing damage.

Atom displacement is another way to disrupt the normal chemistry within an organism. This happens when an incident particle or particles like the ones above have such energy that they displace an atom out of its normal position within the compound it is bonded to. This is all detrimental to the human body specifically tissues that have cells that repeatedly undergo mitosis. In extreme cases the cell can immediately die or in other cases the radiation can alter DNA sequencing. This can lead to mutated genes, which is why nuclear radiation is said to be mutagenic. When the DNA sequence that controls growth is affected, the cell can grow without any sized limit. This same cell when undergoing mitosis passes on its now altered DNA to its daughter cells and repeatedly does this without regard

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to the overall wellbeing of the organism. This then leads to out of control cancerous tumor growth. This is all dependent on the amount of radiation absorbed by the organism. This is called the absorbed dose (D) and is a quantity that approximates the amount of absorption in any type of material. The various forms of radiation have different effects on different living tissues for example neutrons and alpha particles have more of an effect on tissues when compared to beta particles and gamma rays; therefore the below equation accounts for this by multiplying the absorbed dose by a radiation weighting factor (Q), which is different for each type of radiation (see table for radiation weighting factor). The product is called the equivalent dose (H), which is measured Gray’s, which as illustrated before, is joule/kg (Atomic Dose Info).

H=QD The same equation accounts for the various types of tissues that have react differently with same equivalent dose. For these cases a tissue weighting factor (Q) is used instead of the one used before (refer to the next table). The weighting factor is again multiplied by the absorbed dose (D). The result in this case is called the effective dose (H) that varies

according to the tissue. The SI unit for this product is a sievert (Sv), which is also a joule/kg. Depending on the amount of radiation absorption the short-‐term effects vary. An absorbed dose of 100 gray causes unconsciousness and death within a few hours while an absorbed dose below 0.25 gray will yield no short-‐term effects. An absorbed dose between 1-‐10 gray can cause vomiting, rapid weight loss, decrease in white blood cells, damaged bone marrow, and finally severe radiation sickness leading to death within 30 days. This information demonstrates how lethal nuclear radiation can be to a living organism.

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While this might be controversial to some, the nuclear weapon is a beautiful example of the power of human ingenuity. When we were threatened with a war that could cost millions of casualties on both sides; civilian and military alike, the brightest minds figured out a way to take the smallest object imaginable, an atomic nucleus, and cut it in half. They figured out how to harness this energy into a bomb, a piece of weaponry never before seen. This was all possible because of the fellow voyagers who came before them that too, were on the quest for knowledge.

Science is all about proving your colleagues wrong; in fact, an award is actually given out for this: The Nobel Prize. Named after Alfred Nobel, the man who created dynamite, it is awarded to the man or women who has made a substantial contribution to the world in the realms of “physics, chemistry, physiology or medicine, literature and for peace” (Nobel Prize). What is meant by “proving them wrong” can be thought of more like discovering or postulating something that better explains natural phenomena, and contradicting the current model. When this new hypothesis is then vigorously tested, and if it holds up to all experimentation, it becomes labeled as a “theory.” Unlike common usage, a theory is the highest point imaginable in science; it is the graduation point. We know these theories, equations and postulate’s most of the time by their discoverer’s name; Newton’s Second Law, Einstein’s Theory of General Relativity. It is because of these brave souls journeying to the edges of human knowledge that we are able to live in a world with cell phones, airplanes, every modern day luxury, and yes, even nuclear weapons. What was a necessary evil at their inception, has turned into a possibility for a near unlimited power supply, as well as a tool for total destruction. The energy stored inside a nucleus could be harnessed and used to power cities and infrastructure. This energy has a deadly downside. As displayed earlier, even slight exposure to nuclear radiation can be deadly. Along with that comes the potential for meltdowns, such as the cases of Cherboyl or Three Mile Island, leading to hesitation to about this technology.

None of forces of nature are here to serve humans; we are here because of these forces. That is a fact that is too often over looked today. No force or new idea, or any discovery for that matter, comes with a set of instructions, a list of do’s and don’ts. As fallible beings, it is up to us on how it is used. The same is true in the case of nuclear technology. With the benefits great and the consequences dire, I think that we need to remember the great words of uncle Ben Parker from Marvel’s Spiderman when he says that “with great power comes great responsibility”. We are not the only ones who inhabit this planet; there are another seven billion people and over eight million species of life. The decisions we make today will echo throughout history and it is us who it writing our chapter.

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