The Physics of Nuclear Weaponry: Fission Reactions

As evident by Hiroshima and Nagasaki, and various nuclear bomb experiments, the knowledge of physics can be used to do terrible things. Nuclear weaponry has played a prevalent role in our societies past, so it is important to understand what physics concepts are related to it and how exactly the fission bomb works.

Image of and atomic bomb explosion courtesy of: http://wikis.lib.ncsu.edu/images/2/29/Atomic_Bomb.gif

The nucleus is a tightly packed array of neutrons and protons held together by a nuclear force.  The nucleus is tiny, one ten-thousandth of the radius of the atoms’, yet is held together by a strong force. In order for an atom and nucleus to be stable, the number of protons to neutrons should fall under the ratio of about three neutrons to two protons. Although the nuclear force is very strong it must compete with the repulsive electromagnetic force that acts between protons and threatens the composition of the nucleus. A bounded nucleus with, for example, two protons and two neutrons, has a lesser mass when bound than if the items were massed separately. Thus as a nucleus splits, the change in mass generates an energy following Einstein’s equation E=MC^2. This loss of mass and release of energy also increases the binding energy per nucleon. Binding energy is the energy that must be added to dissemble the nucleus.

Neutrons strike a stable atom which causes the fission reaction. In this unstable state the repulsive electromagnetic force dominates the nuclear force and the nucleus splits. If piece of U-235 or P-239 is larger enough, a sustained fission reaction can be achieved.  Knowing this background information, let’s examine a fission bomb. A fission bomb comprises of two spheres of U-235. When they are separate, too many neutrons escape and no chain reaction occurs. However, when they are pushed together by TNT, and neutrons are supplied from a radioactive source, there are enough neutrons to sustain the chain reaction and……..KAAABOOOOOOOM. Although relatively simple in principle, building a fission bomb encompasses difficulties like the fact that U-235 is very hard to come by. Plus no one benefits from a nuclear explosion as its effects can be catastrophic.

Iridescence

On a wet parking lot floor, you may notice colors that seem to coat the floor where oil has been spilled. This rainbow-like array of colors on the surface of the oil illustrates the physics concept of iridescence or the interference of reflected waves. In order to understand how and why these colors reflect we must understand interference and the wave nature of light.

 

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The mediums in our example are air, gas and water (the gas resides on the top of a puddle of water). As the incident beams of light travel from air to gas to water, the indices of refraction get successively larger. As the beams enter oil than water, the greater medium acts as a fixed boundary, causing the reflected wave to experience a phase change of 180 degrees. Thus two beams of blue light, for example, in phase with each other and thus experiencing constructive interference will now experience destructive interference when reflected (assuming the correct thickness). The destructive interference of these blue reflected beams prevents the human eye from viewing the blue reflection. Various thicknesses of a medium determine which lights are reflected and which are not as red through blue beams have different wavelengths. In our example let’s say the thickness of the oil film prevents blue from being reflected, but allows red to reflect. This means that we will see a reddish reflection on the puddle of oil. This beam of red light, which has a longer wavelength than that of the blue, will reflect because the 180 degree phase changes induced by the entrances into oil than water do not cause complete destructive interference or a misalignment of half a wavelength. This example involves light beams entering slower mediums (with higher indices of refraction), but the outcomes will be slightly different upon entering a faster medium (lesser indices of refraction). These thin film interferences can be quantified using these equations below:

On top of a slower medium-

            Constructive: 2(index of refraction)(thickness)=m(wavelength)

            Destructive: 2(index of refraction)(thickness)=(m+1/2)(wavelength)

On top of a faster medium-

            Constructive: 2(index of refraction)(thickness)=(m+1/2)(wavelength)

            Destructive: 2(index of refraction)(thickness)=m(wavelength)

Refraction

On a drive home through the rain, a faulty set of windshield wipers might help you experience the physics concept of refraction. The rain droplets on the windshield distort your image of the outside which is why they need to be dried off. How and why is it that a clear liquid can distort your picture so greatly? After all, common sense might tell us that a clear substance should have no trouble letting light pass through, but understanding the answer to this question requires a basic understanding of refraction.

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The fundamental theory behind refraction is that light will adjust its path to maintain its wavelength. Light is an electromagnetic (EM) wave that can travel through (some) solid, liquid and gas. Because this EM wave must travel from molecule to molecule, it will travel slower in denser objects. While Light can travel and 3×10^8 M/S in a vacuum, this speed can be decreased in liquid or solids. According to Fermat’s Principle, light will take the path that requires the least time. It will thus bend and contort depending on the density of its medium to fulfill the path that takes the least amount of time. Thus as the light travels through the air and then into the water, its path bends as its speed changes and it maintains its wavelength. The windshield itself of course also elicits refraction but its smooth surface prevents the dangerous distortion. The uneven surface created by the water causes the chaotic refraction and image distortion. Of course, physics has a mathematical qualification for refraction. The index of refraction (n), is defined as C (speed of light) divided by the velocity in the medium. Also the angle of refraction as the light rays enter a new medium can be calculated knowing n1*sin(angle1)=n2*sin(angle2).

Generators

Generators provide much of the electricity and energy that we use in our daily lives. The generators in power plants are very large and contain powerful magnets and rapidly spinning coils of wire. In order to understand how these wonders of physics work, we must understand some basics about magnetism.

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Current (I) can induce a magnetic field (B). Contrastingly, through electromagnetic induction a varying B can cause a voltage (V) difference or emf (electromagnetic force). This emf encompasses an induced current as Ohm’s Law dictates that voltage is equal to current times resistance. As a magnet enters a coil of wire, the hyper conservative nature of the solenoid will cause it to exert an opposing magnetic force, that will seek to prevent the magnet from leaving once it is inside, or enter when it is not. The magnetic flux (equal to B multiplied by the area of magnetic field lines encompassed by the loop times the cosine of the angle formed between the loop current and magnetic field), number of loops, and rate of rotation (in the above example the time for the magnet to enter and exit) are the important determinants of induced voltage. The stronger the magnetic field, the greater the area encompassed by the loop, and the greater the number of loops (N) are all directly proportional to the induced voltage. Also, the amount of time (t) it takes for the cycle to occur is indirectly proportional to the emf. From this we can deduce that emf or V is equal to negative N times magnetic flux divided by delta t. The example of a magnet entering and exiting a coil of wire and inducing a voltage is a very simple example of how generators work. The emf requires a varying magnetic field so either the magnet or the wire must rotate (it is generally easier to rotate the wire). In alternating current generators (of which most large scale generators are comprised), as the loop rotates, the area of magnetic field lines encompassed varies which causes the changing in B. This area encompassed changes in a cyclical fashion as the wire rotates, thus the voltage alternates and an alternating current is produced. Power plants use various sources like steam, fuel or wind turbines to generate the rotation which converts mechanical to electrical energy that households use.

Circuits and Resistors

Why is it that if one Christmas light goes out, more than one bulb does the same? In order to understand the physics behind the answer to this question we must understand some basics about circuits and current. In fact, the electrical systems of houses are large circuits that utilize a energy source to create a voltage difference that allows for the flow of electrons. This provides the electricity that we use to power our refrigerators, televisions and lights which function as resistors in the circuit.

 

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Batteries, generators and photovoltaic cells are some examples of energy sources that power a circuit. Current is equal to voltage over resistance, thus the greater the resistance, the harder it is for the electrons to pass through. Also, resistance (R) is defined as resistivity (p) times length (L) over area (a), or voltage (v) over current (I).Electrons flow from the energy source into the system and through the resistors. Batteries transform chemical potential energy to electrical potential energy and the resistors in the circuit consume the electrical PE converted by the battery and produce heat, light or any other desired function of electricity. The greater the resistance of the resistor, the more electrons it hogs up and the greater power outage (P=IV) of the light bulb, refrigerator or other resistor in question. The voltage right after is has left the energy source is at its greatest and is zero at the end of the circuit. Electrons thus flow from high to low voltage throughout the circuit, passing through various resistors arranged in series or in parallel. Voltage remains constant for a resistor in parallel, and overall resistance is decreased as subsequent resistors are added. In series, current remains constant and resistance increases with marginal resistors. Famously, Christmas lights all go out if one bulb burns out. This is because the resistors or bulbs are arranged in series. Most electrical systems, however, are an assortment of resistors in both parallel and series.

Static Electricity

If you rub a ruler and fur together, then hold the ruler over a pile of scrap pieces of paper, the paper will fly up and stick to the ruler. The physics explanation for this phenomenon is static electricity and more specifically, charging by friction. As two objects rub against each other, the electrons move according to their preferences of one object. Thus, from the rubbing of our fur and ruler, we have created positively and negatively charged objects. As the basic rules of electricity explain, opposites attract and likes repel. The positively charged fur will now repel with any positively charged object it faces and likewise, the negatively charged ruler will attract to any positively charged object it encounters (like the paper scraps) and vice versa. The triboelectric sequence, developed by Benjamin Frankiln places basic substances in order from ability to loose and gain electrons (become positive and negative). Fur is very high on this list and is thus very willing to lose electrons, while say a rubber or wooden ruler has the tendency to gain these electrons and become subsequently more negative in charge upon frictional contact. Transfers of electrons do not require friction, however. Simple contact results in a transfer of electrons. When two objects contact, electrons flow to the lower concentration (similar in theory to diffusion between solutions). Also as in diffusion, this flow of electrons ceases when equilibrium is attained. As soon as the contact is broken however, the electrons return to locations on the outer shells of the objects. Induction is another charging method. Some basic quantities necessary in our analysis of static electricity are Q (charge), K (constant), radius, electrostatic force, electric potential, electric field and electric potential energy. 

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Heat Engines

Just as with all the areas of physics, there are many examples of thermodynamics in daily life. For example, a power plant represents a heat engine and refrigerator represents the reversed system. In order to understand how the heat engine works, we must first understand some basic concepts about thermodynamics.

Heat is defines as a transfer of thermal energy (or temperature) between objects. Physicists use the abbreviation Q to represent the thermal energy transferred to or removed from a system. Q is equal to the sum of the change in internal energy of a system (delta U) and work done on or by the system (W). These three sets of values are measured in joules. Internal energy change can be found by multiplying three halves by the moles by R by delta temperature, and work can be calculated differently depending on whether or not the heat engine is Isothermal (work equals zero), isobaric (work equals pressure times delta volume), isothermal (delta U equals zero and work equals moles times R times temperature time the natural log of the volume final over volume initial) or adiabatic (work equal to negative delta U). We can also use various gas laws to calculate volume, moles, temperature or pressure through the use of the Ideal Gas Law (PV=nRT), Boyle’s Law (P1V1=P2V2) and/ or Charles’ Law (V1/T1=V2/T2).

Now that we know some of the basics of thermodynamics, let’s examine the concepts behind the heat engine. Heat flows into the heat engine where it is used to do work (in the power plant example, create some form of usable energy). The heat then flows out of the engine and the cycle is repeated as the system returns to its initial state. The work created can be calculated by finding the difference between the Qhot (heat in) and the Qcold (heat out). A refrigerator is a heat engine in reverse as it uses work to create colder temperatures. 

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