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# Nuclear [Mass Deficit]

Mass deficit, E=mc2, Fission, Fusion
by

## Kev Knowles

on 28 February 2014

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#### Transcript of Nuclear [Mass Deficit]

Binding Energy
Fission
Fusion
E = mc
2
Mass deficit
Proton mass = 1.007276u
Neutron mass = 1.008664u
Data
Atomic mass unit [u] =
1.66053886 × 10 kg
-27
It is now possible to measure the mass of a nucleus very accurately.
If we look at this mass and compare it to to the total mass of the protons and neutrons that make up that nucleus then we see something very strange.
The mass of the nucleus is always LESS than the total of it's constituent parts.

This leaves us with the question "Where did the mass go?"
Proton mass = 1.007276u
Neutron mass = 1.008664u
Data
Atomic mass unit [u] =
1.66053886 × 10 kg
-27
Proton mass = 1.007276u
Neutron mass = 1.008664u
Data
Atomic mass unit [u] =
1.66053886 × 10 kg
-27
Helium-4
Carbon-12
Uranium-235
The mass of a helium-4 nucleus is 4.002602u

Calculate the mass deficit.
The mass of a carbon-12 nucleus is 12u

Calculate the mass deficit.
The mass of a uranium-235 nucleus is 235.0439299u

Calculate the mass deficit.
The mass lost in forming the nucleus is converted to pure energy according to Einsteins famous equation.

Where E is the energy in joules [J], m the mass in kilograms [kg] and c is the velocity of light [3x10 ms ]
8
-1
E = mc
2
This is known as the binding energy of the nucleus.
Data
Atomic mass unit [u] =
1.66053886 × 10 kg
-19
Oxygen-16
The mass deficit of an oxygen-16 nucleus is 0.1326u

Calculate the binding energy in joules[J] and electron-volts[eV]
1 eV = 1.602×10 joules
-27
Data
Atomic mass unit [u] =
1.66053886 × 10 kg
-19
Iron-56
The mass of an iron-56 nucleus is 55.934u

Calculate the binding energy in joules[J] and electron-volts[eV]
1 eV = 1.602×10 joules
-27
Data
Atomic mass unit [u] =
1.66053886 × 10 kg
-19
Deuterium
[H-2]
The mass of a deuterium nucleus is 2.014101u

Calculate the binding energy in joules[J] and electron-volts[eV]
1 eV = 1.602×10 joules
-27
Nuclear Stability
If we look at the binding energy calculations then it is obvious that the larger nuclei will have larger binding energies.
To compare between nuclei of different masses we can use the BINDING ENERGY PER NUCLEON.

i.e. take the total binding energy and divide by the mass number A.
If we graph this against the nucleon number [mass number] we get the following graphs.
If we graph this against the nucleon number [mass number] we get the following graphs.
We can also express binding energy as the energy required to break up a nucleus into it's constituent parts. A sort of "destruction' energy.

As we can see from the graphs the most stable isotope is therefore iron-56.
Nuclear Physics
Theory
Theory
Power Stations
Atomic Bombs
Power Stations
Stars
Hydrogen Bombs
In nuclear physics and nuclear chemistry, nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts, often producing free neutrons and lighter nuclei.
Fission of heavy elements is an exothermic reaction which can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments. For fission to produce energy, the total binding energy of the resulting elements has to be higher than that of the starting element.
Fission is a form of nuclear transmutation because the resulting fragments are not the same element as the original atom.
Example
Uranium is used in nuclear power stations as a fuel.
U-235 is hit by a neutron and splits into Ba-144, Kr-89 and 3 more neutrons.
Use the data below to find the energy released,
Data
U-235
Ba-144
Kr-89
Neutron
235.04924u
143.9229405u
88.9176325u
1.008665u
Just as many conventional thermal power stations generate electricity by harnessing the thermal energy released from burning fossil fuels, nuclear power plants convert the energy released from the nucleus of an atom, typically via nuclear fission.
When a relatively large fissile atomic nucleus (usually uranium-235 or plutonium-239) absorbs a neutron, a fission of the atom often results. Fission splits the atom into two or more smaller nuclei with kinetic energy and also releases gamma radiation and free neutrons. A portion of these neutrons may later be absorbed by other fissile atoms and create more fissions, which release more neutrons, and so on.
This nuclear chain reaction can be controlled by using neutron poisons and neutron moderators to change the portion of neutrons that will go on to cause more fissions. Nuclear reactors generally have automatic and manual systems to shut the fission reaction down if unsafe conditions are detected.
Example
Uranium is used in nuclear power stations as a fuel.
U-235 is hit by a neutron and splits into Ba-144, Kr-89 and 3 more neutrons.
Use the data below to find the energy released,
Data
235.04924u
139.9216357u
93.915361u
1.008665u
U-235
Xe-140
Sr-94
Neutron
Just as many conventional thermal power stations generate electricity by harnessing the thermal energy released from burning fossil fuels, nuclear power plants convert the energy released from the nucleus of an atom, typically via nuclear fission.
There are two basic types of nuclear weapon. The first type produces its explosive energy through nuclear fission reactions alone. Such fission weapons are commonly referred to as atomic bombs or atom bombs (abbreviated as A-bombs), though their energy comes specifically from the nucleus of the atom.
In fission weapons, a mass of fissile material (enriched uranium or plutonium) is assembled into a supercritical mass

A major challenge in all nuclear weapon designs is to ensure that a significant fraction of the fuel is consumed before the weapon destroys itself. The amount of energy released by fission bombs can range between the equivalent of less than a ton of TNT upwards to around 500,000 tons (500 kilotons) of TNT.[2]
In nuclear physics and nuclear chemistry, nuclear fusion is the process by which multiple like-charged atomic nuclei join together to form a heavier nucleus. It is accompanied by the release or absorption of energy, which allows matter to enter a plasma state.
The fusion of two nuclei with lower mass than iron (which, along with nickel, has the largest binding energy per nucleon) generally releases energy while the fusion of nuclei heavier than iron absorbs energy; vice-versa for the reverse process, nuclear fission.
Nuclear fusion occurs naturally in stars. Artificial fusion in human enterprises has also been achieved, although has not yet been completely controlled.
Building upon the nuclear transmutation experiments of Ernest Rutherford done a few years earlier, fusion of light nuclei (hydrogen isotopes) was first observed by Mark Oliphant in 1932.
Example
Deuterium-tritium fusion is a possible reaction for a fusion power station, the reaction is shown below:

Calculate the energy released.
Data
Deuterium
Tritium
Helium
Neutron
2.01410178u
3.0160492u
4.00260u
1.008665u
Example
In one part of the sequence of fusion reactions that power a star we get the fusion of helium-3 to helium-4.

Calculate the energy released.
Data
Helium-3
Helium-4
Beryllium
3.0160293u
4.00260u
7.01692983u
Fusion power is the power generated by nuclear fusion reactions. In this kind of reaction, two light atomic nuclei fuse together to form a heavier nucleus and in doing so, release a large amount of energy.
Most design studies for fusion power plants involve using the fusion reactions to create heat, which is then used to operate a steam turbine, which drives generators to produce electricity. Except for the use of a thermonuclear heat source, this is similar to most coal-fired power stations and fission-driven nuclear power stations.
A tokamak is a machine producing a toroidal magnetic field for confining a plasma. It is one of several types of magnetic confinement devices, and it is one of the most-researched candidates for producing controlled thermonuclear fusion power.
Inertial confinement fusion is a process where nuclear fusion reactions are initiated by heating and compressing a fuel target, typically in the form of a pellet that most often contains a mixture of deuterium and tritium.

To compress and heat the fuel, energy is delivered to the outer layer of the target using high-energy beams of laser light, electrons or ions.
The heated outer layer explodes outward, producing a reaction force against the remainder of the target, accelerating it inwards, and sending shock waves into the center.

A sufficiently powerful set of shock waves can compress and heat the fuel at the center so much that fusion reactions occur. The energy released by these reactions will then heat the surrounding fuel, which may also begin to undergo fusion. The aim of ICF is to produce a condition known as "ignition", where this heating process causes a chain reaction that burns a significant portion of the fuel.
Stars are giant nuclear reactors. In the center of stars, atoms are taken apart by tremendous atomic collisions that alter the atomic structure and release an enormous amount of energy. This makes stars hot and bright.

Nuclear fusion is an atomic reaction that fuels stars. In fusion, many nuclei (the centers of atoms) combine together to make a larger one (which is a different element). The result of this process is the release of a lot of energy (the resultant nucleus is smaller in mass than the sum of the ones that made it; the difference in mass is converted into energy)
Stars are powered by nuclear fusion in their cores, mostly converting hydrogen into helium.

The production of new elements via nuclear reactions is called nucleosynthesis. A star's mass determines what other type of nucleosynthesis occurs in its core (or during explosive changes in its life cycle). Each of us is made from atoms that were produced in stars and went through a supernova.
Small stars: The smallest stars only convert hydrogen into helium.
Medium-sized stars (like our Sun): Late in their lives, when the hydrogen becomes depleted, stars like our Sun can convert helium into oxygen and carbon.
Massive stars (greater than five times the mass of the Sun): When their hydrogen becomes depleted, high mass stars convert helium atoms into carbon and oxygen, followed by the fusion of carbon and oxygen into neon, sodium, magnesium, sulfur and silicon. Later reactions transform these elements into calcium, iron, nickel, chromium, copper and others. When these old, large stars with depleted cores supernova, they create heavy elements (all the natural elements heavier than iron) and spew them into space, forming the basis for life.
A thermonuclear bomb differs fundamentally from an atomic bomb in that it utilizes the energy released when two light atomic nuclei combine, or fuse, to form a heavier nucleus. An atomic bomb, by contrast, uses the energy released when a heavy atomic nucleus splits, or fissions, into two lighter nuclei. Under ordinary circumstances atomic nuclei carry positive electrical charges that act to strongly repel other nuclei and prevent them from getting close to one another. Only under temperatures of millions of degrees can the positively charged nuclei gain sufficient kinetic energy, or speed, to overcome their mutual electric repulsion and approach close enough to each other to combine under the attraction of the short-range nuclear force. The very light nuclei of hydrogen atoms are ideal candidates for this fusion process because they carry weak positive charges and thus have less resistance to overcome.
In a thermonuclear bomb, the explosive process begins with the detonation of what is called the primary stage. This consists of a relatively small quantity of conventional explosives, the detonation of which brings together enough fissionable uranium to create a fission chain reaction, which in turn produces another explosion and a temperature of several million degrees. The force and heat of this explosion are reflected back by a surrounding container of uranium and are channeled toward the secondary stage, made up of tritium or other fusion fuel.
The tremendous heat initiates fusion, and the resulting explosion of the secondary stage blows the uranium container apart and causes it too to fission, thus contributing to the explosion and producing fallout (the deposition of radioactive materials from the atmosphere) in the process. (A neutron bomb is a thermonuclear device in which the uranium container is absent, thus producing much less blast but a lethal “enhanced radiation” of neutrons.) The entire series of explosions in a thermonuclear bomb takes a fraction of a second to occur.
Example
For the example involving the dueterium / tritium reaction work out the energy released per kg of fuel [the deuterium and tritium.
Example
Using your answer from the first example with U-235 work out the energy released per kg of fuel [U-235].
You can ignore the initial neutron in your calculations.
Mass Deficit, fission & fusion
Full transcript