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Nuclear Physics and Nuclear Reactions

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The Nucleus Proton:

The charge on a proton is +1.6x10-19C.

The mass of a proton is 1.6726x10-27kg.

Neutron:

The neutron is neutral.

The mass of a neutron is 1.6749x10-27kg.

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The NucleusProton and neutrons are collectively called nucleons.

The number of protons in a nucleus is called the atomic number and it is designated by the letter Z.

The number of nucleons in a nucleus is called the atomic mass number and it is designated by the letter A.

The neutron number, N, is given by N = A - Z.

To specify a nuclide we use the following form:

where X is the chemical symbol for the element.

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The NucleusNuclei with the same number of protons are the same element but if they have different numbers of neutrons they are called isotopes.

For many elements, there are a few different isotopes that occur naturally.

Natural abundance is the percentage of a certain element that occurs as a certain isotope in nature.

Many isotopes that do not occur in nature can be created in a laboratory with nuclear reactions.

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The NucleusThe approximate size of nuclei was originally determined by Rutherford. We say approximate because of wave-particle duality. The size of nuclei is a little fuzzy.

We can get a rough size of a nucleus by scattering high speed electrons off of it.

The approximate radius of a nucleus is given by:

r # (1.2 x 10-15 m)(A1/3)

Where A is the number of nucleons (not the area).

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The NucleusNuclear masses are specified in unified atomic mass units (u). On this scale a neutral carbon atom with 6 protons and 6 neutrons has a mass of 12.000000 u.

1 u = 1.6605 x 10-27 kg = 931.5 MeV/c2

Rest Mass

Object kg u MeV/c2

Electron 9.1094 x 10-31 0.00054858 0.51100

Proton 1.67262 x 10-27 1.007276 938.27

Hydrogen Atom 1.67353 x 10-27 1.007825 938.78

Neutron 1.67493 x 10-27 1.008665 939.57

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Binding Energy and Nuclear ForcesThe total mass of a nucleus is always less than the sum of the masses of its protons and neutrons.

Where has all this mass gone?

It has become energy! (Energy, such as radiation or kinetic energy.)

The difference between the total mass of the nucleons and the mass of the nucleus is called the total binding energy of the nucleus. In energy units, the total binding energy is given by: E = Δmc2

This binding energy is the amount of energy needed to be put into the nucleus in order to break it apart into protons and neutrons.

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Binding Energy and Nuclear Forces

Figure by MIT OpenCourseWare . From Meyerhof.

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Binding Energy and Nuclear Forces

The force that binds the nucleons together is called the strong nuclear force.

This is a very strong but a close range force. It is nearly zero if the distance between nucleons is more that 10-15 m.

The Coulomb (Electric) Force is a long range force. Since protons repel at larger distances, neutrons are needed in nuclei with a large number of protons.

There is another nuclear force called the weak nuclear force which governs radioactive decay.

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Radioactivity

· Radioactivity is the spontaneous emission of radiation by an atom.

· It was first observed by Henri Becquerel.

· Marie and Pierre Curie also studied it.

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Radioactivity· Three types of radiation were discovered by Ernest Rutherford:

· a particles· b particles· g rays

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Radioactivity

· a particles accelerate with the E-field, so they are positive

· b particles accelerate against the E-filed, so they are negative

· g rays are unaffected by the E-field, so they have no charge

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Radioactivity

· a particles turned out to be the same as Helium nuclei, having two protons and two neutrons

· b particles turned out to be electrons, the same particle as found in the cathode ray tube experiments.

· g rays turned out to be electromagnetic radiation, like light but with much greater energy (higher frequency)

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Alpha Decay

Alpha decay happens when a nucleus emits an alpha particle (helium with two neutrons). This decay is written as:

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Beta Decay

Beta decay happens when a nucleus emits a beta particle (an electron or positron). This decay is written as:

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Gamma Decay

Gamma decay happens when a nucleus in an excited state emits a Gamma particle (a high energy photon). This decay is written as:

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Conservation of Nucleon NumberIn addition to the other conservation laws, there is the law of conservation of nucleon number.

This law states that the total number of nucleons (A) remains constant in any process. However, one type can change into the other type.

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Half Life and Rate of DecayA macroscopic sample of any radioactive substance consists of a great number of nuclei. These nuclei do not decay at one time.

Actually, the decay is random and the decay of one nuclei has nothing to do with the decay of any other nuclei.

Then number of decays during a short time period is proportional to the number of nuclei as well as the time period.

#N = -#N # t

Where # is the decay constant.

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Half Life and Rate of DecayThe rate of decay is usually given by its half life rather than its decay constant.

A half life of an isotope is defined as the amount of time it takes for half of the original amount of the isotope to decay.

A half life is given by:

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Nuclear Reactions and Transmutation of Elements

A nuclear reaction takes place when a nucleus (or particle) collides with another nucleus (or particle).

This process is called transmutation if the original nucleus is transformed into a new nucleus.

For Example:

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Nuclear Reactions and Transmutation of Elements

Energy and momentum must be conserved in nuclear reactions.

General Reaction:

The reaction energy, or Q-value, is the sum of the initial masses minus the sum of the final masses, multiplied by c2:

a + X Y + b

Q = (Ma + MX - Mb - MY) c2

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Nuclear Reactions and Transmutation of Elements

Since energy is conserved, Q is equal to the change in kinetic energy:

If Q is positive, the products have more kinetic energy (energy is released in the reaction). The reaction is exothermic, and will occur no matter how small the initial kinetic energy is.

If Q is negative, the reactants have more kinetic energy (energy is absorbed in the reaction). The reaction is endothermic and there is a minimum kinetic energy that must be available before the reaction can occur.

Threshold energy is the minimum energy necessary for the reaction to occur.

Q = KEb + KEY - KEa - KEX

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Nuclear Reactions and Transmutation of Elements

Neutrons are very effective in nuclear reactions.

They have no charge, so they are not repelled by the nucleus.

Scientists were able to create transuranic elements by neutron bombardment.

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Nuclear Fission and Nuclear ReactorsAfter absorbing a neutron, a U-235 nucleus will split into two parts.

This can be visualized as a kind of liquid drop.

As the nucleus splits, neutrons are released.

A typical reaction is:

Although others may occur.

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Nuclear Fission and Nuclear Reactors

The energy release in a fission reaction is quite large. The smaller nuclei are stable with fewer neutrons, so multiple neutrons emerge from each fission.

The neutrons can be used to induce fission in surrounding nuclei, causing a chain reaction.

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The chain reaction needs to be self sustaining in order to create a nuclear reactor. The reaction must continue indefinitely in a controlled manner.

Nuclear Fission and Nuclear Reactors

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Nuclear Fission and Nuclear Reactors

Neutrons that escape from the uranium do not contribute to fission.

There is a critical mass below which a chain reaction will not occur because too many neutrons escape.

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Nuclear Fission and Nuclear ReactorsControl rods, usually made from cadmium or boron, absorb neutrons and are used for fine control of the reaction. They keep the reaction just barely critical.

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Nuclear Fission and Nuclear Reactors

Atomic bombs use fission as well. The core is deliberately designed to undergo a massive uncontrolled chain reaction. This releases huge amounts of energy.

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Nuclear Fusion

The lightest nuclei can fuse to form heavier nuclei, releasing energy in the process. An example is the sequence of fusion processes that change hydrogen into helium in the Sun, as shown below.

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Nuclear FusionThe net effect is to transform four protons into a helium nucleus plus two positrons, two neutrinos and two gamma rays.

More massive stars can fuse elements as heavy as iron in their cores.

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There are three fusion reactions that are being considered for power reactors:

These reactions use relatively common fuels (deuterium or tritium) and release much more energy than fission does.

Nuclear Fusion

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A successful fusion reactor has not yet been achieved.

Fusion (or thermonuclear) bombs have been built.

Nuclear Fusion