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Nuclear Physics

  • Atoms are described by their atomic number (Z=# of protons), mass number (A=# of protons + neutrons), and their net charge.
  • Mass is a measure of how much energy an object contains, and can be calculated using E=mc^2.
  • The strong nuclear force holds the particles of the nucleus together. It is the strongest fundamental force, but only operates at very small distances.
  • When nucleons are combined to make a nucleus, some of the mass of the constituents is converted to energy to hold the nucleus together. This energy is known as the binding energy. The difference in mass is known as the mass defect.
  • The three main types of nuclear decay processes are alpha decay (emission of alpha particle), beta decay (emission of electron or positron), and gamma decay (emission of a gamma photon).
  • Fission is the splitting of a nucleus into two or more nuclei.
  • Fusion is the combining of two or more nuclei into a large nucleus.
  • The fundamental forces in the universe, from strongest to weakest, are the strong nuclear force, the electromagnetic force, the weak nuclear force, and the gravitational force.

Nuclear Physics

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Objectives 0:08
  • The Nucleus 0:33
    • Protons Have a Charge or +1 e
    • Neutrons Are Neutral (0 Charge)
    • Held Together by the Strong Nuclear Force
  • Example 1: Deconstructing an Atom 1:20
  • Mass-Energy Equivalence 2:06
    • Mass is a Measure of How Much Energy an Object Contains
    • Universal Conservation of Laws
  • Nuclear Binding Energy 2:53
    • A Strong Nuclear Force Holds Nucleons Together
    • Mass of the Individual Constituents is Greater Than the Mass of the Combined Nucleus
    • Binding Energy of the Nucleus
    • Mass Defect
  • Nuclear Decay 4:30
    • Alpha Decay
    • Beta Decay
    • Gamma Decay
  • Fission 6:40
    • The Splitting of a Nucleus Into Two or More Nuclei
    • For Larger Nuclei, the Mass of Original Nucleus is Greater Than the Sum of the Mass of the Products When Split
  • Fusion 8:14
    • The Process of Combining Two Or More Smaller Nuclei Into a Larger Nucleus
    • This Fuels Our Sun and Stars
    • Basis of Hydrogen Bomb
  • Forces in the Universe 9:00
    • Strong Nuclear Force
    • Electromagnetic Force
    • Weak Nuclear Force
    • Gravitational Force
  • Example 2: Deuterium Nucleus 9:39
  • Example 3: Particle Accelerator 10:24
  • Example 4: Tritium Formation 12:03
  • Example 5: Beta Decay 13:02
  • Example 6: Gamma Decay 14:15
  • Example 7: Annihilation 14:39

Transcription: Nuclear Physics

Hi everyone and welcome back to 0000

I am Dan Fullerton and today we are going to talk about nuclear physics. 0003

Our objectives are going to be to identify the number of protons and neutrons in a nucleus from a chemical symbol, to determine the energy produced or required to complete a variety of nuclear reaction processes, identifying and analyzing three types of radioactive decay...0007

...explaining the process of fission and fusion given examples of each, and identifying the fundamental forces in the universe and order of strength. 0023

Let us start by talking about the nucleus. 0033

The nucleus is made up of protons and neutrons, where protons have a charge of +1 elementary charge and neutrons are neutral and they are held together by the strong nuclear force. 0036

Now when we write these, the atomic number, which gets the symbol (Z) is the number of protons. 0048

The mass number, (A), is the number of protons plus neutrons. 0054

We would write an element as (X), the symbol, (Z), in the bottom left, the atomic number, and (A) the mass number. 0059

Now you can have the same element, but have different atomic mass numbers. 0069

If you have different atomic masses for the same element, we call those isotopes. 0074

Let us take a look here and see if we cannot deconstruct what is going on in this atom. 0080

For the following atom, determine the number of protons, neutrons, and electrons present. 0085

It is titanium and its atomic number is 22, so it must have 22 protons. 0089

Its mass number is 48 and that is protons plus neutrons, therefore the number of neutrons must be 48 - 22 protons, or 26 neutrons. 0098

It has a net charge of +2, which means it must have two fewer electrons than protons, so it must have 20 electrons. 0110

That is how we read those symbols. 0122

Einstein wrote a paradigm changing paper in 1905 titled "Does the Inertia of a Body Depend Upon Its Energy Content?" 0127

In it, he explains how mass is a measure of how much energy an object contains and he talks about this formula, E = mc2, a conversion ratio for mass and energy. 0136

That led us to adjusting our conservation laws.0147

Now if energy and mass are really different sides of the same coin, we have conservation of mass energy, not conservation of mass and conservation of energy, it is conservation of mass energy; they are two sides of the same coin -- conservation of charge, conservation of linear momentum, conservation of angular momentum. 0151

Let us talk about nuclear binding energy because there is some cool stuff you can do with this. 0175

The protons in a nucleus repel each other, so how does the nucleus stay together? 0179

Well, that strong nuclear force is what holds all of those particles together, all those nucleons or particles of the nucleus. 0183

It is extremely strong, but only works over very, very, very short distances, which is why it works in the nucleus, but nowhere else. 0190

Now combining nucleons to bake a nucleus takes energy. 0199

If you have positive charges and protons, you have to do a lot of work to get them together, to get to the point where the strong nuclear force is going to take over and hold them together. 0202

That energy is known as the binding energy of the nucleus and where does it come from? 0211

Well, a fraction of the mass of the nucleons themselves, gets converted in order to hold those together. 0217

So the mass of the individual constituents is greater than the mass of the combined nucleus and this difference in mass is what we call the mass defect, δm. 0223

That is one that you can convert to energy. 0234

Now one atomic mass unit -- if you completely convert it into energy will provide 931 mega-electron volts (MeV). 0236

That is the same thing as if we took one mass unit and used E = mc2 to determine the energy in joules and then converted that to electron volts, but that can save you a little bit of time knowing that one atomic mass unit, when converted to energy is 931 MeV. 0243

The binding energy then, is going to be the mass defect times the square of the speed of light, E = mc2 applied to that mass defect. 0261

Now, in the early 1900s, scientists started investigating radioactive materials and what they found were three different types of nuclear decay, of radioactive decay. 0271

Now in alpha decay, we have the emission of an alpha particle, a helium nucleus, so we start off with our elements symbol (X) with (Z) protons and an atomic mass of (A). 0282

It is going to split into a helium nucleus of 2 protons, 2 neutrons for an atomic mass of 4, so what you have left over is going to be a new element that has 2 fewer protons and 4 fewer protons and neutrons or 2 fewer neutrons from its original. 0293

Beta decay, which can be beta plus or beta minus decay, is the emission of an electron or a positron, where a positron is the anti-matter version of an electron, an anti-electron. 0310

A neutron decays into a proton and an electron. 0319

If we have our element symbol (X), (Z) protons, (A) mass number, and we give off an electron, we are going to take away as this neutron decays into a proton and an electron...0322

...we are going to take away 1 charge here, so we are going to have to have an extra proton because that neutron became a proton and we still have the same total mass number. 0334

Now gamma decay is the emission of a gamma photon. 0346

We have our initial element, we give off a gamma ray and we still have our initial element. 0349

Now a couple of things here. 0355

As we talk about nuclear decay, first off, let us talk about half-life for just a second. 0356

Half-life is the amount of time for half of the material to decompose, which is pretty straightforward. 0361

I also want to talk about what happens -- now that we have mentioned an electron and an anti-electron are a positron -- what happens if they come in contact? 0368

If they come in contact, they will completely annihilate each other; they will completely convert their mass to energy. 0376

In so doing, they are going to release 2 photons traveling in opposite directions and each is going to have an energy of .511 MeV -- complete annihilation if you have a positron and an electron; they will annihilate each other. 0381

Let us talk about fission. 0400

Fission is the splitting of a nucleus into two or more nuclei and it is the basis of our nuclear power plants. 0402

For larger nuclei, such as Uranium-235, the mass of the original nucleus is greater than the sum of the mass of the products when split, so that extra mass becomes energy. 0407

What does it look like? 0417

Well, let us assume that we are going to shoot a neutron at some Uranium-235, so let us give ourselves a little neutron and we will shoot it here to the right and we are going to hit some of our Uranium-235. 0419

When that neutron hits it, very briefly, it is going to become Uranium-236, an isotope, but an unstable isotope. 0439

Uranium is not happy being Uranium-236, so what it is going to do then, is it is going to split into Barium-141 and Krypton-92, and as it does that it is also going to give off three more neutrons, that can go hit other Uranium-235 atoms. 0448

Well what is the big 'whoop' you say? As we do this, as we are splitting this nucleus, we are going to get a bunch of energy released. 0472

We have a bunch of energy as the output here as well and three more neutrons to continue to cascade this effect. 0483

Fusion, on the other hand, is the process of combining two or more smaller nuclei into a larger nucleus. 0494

If fusion occurs with small nuclei, the product of the reaction can have a smaller mass than its precursors and therefore releases energy. 0500

This is what fuels suns, stars, and it is also the basis of the hydrogen bomb. 0508

Now it is a tremendous potential energy source for a clean source of power as it creates hydrogen precursor straight from water, but fusion releases much more energy than fission, has minimal radioactive by-products...0513

...but it is way too hot to run for long periods of time with our current technology, which is why you may hear about the search for cold fusion. 0525

In the universe, we have four fundamental forces and we are going to rank them from strongest to weakest. 0540

The strongest of course, is the strong nuclear force, what holds the nucleons together or the protons and the neutrons together in the nucleus. 0546

The electromagnetic force -- we have done a lot of study on that already. 0553

The electrical and magnetic attractive and repulsive forces; the weak nuclear force, which is responsible for radioactive beta decay and finally, the gravitational force, which is the weakest force -- that is the attractive force that we have between objects that have mass; it is the weakest of those four forces. 0558

All right. An example problem -- If we have a Deuterium nucleus, it has a mass of 1.53 × 10-3 atomic mass units less than its component, what is its binding energy? 0579

Well, if it has 1.53 × 10-3 atomic mass units less than its component, let us convert that into energy. 0590

That will be -- we want universal mass units or atomic mass units to go away and we will convert it to MeV's and we know that 1 U converts to 931 MeV's and universal mass units make a ratio of 1 and I end up with about 1.42 MeV. 0600

Another one with a particle accelerator -- In the first nuclear reaction using a particle accelerator, accelerated protons bombarded Lithium atoms, producing alpha particles in energy. 0625

The energy resulted from the conversion of mass into energy. 0636

The reaction could be written as Hydrogen plus Lithium, which gives you two Helium's plus energy. 0639

Determine the energy and MeV produced in the reaction. 0646

Let us see what the difference is in mass; how much of that mass was converted into energy?0649

Our total mass defect is going to be -- well we started off with a proton (1.00783) and a Lithium (7.01600 atomic mass units) and at the end we have two Helium's... 0654

...which is going to be 2 times 2 alpha particles (4.00260 atomic mass units). 0674

That comes out to be about .01863 atomic mass units, so let us convert that into energy. 0683

We want .01863 atomic mass units to go away and we want MeV and we know that 1 atomic mass unit is equal to 931 MeV...0692 again we are just multiplying by 1, our units are going to cancel out there, and we will be left with 931 × .01863 or about 17.39 MeV. 0703

Let us take a look at another one. 0724

A Tritium nucleus is formed by combining two neutrons and a proton. 0726

The mass of this nucleus is 9.106 × 10-3 atomic mass units less than the combined mass of the particles from which it is formed. 0730

How much energy is released when this nucleus is formed? 0739

That means that our mass defect (δm) is 9.106 × 10-3 U and all we have to do is convert that to energy. 0742

9.106 × 10-3 U times -- we want universal mass units to go away and we will convert to MeV and 1 universal mass unit is 931 MeV, and again we will cancel out our universal mass units and I come up with about 8.48 MeV. 0753

Let us take a look at an example involving beta decay. 0782

A radioactive Hafnium nucleus emits a positron and becomes what? 0786

Well, it is emitting a positron, so that is beta plus decay and when that happens we have a proton that is becoming a neutron and a positron, a beta plus. 0791

So let us start off with our Hafnium (Hf-72-178) and it is going to become -- well first off we have our beta plus particle and that is 0 + 1e. 0806

Now if we have 72 here, we must have 71 as our atomic number here and nothing is changed on the top, so 178 -- I have to look up what element atomic number 71 is and I did that and I found out that that was Lutetium. 0824

That is how you would deal with a positive beta decay sort of problem. 0849

Gamma decay -- a radioactive Hafnium nucleus now emits a gamma ray. 0855

Well, let us try this again. 0861

Hafnium 72-178 is going to decompose and we are going to get a gamma ray and -- well we have not lost any nuclear particles, so 72-178 Hf. 0862

One last problem here -- A proton and its anti-matter equivalent, an anti-proton, which has the same mass as a proton, but the opposite charge, collide and completely annihilate each other. 0879

How much energy is released in joules? 0890

Well, E = mc2 -- we will go back to that formula because we are going to look for an SI unit output in joules. 0893

The mass that is converted to energy is going to be 2 times the mass of the proton because it's anti-matter equivalent -- we have two of these that are actually being converted to energy. 0901

That is 1.67 × 10-27 kg and the speed of light is 3 × 108 m/s2.0912

We have 2 × 1.67 × 10-27 × 3 × 108 × 3 × 108 gives me 3 × 10-10 J. 0923

That is a lot of energy for one proton and one anti-proton. 0935

Hopefully that gets you a good start on nuclear physics. 0939

Thanks so much for your time. Make it a great day everyone!0944