AP Chemistry - Nuclear Chemistry
Except for H all nuclei have more than 1 p+.   Since like charges repel, how can any nucleus be stable? The electrostatic +ve forces are not the only one's present in a nucleus. p+ in fact do repel each other but also at work in the nucleus is a "strong force" which acts to overcome the electrostatic force of repulsion within the nucleus, and it binds nucleons into a package. This "strong force" has some of its own peculiar characteristics. It decreases far more rapidly with distance than an electrostatic force. The strong force exerted by one nucleon on another nucleon falls to zero within the nucleus. The strong force between two adjacent nucleons, therefore, does not contribute anything to the binding of the nucleons on the other side of the nucleus. The electrostatic force of repulsion of p+ in the nucleus does not fall off to zero. p+ in one nuclear region repel p+ in all other regions. Such repulsions are toned down by the intervening no because they help separate the p+
When nuclei carry large numbers of p+ without enough intermingled neutrons to dilute the electrostatic repulsions, the result is an unstable nucleus. Fission is a possible consequence of this instability only in U-235 and other fissile material. Other mechanisms used by all isotopes, including U-235, include ejection of small nuclear fragments and high-energy electromagnetic radiation in order to achieve stability. 
radionuclides - isotopes whose nuclei emit particles or energy 
radioactivity - the emission itself 
radioactive - materials that have the ability to be radionuclides
Types of Radioactivity

Alpha radiation, symbol 'α'
Alpha radiation is actually a particle of 42He striped of it's electrons which gives it a very strong charge of +2. Alpha particles are very massive in comparison with the other types of radioactive particles below. It may reach up to 1/10 of light speed in a particle accelerator. Within a few centimetres of travelling through the air the alpha particle will collide with the air molecules, lose kinetic energy in the collisions, pick up electrons and become a neutral stable helium atom. 

Alpha particles cannot penetrate skin, although enough exposure will cause a severe skin burn. 

eg. of decay 

22286Rn ------> 42He + 21884Po + radiation 

When an alpha particle is ejected the mass number drops by 4, the atomic number drops by 2. The particle also emits gamma radiation which sheds excess energy leaving a more stable isotope. 


Beta radiation, symbol 'β'
Beta radiation is actually a high speed electron, 0-1e. Beta particles arise from the decay of a neutron. A neutron first decays into a p+ and an e- and then the e- is ejected. This e- did not come from the e- configuration cloud. It did not exist before decay occurred. In addition to the e- (), a small massless, electrically neutral "antineutrino" is also ejected. Think of the antineutrino as a holder which held the e- in place on the p+ so that a no is formed. 

eg. of beta decay 

10no ----> 11p+ + o-1e- + antineutrino + radiation 
Each isotope gives off its own unique characteristic beta energy. ie; speed varies from zero to a fixed limit. Since an e- has only 1/7000th the mass of an alpha, the is less likely to collide with the molecules of the substance through which it travels. (ie. air) 

The fastest particles travel at 300 cm/sec in dry air. Only the highest energy can penetrate skin. However, an antineutrino can travel 3000 light years in water before striking a p+ in the water molecule. Since most of our radiation detectors depend on collisions between radiation particles and a gas, antineutrinos where only isolated very recently. 

examples of β Decay 

13153I ----> 0-1e- + antineutrino + radiation + 13154Xe 

31H ----> 0-1e- + antineutrino + radiation + 32He 

When a particle is ejected the atomic number increase by 1 but the mass number remains constant. 

Gamma radiation, symbol ''γ''
Gamma radiation is high energy photons of the electromagnetic spectrum and usually accompanies and . The emission of an or can leave the nucleus in an excited state. The emission of a photon strips energy from the nucleus relaxing it into a more stable state. radiation is very penetrating but it can be blocked with lead and concrete. In dry air radiation penetrates 400 metres, or 50 cm of tissue or 30 mm of lead. 

The energy units most often used to describe the energy for radiation is the electron volt (eV). One eV is the energy 1 e- receives when accelerated by a charge of 1 V. A simple device used to determine this energy is two plates with a charge. You then measure the amount of electricity needed to hold an e- in place against gravity. 

1 eV = 1.602 x 10-19

1 KeV = 103 eV 

1 MeV = 106 eV 
1 GeV = 109 eV 

Gamma Therapeutic Radiations
The Co-60 radiation machine used in the treatment of cancers produces radiation in the range of 1.173-1.332 MeV. An standard X-ray machine used in diagnostic medicine has energies of about 100 KeV or less. X-rays are also high-energy electromagnetic radiation but are of less energy than rays. 

X-rays - are made deliberately in a X-ray Cathode tube. They are made by directing a high energy e- beam, just like the electron gun at the back of your TV, at a metal target. This e- beam knocks e- out of the metal's atomic orbitals. 

In the metal target holes are created in the orbitals. If the e- knocked out comes from a lower energy level then a higher energy e- drops down to fill in the hole. This cascade of e- transitions from a higher to a lower level cause the release of electromagnetic energy in the X-ray range of emissions. X-rays come from e- level transition in the orbitals and radiation comes from transitions between nuclear energy levels. 
Penetrating Ability


Radiation Disintegration Series
Often a radionuclide decays not to a stable isotope but to another radioactive isotope. The process will continue through a series until a stable isotope forms. There are four well charted disintegration series, the Thorium, Neptunium, Uranium and Actinium Series. Your teacher will provide copies of these series for inclusion in your databooks. 
Other Radiations

The first three radiations occur naturally. Since the advent of nuclear fission reactors and particle accelerators some very unnatural radioisotopes have been created, identified and studied. Because these unnatural radioisotopes are very unstable they exhibit several types of special emission. 

Positron particle, symbol 0+1e+
Think of this emission as a positive electron. It has the same mass as an electron but with a positive charge. It is formed when a p+ decays into a neutron. The positive charge holder is another massless particle called the neutrino. 

eg. of positron emission 

11p+ ----> 10n0 + 0+1e+ + neutrino 

5427Co ---> 5426Fe + 0+1e+ + neutrino 

116C ----> 115B + 0+1e+ + neutrino 

When the positron moves out through the outer orbital e- there is of course an attraction. When the 0+1e- (positron) and the 0-1e- (electron) collide they annihilate each other. Their masses change into 2 photons of radiation of what is called "annihilation radiation photons" each with an energy of 511 KeV. The positron is called "antimatter" because it destroys a particle of ordinary matter. To be called antimatter a particle must have a counterpart of ordinary matter and they must collide to complete annihilation. The neutrino, being uncharged and massless, plays no part in this annihilation. 

Neutron Emission

When the number of neutrons in an isotope are to high the isotope can eject neutrons in order to stabilize the nucleus. This reaction simply lowers the mass of the isotope without changing it to a new element. 

eg. 8736Kr ----> 8636Kr + no

Electron Capture or K-Capture

This event is very rare among natural isotopes but is quite common in the synthetic isotopes. 

eg. 5023V + 0-1e- -----> 5022Ti + X-rays 

Below is a diagram showing how a K shell electron gets captured and pulled into the nucleus. A high energy level electron falls to fill the hole left. As the e- falls from the higher to a lower orbital it must release energy, most of which is dispersed as X-rays. 

An orbital K shell e- is drawn into the nucleus where it neutralizes a p+, therefore the atomic number drops by 1. A hole is left in the K shell and the atom emits X-rays as the outer orbital e- falls in to fill the hole. Normally the rate of decay is independent of the oxidation state, pressure, temperature, or combination with other elements. This appears to be true for and decay. When the decay is by e- capture however, very small differences have been noted. 

eg. Be-7 decays faster as a metal than it does as an oxide. 
The e- density next to the beryllium nucleus is higher than the density on the BeO, therefore it takes longer to pull in stray K shell electrons. 

Go to the Nuclear Decay and Radiation Worksheet

Conservation of Mass and Energy
Nuclear chemistry forces us to modify the Law of Conservation of Mass to include an energy term as well. The energy term is derived from Albert Einstein's famous E=mc2 equation. Actually this equation was rewritten for the layman, in its true form it is E = moc2, where E is the change in energy that takes place, mo is the change in rest mass, and c is the speed of light.

Because the speed of light is very large and it's square even larger, even a very small change in mass would translate into an enormous change in energy.

For example lets take a look at an ordinary chemical reaction.

The combustion of the gas methane.

CH4(g) + 2 O2(g) ---> CO2(g) + 2 H2O(g)      Ho = -890 kJ/mol
since E = moc2 then upon rearrangement we get mo = E
Fact: 1 J = 1 kg m2 This a fact that should be memorized.
therefore mo = ___890 kJ     X 1000 J  1 kg m2
                           (3.0 x 108 m)2       1 kJ              s2

                       = 9.89 x 10-12 kg

                      = 9.89 x 100 ng

The 890 kJ of energy released by the combustion of one mole of methane thus originates from the conversion of 9.89 ng of mass into energy. Such a small change, about 10 ng out of 80 g cannot be detected by balances. It amounts to the loss of 1.0 x 10-7% of the mass. So we ignore Einstein's equation when doing regular chemical stoichiometric calculations. However this equation is very useful in nuclear chemistry.

Nuclear Binding Energy
The sum of the rest masses of the nucleons of an atom does not equal the measured mass of any nucleus. The actual mass of an atomic nucleus is always a trifle smaller then the sum of the rest masses of all it's nucleons (p+ + no). This mass difference is changed into energy as the nucleus formed, and was emitted as high energy electromagnetic radiation. It would cost this much energy to break the nucleus apart into its nucleons again, so the energy is called the 'binding energy of the nucleus'.
Lets take a look at the manufacture of a Helium nucleus.
Binding energy of 42He - actual rest mass is 4.001506 amu.
The rest masses of the nucleons are:
p+ = 1.007277 amu no = 1.008665 amu You should include these numbers in your data book.

For 42He then 2 p+ = 2 x 1.007277 amu = 2.014554 amu
                        2 no = 2 x 1.008665 amu = 2.017330 amu
                                                                    4.031884 amu

The difference in mass = calculated mass - actual mass
                                      = 4.031884 amu - 4.001506 amu
                                      = 0.030378 amu
1 kg = 1000 g          1 amu = 1.6606 x 10-24 g {Include these facts as well}


E = moc2

= (0.030378 amu X 1.6606 x 1024 g  1 kg    )(3.0 x 108 m)2
                                          amu           1000 g                     s
= 4.54 x 10-12 kg m2
= 4.54 x 10-12 J This is the energy release for 1 atom of 42He
A mole of He would be 6.02 x 1023 nuclei more, therefore,
6.02 x 1023 nuclei/mole * 4.54 x 10-12 J/nuclei
= 2.73 x 1012 J/mole (enough energy to power a 100 watt light bulb for 900 years)
How do I know this?
P=E/t from grade 11 chemistry class.

therefore t = E/P

= 2.73 x 1012 J
      100 W

= 2.73 x 1012 J
        100 J/s

= 2.73 x 1010 s (X 1 min/60 s)

= 4.55 x 108 min (X 1 hr/60 min)

= 7.583 x 106 h (X 1 day/24 h)

= 315972.2 days (X 1 y/365.25 days)

= 865.09 years

Go to the Nuclear Conservation of Energy Worksheet

The Curve Of Binding Energy
The zone of highest stability lies between Fe-56 and Br-66. 

The curve passes through a maximum at iron-56. The nuclei become less stable as the mass numbers become higher therefore we can expect atoms with higher atomic numbers to fission and break into smaller more stable isotopes, On the other hand, it would be the fusion of the lower atomic number nuclei which would result in more stable isotopes. For this reason it is H and He with which fusion attempts are being made.

When a high speed particle is captured by a nucleus, the nucleus can be permanently changed to that of another element. The changing of one isotope to another is called transmutation, and radioactive decay is just one way this can happen. Another way is by bombarding the atoms of an isotope with high-energy particles. Usually these are alpha particles from natural alpha emitters, neutrons from atomic reactors and p+ made by the removal of electrons from H atoms. Alphas and p+ are suitable for acceleration to ultrahigh energies in special accelerators. With sufficient energy, bombarding particles can shoot through the e- orbitals and bury themselves in nuclei. Beta particles are strongly repelled by the orbital e- and are therefore seldom used. When a nucleus captures a bombarding particle it becomes a compound nucleus. At the moment of impact, it has all the energy of the bombarding particle and is therefore unstable. The nucleus must get rid of this excess energy. It can do this by ejecting a high energy particle such as a neutron, a p+, or an e- along with radiation. 

The first transmutation was performed by E. Rutherford 

     alpha  + 147N ---> 169F + 11p+ ------> 158

The first artificial accelerator reaction 

11p+ + 73Li ---> 84Be ---> 2 42He 

Transmutation can be performed on any number of isotopes. Once the new isotope is formed it can then undergo many types of emission to create a variety of new isotopes. Below is an example. The different reactions can be used to make Al-27 but once the Al-27 is made it can under go decay into 5 different isotopes. 

                                              ---> 2311Na + (stable) 
                                         42He + 2311Na ----- ---> 2512Mg + p+ + no (stable) 
                                              |                              | 
      11p + 2612Mg --------> 2713Al -------> 2612Mg + 11p (stable) 
                                              |                          | 
                                       21D + 2512Mg ----- ---> 2713Al + (stabilized) 
                                              ---> 2612Al + 10n (unstable) 
                                                                  t½ = 7.4 x 105

Go to the Nuclear Transmutation Worksheet

Detection and Measurement of Radiation
The ability of radiation to generate ions in matter makes their detection and measurement possible. All of the radiations studied so far are ionizing radiations.  When ions are produced in a gas, even momentarily they become a conductor. 

Geiger Counters


Cloud Chambers
A beaker or dish of supersaturated alcohol vapour. When a particle streaks through it, it ionizes a trail through the vapour. The alcohol vapours condense out around the trail and they become visible. You don't see the particle, only the trail they left behind. 


Scintillation Counters
A device that permits an investigator to see when a collision occurs between a particle and a special surface on the counter. This surface is coated with a substance that gives off a tiny light flash when it is hit by a particle of radiation. For example, if the coating contains zinc sulphide phosphor, then an alpha particle will cause visible scintillations. A TV screen and a fluorescent tube are both scintillation screens with phosphors that react to particles. 

A dosimeter is used to measure the total quantity of radiation received by a surface during a specified period of time. Some dosimeters use photographic plates that are kept completely shielded (from visible light) but that are sensitive to radiations. The amount of darkening is proportional to the amount of received radiation. The dosimeter is made up of a plate of photographic emulsion and is covered by three layers. One layer is lead and will stop alpha and beta radiation so only gamma will get through. The plastic cover will let gamma and beta through but not alpha. The last cover is paper, thick enough to stop light from getting to the emulsion but thin enough to let alpha particle through. The emulsion is developed just like a regular black and white picture. The degree of darkening in each area gives a breakdown and dosage for each of the three types of radiations. 

 For a view of actual dosimeters past and current

Radiation Protection
Those who routinely work with radioactive materials should use radiation shielding and they should stay as far as practical from the source of the radiation. Cardboard, aluminum and plastic are relatively poor shields, but lead and concrete (if thick enough) are relatively good and inexpensive materials. Keeping one's distance from a radioactive source is effective in providing radiation protection because the intensity of the radiation diminishes with the square of the distance from the source. Thus if a worker doubles the distance, the exposure is reduced by ¼. The relationship between distance and intensity is given by the inverse square law

radiation intensity 

where d is the distance from the source. If the intensity, I1 is known at distance, d1, then the intensity, I2, at distance, d2, can be calculated as: 

     I2     d12

This law applies only to a small source that radiates equally in all directions and with no intervening shields. 

eg. At 1.5 m from a radioactive source the radiation intensity is 40 units. If the operator moves to a distance of 4.5 m from the source, what will be the radiation intensity? 

40 units = (4.5 m)2
    I2         (1.5 m)2

I2 = 40 units X (1.5 m)2
                (4.5 m)2

=  4.4 units 

Measurement and Background Radiation
Becquerel and Curie 
When a radioactive sample is purchased what is of particular interest is its activity. Activity refers to the number of nuclear disintegrations per second that occur in a sample. The nuclear SI unit is the Becquerel (Bq) which is 1 disintegration/second. The older unit, the Curie(Ci) is defined as 1 Ci = 3.7 x 1010 disintegrations per second. If a hospital has a source rated at 1.5 Ci then the source delivers 1.5 x 3.7 x 1010 = 5.6 x 1010 Bq. 

Rad and Gray 
The 'rad' is used to describe the quantity or dose of radiation absorbed by some material. The most common unit is the rad(rd) which stands for radiation absorbed dose) and it is defined as 10-5 J/g of material. The SI unit of absorbed dose if the Gray(Gy). 

1 Gy = 1 J/kg of material 

therefore 1 rd = 10-5 J/g 

1 Gy = 1 J/kg 

therefore 1 Gy = 100 rd 

The rad does not account for the kind of damage done, only for how much radiation goes in. Neutrons are more dangerous then radiation of the same energy and intensity. To take into account this fact the REM was derived. To find the dose in REMS the dosage in rads is multiplied by a conversion factor that reflects the effectiveness of the kind of radiation causing the damage. 

Conversion factors  ??? = 20 
                                no = 2 - 10 depending upon their speed 
    alpha , beta , X-rays = 1 

Doses in REMS are additive whereas doses in rads are not. 

Radioactivity can ionize molecules. ie; as the particulate radiation hits a molecule it can knock electrons out of orbit. The ionized molecule will then chemically react with adjoining molecules to form new compounds. These fragments and new compounds can alter cellular processes and functions. Even gamma rays can excite electrons out of orbit, leaving behind an ion. If radiation passes through a normal body cell the damage is said to be somatic. If the radiation passes through a sex cell the chromosomes may be damaged. Given time, without division the cell can repair this damage. But if a cell is undergoing meiosis or mitosis the damage can be passed on to a new cell without any repairs being implemented. These errors in the DNA code result in mutations of the DNA

Dosage in REMS Biological Effect 

25    notable change in blood cell components 

100  radiation sickness - nausea, vomiting, decrease in white blood cell count, diarrhea, dehydration, prostration, haemorrhaging and loss of hair 

200  the same as above but more pronounced in a shorter period of time 

400  LD50 limit - ½ of any population exposed to this dosage will be dead in 60 days 

600  all exposed to this level will be dead in one week 

Chernobyl - Anyone near the Chernobyl plant received 400 rems also immediately. The day after 1 rem/hr was found in the nearest city. Normal background radiation is 1,000 times lower than this. 

In Canada the Labour Relations Act specifies that radiation workers or anyone or works with radiation can be safely exposed to 0.3 rem/hr only. A typical X-ray that you get taken gives you only 7 mrem. 

No one can escape low level exposure to radiation. Radioactive sources are everywhere and together they make up what is called the natural background radiation and this gives an average of about 160 mrem of exposure/year/person. This radiation includes cosmic rays from above and radiations from radionuclides in the earth. C-14 is present in all the food we eat. The human body (adult) has approximately 5 x 105 disintegrations/minute. 

Tracer Analysis
Tracer chemicals are used to locate areas of concentration. If these chemicals are radioactive then they can be found easily with a radiation scanner. The most favoured is pertechnitate ion TcO4- which brain tumours seem to be able to concentrate readily. The pertechnitate ion, which is made from technicium-99m(metastable) drops from Tc-99m to Tc-99 as it gives off a burst of gamma radiation. The whole body scanner will pick up this burst and display it on a computer terminal. 

Iodine-131, a beta emitter(T½ = 8.07 d) is used to test thyroid function. 
Plants dipped in solutions consisting of HCO3- ions made from C-14 (t½ = 5730 y, ). When the plant uses this ion we can determine not only what compounds are made but which C's in each individual molecules consists of C-14 instead of C-12. 

Neutron Activation Analysis
A technique for analyzing the concentration of some element in a substance. It is based on the fact that a number of stable nuclei can be changed into a gamma radiation emitter by capturing neutrons. 

MAX + 10n ---> M+1AX ---> M+1AX + 

But each kind of neutron enriched nuclei emits gamma radiation at its own unique frequencies. By measuring the frequencies emitted, the element can be identified. By measuring the intensity of the gamma radiation, the concentration of the elements can be determined. This technique is so sensitive that concentrations as low as 10-9% can be determined.

Radiological Dating and Half-Lives
The determination of the age of a geological deposit or an archeological artifact can be found through the use of radionuclides in the sample. This technique is called radiological dating. It takes advantage of the known half-lives of the radionuclides, and the premise that these half-lives have been constant throughout the entire period in question. This premise is strongly supported by the finding that half-lives are insensitive to all external forces such as heat, pressure, magnetic, or electrical stresses.
In geological dating, a pair of isotopes is sought that are related as a "parent" and "daughter" in a radioactive disintegration series such as U-238 and Pb-206. A sample whose age is desired has the concentration of U-238 and Pb-206 determined. The ratio of these concentrations together with the t½ of U-238 can then be used to calculate the age of the rock. For dating organic remains we restrict ourselves to C-14 dating. A new method using an accelerator mass spectrometer counts each particle of a sample and separates all the isotopes. It is far more effective and efficient and gives better results. The older method uses C-14, a beta emitter, that has been made from cosmic radiation in atmospheric nitrogen.
           10n + 147N ---> 157N ---> 146C + 11p
The C-14 migrates to the lower atmosphere where it gets used by all organic life. As long as an animal is alive the C-14:C-12 ratio is constant. At death, the ingestion of food ceases and the ratio of C-14 to C-12 begins to change.
Calculation of half-life
The determination of the half-life of an isotope is critical in understanding just how radioactive an isotope is. Let's say we have two isotopes. One has a half-life measured in years, the other in seconds. Which one is more radioactive. The one in seconds of course. If we start with equal amounts, then in seconds ½ of the second isotope is gone. In the next half-life ½ of what is left is gone, and so on.
The half-life equation is: 
where        Ao is the initial amount of substance at time zero
                  At  is the amount of substance left
                  t½  is the half-life
                  t     is the amount of elapsed time in the same units as the half-life.
A more useful rearrangement of this formula can be used to find the amount of time elapsed.


If we find an artifact that as a C-14 activity of 708 Bq/g and if the normal C-14 is 918 Bq/g, what is the age of the artifact?
t½ for C-14 = 5730 y

therefore t = 5730 y X ln 918 Bq/g
                     0.693          708 Bq/g

= 8268.40 y X ln 1.30

= 8268.40 y X 0.262364

= 2169.33 years

= 2.2 x 103 years

This is of course the more difficult way to do it. A more elegant way is to see if the half-life divides evenly into the time elapsed.
A sample of C-14 decays through a time period of 34380 years. If you started with 1000 g how much of it is left?

How many half lives? 34380 y = 6 half-lives
                                   5730 y

Therefore Amount left = Amount at start X ½half-lives
                                  = 1000 g X ½6
                                  = 1000 g X 1
                                 = 15.625 grams are left after 34380 years.
Go to the Half-Lives Calculations Worksheet

Please recall that the lower atomic number isotopes should tend to fuse in order to make more stable isotopes. At sufficiently high temperatures and densities atomic nuclei of deuterium and tritium will fuse to give helium-4, a neutron and some energy. 1% of the deuterium in the world's oceans could supply the energy equivalent to 500,000 X the combined total of what was the original fossil fuel supply on earth. 

The central problem to fusion is to get the fusing nuclei close enough, for long enough, so that the strong force can overcome the p+ repulsion. Two nuclei on a collision course repel each other virtually until they touch. The combined kinetic energy of two approaching nuclei must therefore be very substantial if they are to overcome this electrostatic barrier. The only practical approach is to give batches of nuclei enough energy is to heat them, so the process is called thermonuclear fusion. The atoms whose nuclei we want to fuse must first be stripped of their electrons. The product of the change is an electrostatically neutral gaseous mixture of nuclei and unattached e- called plasma. (This, by the way, is the fourth state of matter). Then the plasma must be made so dense that like charged nuclei are forced to within a distance of 2 x 10-5 m of each other, which means that the density must become about 200 kg/cm3. Another way to describe this change is that the gaseous plasma must be confined at a pressure of several billion atmospheres long enough for the separate nuclei to fuse. 
Physicist J.D. Lawson has calculated that thermonuclear fusion will provide a net production of energy only if the product of the particle density, n, and the confinement time, t, equals or exceeds a certain value, called the Lawson Criteria number. 

nt = 3 x 104 s/cm3

This means that if a long confinement time is unworkable, then a compensating high particle density would be needed or if a high particle density were to difficult then the confinement time would have to be extra long. The Lawson number and the temperature are the two major scientific hurdles needed to be overcome. The temperature needed is about 1 million oC which is several times the temperature at the centre of the sun. Two broad approaches are currently being pursued. 

Inertial Confinement Method
Inertial Confinement means enclosing the fuel 31H and 21H within a pellet made of glass, plastic, or metal with a diameter of about 1 mm. The pellet is then given so much energy so rapidly from all angles from laser beams, that the material on the outer surface of the pellet suddenly vaporizes and becomes plasma. The conversion of the fuel atoms into their own plasma begins as the shell of the pellet begins to expand outwards in all directions. The reaction to the explosion of the pellet is an implosion (Newton's Third Law) of the fuel itself, now a plasma, in upon itself. If the explosion is symmetrical the fuel will be condensed into a much denser, very hot ball of much smaller radius then the fuel had initially. If this ball is made small enough, its density will be high enough for fusion to occur. 

Magnetic Confinement Method
This process uses a magnetic bottle to confine the hot, plasma. The field constricts this plasma forcing it to become more and more dense until fusion occurs. The plasma is made hot by acceleration around the ring made from huge electromagnets. Only a magnetic field could withstand the temperature and pressure.

Go to the Nuclear Fusion Worksheet

In fission, a heavy nucleus absorbs a neutron and breaks apart to give back lighter nuclei plus 2 or more neutrons and some energy. Room temperature or slow thermal neutrons have enough kinetic energy to approach a nucleus of U-235. Lise Meitner and Otte Frisch were able to show that one of the rare isotopes, U-235, was able to split into roughly two equal parts. This they termed nuclear fission.
23592U + 10n -----> 23692U -----> X + Y + b no

X + Y can be anything, but are usually in the midrange of mass numbers. The factor 'b' in this equation has a value of 2.47 which is the average of many fissions. When the U-235 is struck by the slow thermal neutron it becomes the unstable U-236. This U-236 fissions into Kr and Ba (most often) isotopes with the same no/p+ ratio as the U-236. This ratio is to high for the Kr and Ba and therefore they must eject no of a higher energy then the initial slow thermal neutrons. 

An isotope capable of undergoing fission is called a fissile isotope. Only U-235 is a natural fissile isotope. U-233 and Pu-239 are synthetic fissile isotopes. Since each fission results in 2 or 3 no and, if these can be slowed down by collisions with their surroundings, then the potential for a nuclear chain reaction exists. A chain reaction is a self-sustaining process whereby products from one event cause one or more new events. If the mass of U-235 is small enough, the loss of no to the surroundings is to rapid to initiate chaining. 

However, at the critical mass the loss is small. Most of the neutrons get trapped and strike other fissile nuclei. The result is a virtually instantaneous fission of the entire sample. An atomic bomb filled with weapons grade U-235 is essentially only 2 subcritical masses with an explosive trigger which drives them together. The explosion forces the sub-critical masses together and not only creates a critical mass but continues to compress the mass into an even more dense state. Any neutrons released spontaneously will not escape and start the chain reaction. 

A reactor cannot be made to fission like a bomb. The bomb requires pure U-235 or Pu-239. The concentration of fissile isotopes in a reactor is only 2-4% with much of the remainder being U-238 (non-fissile). Even if all the fuel melted into a pool at the bottom of the reactor chamber (The China Syndrome) there would not be enough U-235 to form a critical mass. To have controlled fission take place in a reactor, the leakage of neutrons away from the core must be controlled, and the fast neutrons produced by fission must be slowed. Leakage occurs at the surface of the core, whereas no are generated throughout the volume of the core. By making the fuel core large enough, the ratio of surface area to volume can be reduced to where enough neutrons are retained to cause further fission events. To slow neutrons down, the fuel core is provided with a moderator. Water itself is a good moderator and D2O is used in the CANDU reactors. Graphite is also a good moderator and it was in use in the Chernobyl reactor. The safe operation of a reactor requires that the multiplication of slow neutrons be controlled throughout the fission cycle. This cycle begins with the fission of a U-235 nuclei and the production of fast neutrons, their moderation and the use of the survivors of the moderation to launch additional fission events. The ratio of neutrons at the end of the cycle to those that started it is called the multiplication factor, k. For smooth safe, continuous operation, the value of k in the reactor should be exactly 1. When it is, the reactor is critical. When k>1 fission is accelerating and the reactor is supercritical. When k<1, fission is slowing down and the reactor is subcritical. The reactor must have a built-in ability to go supercritical and then be controlled. The system uses cadmium control rods to capture neutrons to keep the reactor at the desired level of criticality. The nuclear fuel is in the form of sintered pellets of uranium or plutonium oxide. These pellets are packed into cladding tubes made of zirconium alloy. These zirconium alloy tubes must be gas proof to prevent the escape of any gaseous radioactive wastes. As fission continues the wastes build-up in the cladding tubes and poison the U-235 still left. This slows the rate of fission. Only 3% of the U-235 in a tube actually fissions before it must be replaced. They still contain 97% of the original U-235 and newly synthesized Pu-239 made from U-238. 

Electrical Energy From Fission
All fission reactors are based primarily on the premise of taking heat away from the reactor, warming another substance like water to the boiling point, and then using this steam to power a turbine. The fluid in the 1o loop circulates water through the reactor vessel itself, where it picks up thermal energy (hence the name, thermal reactor). This water is keep under pressure so that it can carry many times its normal heat carrying capacity. (hence the name pressurized water reactor). In some reactors the 1o loop contains helium gas, heavy water or in some cases liquid sodium metal.
Loss of Coolant Emergencies
It is essential to a reactor's operation that any heat produced by fission be removed as fast as it is produced. The 1o coolant must do this or the temperature of the core would increase very rapidly. If this heat is not removed the water in the 1o coolant loop will flash into steam and quickly develop enough pressure to blow the reactor apart. The first of the two explosions at the Chernobyl reactor was of the steam explosion type. It blew off a cover plate from the calendra weighing 1000 tonnes and tore off the tops of all 1661 cladding tubes. Each cladding tube then became a large-bore shotgun that sent a fireworks display of 8 tonnes of incandescent, radioactive fuel elements and wastes into the night sky. The emergency coolant water to both reactants was linked together and when the 1st explosion disabled this system the 2nd reactor went supercritical. It's steam explosion helped to carry radioactive wasters 1100 m into the air. The fire ignited the graphite moderator which burned like any other kind of carbon based charcoal fire. Each person at the site received approximately 400 rems of exposure within the first few minutes. Even if insufficient steam is present from which to generate enough pressure for a steam explosion, the temperature in the core can make the cladding melt, and the now superhot metal could then react with the steam to make H2 gas which can then lead to a chemical explosion. Eventually the fuel elements melt and gather in a molten puddle in which fission energy continues to be produced. 

Radioactive Wastes
The wastes that come from a nuclear reactor are mostly Kr and Xe, but with the exception of Xe-85 (t½ = 10.4 years), these have short half-lives and decay quickly. Until they do they are contained in the cladding tubes. If radioactive gases escape they will include I-131, Sr-90 and Cs-137 and many more including tritium, H-3. Since the human thyroid concentrates I-131 it is advisable to take normal I as NaI orally to statistically increase the average of safe I over I-131. 
Both Ca and Na are in Group IA and Sr and Ca are in Group IIA. Therefore Cs goes anywhere Na goes and Sr-90 tends to replace Ca in bones. 
Liquid Sodium Cooled Reactors
A reactor that uses sodium as a coolant and a metal alloy as a fuel instead of a metal oxide cannot run out of control. Water can be heated under pressure and remain a liquid only to 374.1oC, the critical temperature of water. Pipe materials therefore suffer tremendous deterioration from water vapour at 500oC... but Na boils at 880oC, therefore a reactor can operate at temperatures above water's critical temperature while still being at atmospheric pressure. The reactor itself sits in a huge liquid pool of metallic sodium metal which is itself the emergency coolant. Fuel as a metal alloy moves heat away and through itself faster than a metal oxide. 
The Breeder Reactor 
Mathematics in the nuclear age. 
Johnny has a breeder reactor that uses 3 tonnes of fuel in its first year. How much fuel does Johnny have left? 

Answer: 4 tonnes 

In a breeder reactor useless U-238 is transmuted by slow neutrons into Pu-239. For every Pu-239 that fissions a U-238 non-fissile nuclei gets converted back into Pu-239. Therefore a breeder reactor running at slightly over 'k' will produce more fuel that it uses. 

Go to the Nuclear Fission Worksheet

Go to the Nuclear Review