Lectures #26 and #27

First and Second Lectures on Nuclear Energy

Nuclear energy evokes significant passion – much more than other types of energy. Hollywood even made a movie a few years back!

Nuclear energy for the generation of electricity got its start after WWII. In the 1950s there was great excitement about the use of nuclear energy for peaceful applications – in significant part as a counter-reaction to the horror of using it in war.

By the 1960s, the essential technology for the generation of electrical energy from nuclear energy was developed. Nuclear power-plants were ordered by the utilities and construction began.

Today, there are:

The nominal rating of a nuclear power-plant is 1000 MW. The capacity factor of nuclear power-plants has been increasing over the 1980s and 1990s, as experienced is gained on keeping them on-line.

About 20% of the electricity generated in the USA is from nuclear energy.

Slightly under 20% of the world’s electricity is generated from nuclear energy.

France produces 80-90% of its electricity from nuclear energy. The figure for Sweden has been as large as about 50%. For Japan it is about 30%.

Most of the reactors in operation today were:

Early on, it took about 6 years to build a nuclear power-plant. However, later, in the 1980s, this increased to about 12 years.

Some nuclear reactors are nearing the end of their originally assigned lifetimes of 30-40 years. Most of today’s reactors will reach the end of their lifetimes in the 2000-2030 period.

However, there is now a major push to license many reactors for an additional 20 years, pushing the end of lifetimes to the 2020-2050 period.

Thus, probably in the 2010-2030 period, many societies will need to face up to either building a new round of nuclear reactors or turning away from nuclear energy.

All of today’s nuclear reactors are fission reactors, meaning they release the energy of nuclear bonding by breaking about the nuclear fuel. The fuels are U-235 and Pu-239, bombarded by neutrons to cause the breaking. One fission reaction releases about 108 as much energy as one combustion reaction.

Fission is not the only method of releasing energy. The methods are:

Most nuclear power-plants operate on the Rankine cycle. Figure 14.5 in the text shows the boiling water reactor. Light (normal) water is converted to steam in the reactor. Figure 14.10 shows the pressurized water reactor. Water is heated in the reactor. Its heat is transferred to a second loop of water at lower pressure. Because of the lower pressure, the second loop of water boils, thereby producing steam to drive the turbine. The Canadians use heavy water (D2O) in the high-pressure loop – heavy water is expensive, but its use allows natural uranium (rather than uranium enriched in U-235) to be used as the fuel.

Note the steam temperature of nuclear power-plants is not as hot as the ~600 degrees C maximum mentioned for fossil fuel-fired steam power-plants. Thus, the overall efficiency of nuclear power-plants is restricted to about 29-33%.

However, there are some new reactor designs, based on the gas turbine cycle, that have the potential for efficiencies in the 40% range.

 

In order to understand nuclear energy, we need to study both principles and practical fission technology. Chapter 13 contains the former, Chapter 14 the latter. We will also study fusion, Chapter 16.

With respect to the basics, we need to understand:

The atomic number (Z) is the number of protons in the nucleus of an atom. The mass number (A) is the sum of the number of protons (Z) and neutrons (A-Z) in the nucleus, or the number of nucleons (A).

The atomic number defines the element – that is, it defines its number of protons (and electrons) and its chemical properties. The mass number defines the isotope.

The "coding" for element X is: ZAX, for example 92235U for the fissionable isotope of uranium.

Stable isotopes do not undergo (spontaneous) radioactive decay. Unstable isotopes undergo radioactive decay.

Of the 115 known elements (not all of which are naturally occurring), 81 have at least one stable isotope. There are over 1500 isotopes (nuclides), and 279 of these are stable. Many elements have only stable isotope, whereas others have several stable isotopes.

For isotopes of A < 40, the number of neutrons generally equals the number of protons, that is, A = 2Z.

For A > 40, the number of neutrons tends to exceed the number of protons.

The most stable isotope is Iron-56. Fission reactions proceed from a heavy isotope to smaller products, that is, towards increased stability (though they don’t get as small as Fe-56). Fusion reactions proceed from light isotopes to bigger products, that is, towards increased stability (though they don’t get as big as Fe-56). This is analogous to combustion, which proceeds from fuel and oxygen to the very stable CO2 and H2O molecules.

Radioactive decay leads to the emission of either an alpha particle (that is, a helium nucleus with A = 4 and Z =2) or a beta particle (a charged particle with the mass of an electron, but lacking the spin of an electron). Very short wavelength electromagnetic radiation is also emitted along with the alpha or beta particle – these are the gamma rays.

The important radionuclides in the earth’s crust are:

K-40

Rb-87

U-238 (and its decay products)

Th-232 (and its decay products)

The stable end point for the decay of the heavy isotopes is one of the 3 stable isotopes of lead.

The decay of U-238 involves 14 reactions:

92238U ® 90234Th ® 91234Pa ® 92234U ® 90230Th ® 88226Ra ® 86222Rn ® 84218Po ® 82214Pb ® 83214Bi ® 84214Po ® 82210Pb ® 83210Bi ® 84210Po ® 82206Pb

Overall, one may write:

92238U ® 82206Pb + 8a + 6(-1b)

All of the beta particles emitted carry a negative charge.

The number of disintegrations per second determines the activity of the decay.

The relation for activity is: Activity = 0.693*Number of Isotopes/Half-Life

Each reaction has a half-life. The decay half-life of U-238 is very long, 4.5 billion years (about the age of the earth). Thus, about ˝ of the original U-238 remains. U-235 has a shorter half-life – thus there is less of it in the earth’s crust than U-238.

Note the decay of U-238 leads to Radium (Ra) and Radon (Rn). The half-life of Ra is 1600 yrs, and that of Rn is 3.8 days. The danger from radon arises from its decay to isotopes that can become trapped in the lungs and the release of alpha particles from the subsequent decays. These isotopes have short half-lives, and the alpha particles damage human tissue. See Figure 15.5 and the text on page 506.

One disintegration per second = 1 Becquerel (Bq).

37 billion disintegrations per second = 1 Curie (Ci).

The radioactivity of the earth’s crust (per kg of crust) is estimated as follows:

K-40 870 Bq/kg

Rb-87 102 Bq/kg

U-238 35 Bq/kg x 10 (for the activity from its decay products)

Th-232 43 Bq/kg x 10 (for the activity from its decay products)

 

The only naturally occurring fissionable isotope is U-235. However, there are two fertile isotopes found in nature. U-238 is the fertile isotope for producing Pu-239, which is fissionable. Th-232 can be used as the fertile isotope for fissionable U-233.

The isotopes of Uranium found in nature are:

U-238: 99.274% of the U.

U-235: 0.720% of the U.

U-234: 0.006% of the U.

Neutron collisions with U-235 are used to cause the fission reaction. The lack of charge on the neutron allows it to reach the positive nucleus of the U-235. It is not repelled.

Four things can happen when a neutron strikes a nucleus:

  • Elastic collision, the neutron bounces off of the nucleus. Kinetic energy and momentum are exchanged.
  • Inelastic collision, the nucleus becomes excited, and subsequently stabilizes by releasing electromagnetic gamma radiation, much like a molecule absorbs a photon, attains a higher (excited) energy state, and then emits light.
  • Capture, the neutron is captured and a new isotope is made. An important example of this is the creation of Pu-239:

n + U-238 ® U-239 + gamma radiation

U-239 ® Np-239 + beta particle (23.5 min)

Np-239 ® Pu-239 + beta particle (2.355 days)
  • Fission

n + U-235 ® FP#1 + FP#2 + 2-3 neutrons

There are several key things to note about the fission process:

  • Many fission products are formed. The isotope ranges are:

FP#1: Mass number (A) from 89 to 101

FP#2: Mass number (A) from 133 to 144
  • The reactant neutron (ie, the "n" on the left-hand side of the reaction) is a "thermal" neutron. That is, it has a speed corresponding to a gas of neutrons at room temperature. The mean speed of such neutrons is 2200 m/s. The kinetic energy of a 2200 m/s neutron is 0.025 eV (electron volts).
  • The neutrons produced by the fission reaction are fast neutrons. They have an average kinetic energy of about 2 MeV (million electron volts). These neutrons are not efficient in causing U-235 fission. They need to be slowed down or "thermalized". We need to cause the fast neutrons to exchange kinetic energy by elastic collisions with nuclei. The best nuclei to use in this regard are those of the same mass as that of the neutrons. The H-nuclei in the water work well in this regard. That is, the water serves two purposes in many reactors. It cools the reactor core, picking up heat for the steam cycle, and it moderates or thermalizes the neutrons, allowing fission reactions to continue.
  • The yield of fast neutrons is important. For U-235 fission, about 2.4 neutrons are produced per fission. For Pu-239 fission, the yield is about 2.9 neutrons. This leads to a "chain reaction". That is, the concentration of neutrons geometrically grows, allowing the fission reaction to reach an explosive rate, unless it is controlled. For a reactor operating in steady-state, that is, at the "critical" point, the number of thermal neutrons is constant. That is, for every thermal neutron used in fission, only one is created (and survives) to replace it. Some of the neutrons leak from the reactor, some of fast neutrons are not thermalized, and some of the neutrons are captured by various nuclei in the reactor. If we want to slow down or stop the fission reaction, "control rods" are inserted into the reactor core. These rods are made of material that strongly captures neutrons. Boron is good for this.

The nuclear energy released by a single U-235 fission is about 200 MeV. This can be calculated from the equation:

E = mc2

where m is the "mass difference" of the reaction, and c is the speed of light. The working equation is:

E(MeV) = 931.5 x mass difference (amu)

The term "amu" means atomic mass units. The mass difference is the difference between the mass of the reactants and products of the fission reaction.

Try out a sample case:

n + U-235 ® Ba-144 + Kr-89 + 3n

The amu’s are:

U-235: 235.0439

Ba-144: 143.9228

Kr-89: 88.9177

n: 1.0087

Energy = (235.0439 – 143.9228 – 88.9177 – 2x1.0087)x931.5 = 173 MeV

This energy is distributed as follows:

  • About 93% as the KE of the FPs.
  • About 3% as the KE of neutrons.
  • About 4% as the EM energy of the gamma rays.

About 10% more energy (~17 MeV in our example) is released as the FPs undergo decay. Thus, even if the fission process is shut down, the reactor will continue to generate heat as the FPs decay. This goes on for some time, exponentially decaying over several days (and even months).

There are "prompt" neutrons and there are "delayed" neutrons. The neutrons produced by our fission reactions above are prompt neutrons. They are released very quickly – too quick to be controlled by the insertion of the control rods should the fission process go "supercritical". Fortunately, there are some delayed neutrons. These neutrons are formed from some of the FP decay reactions. They are slowly released (~10 seconds). About 0.65% of the neutrons are delayed neutrons. Thus, reactors are operated "subcritical" with respect to the prompt neutrons, and are brought to "critical" or steady-state condition using the delayed (slowly released) neutrons. The control rods can now respond quickly enough to bring the reactor to a subcritical condition. (However, the control rods failed at Chernobyl – a criticality accident occurred.)