SPH3U1 Lesson 14 EnergyNUCLEAR FISSION AND FUSION

LEARNING GOALS

Students will learn: Large unstable nuclei can split into two smaller nuclei and release energy. This is fission. Small nuclei can join together releasing energy. This is fusion. The energy released in fission and fusion is from some mass that disappears and is converted to

energy given by E = mc2.

MASS AND ENERGY

This lesson is really about converting mass into energy so let’s get some basics covered first. When we talk about masses atomic nuclei, we rarely use units like g or kg as these are too large. We define a very small unit called an atomic mass unit or AMU. The AMU is defined to be exactly 1/12 the mass of a carbon-12 nucleus. It essentially works out to be the average mass of a proton and a neutron. The neutron is slightly more massive than the proton. Explain why this is so (remember what you learned about beta decay):

The mass of 1 AMU works out to be 1.66053886 x 10-27 kg.

1 AMU is given a metric unit symbol “u”. Therefore 1 u = 1.66053886 x 10 -27 kg.

During nuclear fusion of light elements (joining of nuclei) or nuclei fission of heavy elements (splitting of nuclei) a small amount of mass disappears from the nucleus. This small amount is called the missing mass or the mass defect. This is the mass that is turned into energy. The energy can be calculated from Einstein’s famous equation; here we will actually state it as Einstein did. The mass defect is a change in the total mass (m) and it results in a change to the total energy (E) of the system.

E = mc2

where c = speed of light in a vacuum = 3.00 x 108 m/s

EXAMPLE

A nuclear reaction has a mass defect of 0.054 AMU. How much energy is produced in this reaction? (ANS: 8.1 x 10-12 J) (Mass must be converted to kg first!)

Your solution:

NUCLEAR FISSION

Large nuclei have many protons and neutrons. There are two competing forces at work in the nucleus. There is the electrostatic repulsion between each of the positively charged protons (like charges repel) and there is the strong nuclear force that binds the protons to the neutrons. The strong force works only over very small distances. However, the electrostatic force works over much larger distances. In a large nucleus, the neutrons on one side of the nucleus the nucleus do not hold the protons on the opposite side. However, the repulsive force between protons on opposite sides still operates. The slightest change in a large nucleus causes it to become unstable it and it may split apart into two smaller nuclei.

SPH3U1 Lesson 14 EnergyMost nuclear reactors work on the fission of an isotope of uranium, U-235. Uranium-235 can break apart in several different ways. Most of these ways involve the absorption of a slow moving neutron. This slow neutron is captured by the nucleus causing the nucleus to become unstable. It then breaks apart into smaller nuclei. There are several possible splits. One of these possible fission splits is

(see diagram).

Notice that this split produces three free neutrons. These neutrons can go on to cause more U-235 nuclei to split. This continuing process is called a chain reaction.

Once a chain reaction starts, it will continue unless one of several things occurs:1. The process runs out of U-235. If there is too little U-

235 to start with, the free neutrons will escape without hitting any other U-235 nucleus and a chain reaction won’t occur. In a nuclear reactor or a nuclear bomb, there needs to be a minimum mass of U-235 for the chain reaction to occur. This minimum mass is called the critical mass.

2. The free neutrons are moving too fast. Fast neutrons will likely bounce off a nucleus and won’t be absorbed. To prevent this, a nuclear reactor slows the neutrons using some substance like heavy water. Heavy water is water with a high proportion of the water molecules made from hydrogen-2 and hydrogen-3 isotopes.

3. The neutrons are blocked. To control nuclear reactions, the U-235 is separated by rods of some other material like boron rods. These control rods block the neutrons. When we want the reaction to increase, the rods are lifted out of the U-235 core to allow the neutrons to move freely. When we want the reaction to slow, we lower the rods partially into the core to block some of the neutrons. In an emergency, we can drop the rods all the way into the core to stop the reaction completely.

Now for the math!

Consider the reaction masses: 1 neutron = 1.00866 u

U-235 = 235.0439299 uBa-141 = 140.914411 uKr-92 = 91.926156 u

Calculate the total mass of the reactants in AMU’s (1 U-235 and 1 neutron):

Calculate the total mass of the products in AMU’s (1 Ba-141, 1 Kr-92 and 3 neutrons):

Calculate the mass defect in AMU and convert it to kg: (ans: 0.1860 u)

Calculate the energy released from a single U-235 fission: (2.78 x 10-11 J)

Calculate how many U-235 atoms are in 1 kg of pure U-235: (2.56 x 1024)

SPH3U1 Lesson 14 Energy

Calculate the total amount of energy released from the fission of 1 kg of U-235. (ans: 7.12 x 1013 J)

How long in seconds and years will this energy keep a 60 W light bulb burning? (ans 38,000 years)

The above calculation does not take into account that in a nuclear power plant the nuclear energy is used to boil water, which turns a steam turbine which turns a generator to generate electricity. According to the Bruce power website, a single kg of U-235 can provide electricity for 4 homes for a year. Assume a typical home uses 4 x 1010 J of electrical energy in a year. What percentage of the energy released by the fission of 1 kg of U-235 becomes electrical energy in homes? (Overall efficiency.)

NUCLEAR FUSION

Nuclei that are smaller than iron will require more energy to be put in to split them than they will release. The fission of these small nuclei will not happen spontaneously as these reactions are endothermic. However, joining small nuclei together to form a larger nucleus will release more energy than it takes to join them (exothermic).

Recall that nuclei are all positively charged. It takes a large amount of energy to force them together in the first place. One place this does occur is in the core of the sun. In the core of the sun, hydrogen atoms are fused into helium atoms. It takes a temperature of at least 2,000,000 K to fuse H into He. The sun’s core is much hotter than that – close to 15,000,000 K. Under these conditions, all the electrons are stripped off the hydrogen atoms and the hydrogen-1 nuclei are moving so rapidly they can collide together and join in spite of the like charges that try to prevent them from coming together. There are several steps involving intermediate stages where hydrogen-2 and helium-3 isotopes are formed, but the end result is that 4 hydrogen-1 nuclei end up as 1 He-4 nucleus: .

masses: hydrogen-1 (proton) = 1.007276467 uhelium-4 = 4.00260325 u

SPH3U1 Lesson 14 EnergyCalculate the total mass of the reactants in AMU’s (4 hydrogen-1): (4.029 u)

Calculate the total mass of the products in AMU’s (1 heliunm-4): (4.0026 u)

Calculate the mass defect in AMU and convert it to kg: (ans: 0.0265 u)

Calculate the energy released from the fusion of 4 hydrogens into helium: (3.955 x 10-12 J)

Calculate how many H-1 atoms are in 1 kg of hydrogen: (5.98 x 1026)

Calculate the total amount of energy released from the fusion of 1.0 kg of hydrogen. (ans: 5.9 x 1014 J)

How long in seconds and years will this energy keep a 60 W light bulb burning? (ans 313,000 years)

Note that you get about 8 times the energy from a kg of hydrogen as you do from a kg of uranium-235. However, building a fusion reactor for electricity generation has so far proved to be impossible. Because of the extremely high temperatures involved, the reaction is extremely difficult to control. Essentially, it wants to explode. We actually have made prototype hydrogen fusion reactors, but it takes more energy to control the reaction than the reactor produces. As a method of electrical generation, this idea is so far not workable.