Nuclear Fusion & Fission (AQA A Level Physics)

In the research into nuclear fusion, one of the most promising reactions is between deuterons,, and tritium nuclei,, in a gaseous plasma. Although deuterons can be relatively easily extracted from sea water, tritium is difficult to produce. It can, however, be produced by bombarding lithium-6,, with neutrons. 

These reactions can be represented as shown below: 

Complete the two reactions.

Table 1 shows the masses of these nuclei. 

               Table 1

Calculate the energy released, in J, when a deuteron nucleus fuses with a tritium nucleus.

Using Table 1:

In order to fuse, a deuteron and a tritium nucleus must approach one another to within approximately 1.5 × 10^–15 m. 

Calculate the minimum total initial kinetic energy that these nuclei must have.

Explain in terms of the forces acting on nuclei why the deuteron-tritium mixture must be very hot in order to achieve the fusion reaction.

Figure 1 shows the variation in binding energy per nucleon with nucleon number. 

Figure 1

A uranium-235, , nucleus fissions into two approximately equally sized products. 

Use data from the graph in Figure 1 to show that the energy released as a result of the fission is approximately 4 × 10^–11

Show on the graph how you have used the data.

Under the right conditions, two hydrogen-2, , nuclei can fuse to make a helium-4, , nucleus. 

                  Table 1

Nuclei	Mass / u
	2.0135
	4.0026

Using the data in Table 1, calculate the energy available as a result of the fusion of two hydrogen-2 nuclei.

Compare the energy available from the complete fission of 1 kg of uranium-235 with the energy available from the fusion of 1 kg of hydrogen-2.

Fission and fusion reactions release different amounts of energy. 

Discuss other reasons why it would be preferable to use fusion rather than fission for the production of electricity, assuming that the technical problems associated with fusion could be overcome.

The core of a thermal nuclear reactor contains a number of components that are exposed to moving neutrons. 

State what happens to a neutron that is incident on: 

   (i)         The moderator. 

   (ii)        A control rod.

A slow-moving neutron collides with a nucleus of an atom of the fuel which leads to anuclear reaction. 

Describe what happens in the process.

A student sets up the arrangement, shown in Figure 1, to demonstrate the principle of moderation in a nuclear reactor.

A golf ball is initially hanging vertically and just touching a hockey ball which has three times the mass of the golf ball. The golf ball is pulled up to the side and released. After the collision the balls move in opposite directions with equal speeds.

A thermal nuclear reactor produces radioactive waste.

State the source of this waste and discuss some of the problems faced in dealing with the waste at various stages of its treatment. 

Your answer should include:

• The main source of the most dangerous waste
• A brief outline of how waste is treated
• Problems faced in dealing with the waste, with suggestions for overcoming these problems.

Figure 1 shows how the binding energy per nucleon varies with nucleon number. 

Figure 1

Fission and fusion are two nuclear processes in which energy can be released.

Explain, with reference to Figure 1, why the energy released per nucleon from fusion is greater than that from fission.

Explain how the binding energy of an oxygen  nucleus can be calculated with information obtained from Figure 1.

The mass of an   nucleus is 15.991 u. 

Calculate: 

(i)         The mass difference, in kg, of the  nucleus. 

(ii)        The binding energy, in MeV, of an oxygen  nucleus.

In a thermal nuclear reactor, a chain reaction is maintained in the core that is operating normally. 

Explain:

Water is used in many thermal nuclear reactors as it has useful properties for acting as both a moderator and a coolant.

Describe the properties of water which make it useful for acting as:

   (i)         A moderator.

   (ii)        A coolant.

Thermal nuclear reactors are usually fortified with layers of concrete. 

Explain why concrete is a commonly used building material for nuclear reactors.

Plasma is superheated matter – so hot that the electrons are stripped from their atoms, forming an ionised gas. 

The Sun is made up of gas and plasma and can be thought of as a giant fusion reactor. At its core where fusion takes place, the plasma is (mainly) protons with a temperature of about 1.5 × 10⁷ K and a pressure of about 1.0 × 10¹⁶ Pa. 

Near the Sun’s surface, however, protons have a mean kinetic energy of 0.75 eV, which is too low for fusion to take place. 

Calculate the temperature of the Sun near its surface, stating any assumptions you make. 

Hence, by considering the distance of closest approach between two protons, explain why fusion does not occur near the Sun’s surface.

Calculate the density of the Sun’s core.

The energy produced by the Sun comes from a cycle of hydrogen fusion, during which the net effect is the fusion of 3 protons to a helium nucleus.           

One of the steps in the cycle is shown below: 

             energy 

The amount of energy radiated away in this step is 5.49 MeV. 

Calculate the mass of the helium nucleus,  in standard units. 

          mass of   nucleus = 2.01355 u

            mass of proton = 1.00728 u

During a particular fission process, a uranium–236 nucleus is bombarded with a slow-moving neutron creating a krypton–92 nucleus and a barium–141 nucleus, among other fission products. 

Figure 1 shows the relationship between the binding energy per nucleon and the mass number for various nuclides. 

Figure 1

Using Figure 1, calculate the energy released during this fission process.

Identify the other fission products in this process and justify why they can be discounted from the calculation in part (a).

A different fission process, involving uranium–235 is again triggered by the absorption of a slow-moving neutron and releases gamma ray photons of wavelength 2.5 × 10^–12 m. The process is described by the equation below: 

In this process, 90% of the energy released is carried away as kinetic energy of the two daughter nuclei. 

Show that approximately 32 gamma ray photons are released in this process.           

   Mass of  = 235.0439 u

   mass of   = 137.9603 u

   mass of   = 97.9197 u

   mass of   = 1.0087 u

Assuming the nuclei are initially at rest, show that the nucleus is emitted with a speed about 1.4 times larger than the nucleus.

When a uranium–235 nucleus undergoes fission, one of the possible reactions is: 

            energy 

The binding energy per nucleon E is given in Table 1 below: 

            Table 1

nuclide	E / MeV
	8.74
	8.39
	7.60

A 1500 MW nuclear reactor, operating at 27% efficiency, uses enriched fuel containing 2% uranium–235 and 98% uranium–238. 

Estimate the total mass of original fuel required per year in the nuclear reactor. (Assume the molar mass of uranium-235 is 0.235 kg/mol).  

The average energy released by the various modes of fission of uranium–235 is 200 MeV. 

Calculate the number of fission reactions per day in the nuclear reactor (assuming continuous production of power).

Young people have swum for many years in an unusually warm Siberian river near to a secret nuclear reactor like the one described in part (a). It is alleged that this factory has made regular discharges of nuclear waste into the river.  

Explain why the water is unusually warm and evaluate the most significant health risk posed to young swimmers.

In a nuclear reactor the mean energy produced by each uranium-235 nucleus that undergoes induced fission is 3.0 × 10^–11 J. 

Oil releases approximately 50 MJ of heat per kg when it is burned in air. 

Using a suitable calculation, identify and explain one advantage and one disadvantage of using nuclear fuel over fossil fuels, such as oil, to produce electricity. 

   Molar mass of uranium -235 = 0.235 kg mol^–1.

Neutrons travel with very high energies in nuclear reactors. To increase the likelihood of fission, these neutrons need to be sufficiently slowed in order to be captured by uranium-235 nuclei. 

Moderating material is used to slow neutrons without capturing them. The best moderating materials are light elements, which undergo elastic collisions with the high energy neutrons. 

Explain why lighter elements, like hydrogen, tend to be more effective moderators than heavier elements.

The first few collisions of a neutron with the moderator transfer sufficient energy to excite nuclei in the moderator. 

Describe and explain: