Fission (HL IB Physics)

A nuclear fission reaction occurs that has the following equation:

Estimate the amount of energy released during the fission reaction using the following information:                             

• Binding energy per nucleon of Uranium-235 = 7.59 MeV/nucleon
• Binding energy per nucleon of Strontium-90 = 8.70 MeV/nucleon
• Binding energy per nucleon of Xenon-143 = 8.20 MeV/nucleon

The binding energy per nucleon curve is shown:                     

With reference to the binding energy per nucleon curve:

A uranium-235 nucleus undergoes fission into two approximately equally sized products.        

Use the data from the graph in (b) to show that the energy released as a result of the fission is approximately 4 × 10⁻¹¹ J. 

Use the graph to show how you have used the data.

When a uranium-235 nucleus absorbs a slow-moving neutron, it may undergo fission. One of the possible pairs of fission fragments are technetium-112 and indium-122, plus two neutrons are released.

The binding energy per nucleon of these nuclei are shown in the table below.

nucleus	binding energy per nucleon / MeV
	7.59
	8.36
	8.51

Show that the energy released in each fission of uranium-235 is about 200 MeV.

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

Nucleus	Mass / u
	2.0135
	4.0026

Using the data in the table, show that the energy available as a result of the fusion of two hydrogen-2 nuclei is about 4 × 10⁻¹² J.

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 fusion reactions could be produced on Earth as easily as fission reactions.

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

Outline what happens to a neutron that is incident on

A slow-moving neutron is fired at a nucleus and triggers a nuclear reaction. 

Outline what happens in the process.

A teacher demonstrates the principle of moderation in a nuclear reactor by setting up the arrangement shown in the diagram.

In the arrangement, a golf ball initially hangs vertically and just touches a hockey ball which has three times the mass of the golf ball.

In the demonstration, 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.

Discuss some of the problems faced in the management of radioactive waste. 

In your answer you should refer to:

• 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.

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 as

Thermal nuclear reactors are usually fortified with layers of concrete. 

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

The majority of nuclear reactors use the isotope uranium-235 as fuel.

Each fission reaction of uranium-235 generates 180 MeV of energy.

Estimate the specific energy of uranium-235, in J kg⁻¹.

A nuclear power station generates a useful power output of 0.95 GW and has an overall efficiency of 43%.

Determine the mass of uranium-235 required per day to maintain this power output.

The specific energy of natural gas, a type of fossil fuel, is approximately 54 MJ kg^–1.

Using your answer to (a), suggest an advantage of nuclear power compared with a natural gas power station.

Nuclear reactors tend to use enriched uranium as fuel. 

This is fuel in which the ratio of U-235 to U-238 has been artificially increased from that found in naturally occurring uranium ore.

For the same reactor as in (b), estimate the total mass of enriched fuel required per year if it initially contains 3% uranium-235 and 97% uranium-238.

The graph shows the relationship between the binding energy per nucleon and the mass number for various nuclides.

During the process of fission, nuclei of uranium-235 are bombarded by slow-moving neutrons. When a neutron is absorbed, a nucleus of uranium-236 is momentarily formed before splitting into two fission fragments, krypton-92 and barium-141, along with the release of other fission products.

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 (a). 

A different fission process, involving uranium–235 is again triggered by the absorption of a slow−moving neutron and releases gamma ray photons. 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.

The following data are available:

• Mass of = 235.0439u
• Mass of  = 137.9603u
• Mass of  = 97.9197u
• Mass of  = 1.0087u
• Wavelength of  photons emitted = 2.5 × 10^–12 m

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

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

One possible fission reaction of uranium-235 is

The following data are available:

• Mass of one atom of = 235u
• Binding energy per nucleon for = 7.59 MeV
• Binding energy per nucleon for = 8.29 MeV
• Binding energy per nucleon for = 8.59 MeV

Calculate the amount of energy released in the reaction.

A nuclear power station uses the uranium-235 as fuel. The useful power output of the power station is 1.4 GW and it has an efficiency of 30%.

Show that the specific energy of is about 7.5 × 10¹³ J kg⁻¹.

Determine the mass of which undergoes fission in one day.

Young people have swum for many years in an unusually warm Siberian river near to a secret nuclear reactor like the one described in (b). It is alleged that this reactor makes 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, discuss 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

In a nuclear reactor, neutrons released by fission travel with very high energies. To increase the likelihood of further fission reactions, these neutrons need to be sufficiently slowed to be captured by other uranium-235 nuclei. 

An ideal moderator slows neutrons without capturing them. The best moderating materials are light elements, which undergo elastic collisions with the high-energy neutrons. 

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

The first few collisions between a neutron and the nuclei in the moderator transfer sufficient energy to excite the nuclei to higher nuclear energy levels. 

Describe and explain:

By considering the neutrons involved in a nuclear reactor, explain

Natural uranium consists of 99.3%  and 0.7% .

To be used as fuel in a nuclear reactor, natural uranium must be enriched and enclosed in sealed metal containers. 

Explain why

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

The binding energy per nucleon, E, is given in the table below: 

Nuclide	E / MeV
	7.60
	8.39
	8.74

A 1500 MW nuclear reactor, operating at 27% efficiency, uses enriched fuel containing 2% uranium–235 and 98% uranium–238. The molar mass of uranium−235 is 0.235 kg mol^–1.

Estimate the total mass of original fuel required per year in the nuclear reactor. 

Determine the number of fission reactions per day in the nuclear reactor assuming the production of power is continuous. 

The fission products from a large sample of fissioned uranium-235 are analysed. The percentage yield of each fission product is plotted against its nucleon number on the fission yield curve shown below.

The fission of uranium-235 can be described by the equation

The fission products X and Y may have equal masses, however, this is not true for every possible pair of fission products.

Using the fission yield curve

One of the two fission products is a  nucleus.

The second product  is known to be one of the elements shown in the table.

Other data for this reaction:

• Mass of = 235.043923u
• Mass of  = 232.844603u

For this reaction:

Identify the second fission product and determine the percentage yield of the two products.

The products of uranium-235 fission are often radioactive and follow decay series until they form a stable nuclide.

Two examples of fission products with their decay series and half-lives are shown below.

(stable)

(stable)

Discuss the problems associated with the short and long-term storage of these fission fragments and suggest potential solutions for overcoming them.