Nuclear Reactions (DP IB Physics: HL)

A nuclear fission reaction occurs that has the following equation:

Given the following information, estimate the amount of energy released during the fission reaction:                             

• 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:

[2]

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

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

Show on the graph how you have used the data.

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

Nuclei	Mass/ u
	2.0135
	4.0026

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

This question is about nuclear physics. 

If deuterium is combined using fusion, then the following reaction will occur: 

The following data is given for this interaction: 

•    Binding energy per nucleon of deuterium : 1.12 MeV/nucleon
•    Binding energy per nucleon of tritium  : 2.82 MeV/nucleon

Estimate the energy released from this fusion reaction.

In order for the fusion reaction in part (b) to actually take place, very high temperatures are needed such as those found within the core of a star. Suggest why this the case.

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 can be overcome. 

The image below shows how the binding energy per nucleon varies with nucleon number. 

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

[1]

Explain with reference to the figure in part (a), 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 in the figure from part (a).

The mass of an  nucleus is 15.991 u. 

Calculate: 

(i)

The mass difference, in kg, of the  nucleus.

 [2] 

(ii)

The binding energy, in MeV, of an oxygen nucleus.

[1]

Bismuth-214 () decays into Polonium-214 () by beta minus decay. 

The binding energy per nucleon of Bismuth-214 is 7.774 MeV and the binding energy per nucleon of Polonium-214 is 7.785 MeV.

Beta-minus decay is described by the following equation:

Show that the energy released in the decay of bismuth is about 2.35 MeV and state where the energy comes from.

If an additional neutron is accelerated into the Polonium-214 () to produce the isotope Polonium-215 (), use the following information to deduce the binding energy per nucleon of this new isotope.

         Mass of   nucleus = 3.571140 × 10⁻²⁵ kg

Polonium-215 () is radioactive and decays by the producing alpha radiation, which is known to be a particularly stable. 

Determine the binding energy of alpha radiation. 

The following information is available:

• Mass of a Helium-4 nucleus: 4.001265 u

A student claims that the amount of matter within a marble directly converted into energy would be enough to provide 1 year of current human energy consumption globally which is estimated to be 5.80 × 10¹⁸ J.

 If the matter within marble is approximately 6.02 × 10²³ u, determine if this statement is true, using the mass-energy equivalence.

Explain why the mass of an alpha-particle (α) is less than the total mass of two individual protons and two individual neutrons.

Show that the energy equivalence of 1.0 u is 931.5 MeV.

Data for the masses of some nuclei are given below 

Use the data to determine the binding energy of deuterium in MeV.

Using the data given in part (c), determine the binding energy per nucleon of zirconium in MeV.

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. 

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

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

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

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: 

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.

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

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). 

In the research into nuclear fusion, scientists are working with 1.5 kg of Lithium. 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 more difficult to produce. It can, however, be produced by bombarding lithium−6,  , with neutrons. 

These reactions can be represented in the following nuclear equations:

The masses of the nuclei involved are given in the following table:

Suggest why the lithium-6 reaction could be thought to be self-sustaining once the deuteron-tritium reaction is underway.

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.

This is a synoptic question and will need knowledge from previous IB topics.

Plasma is superheated matter. It is 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 × 10⁶ K.

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.

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

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:

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

The following data are available:

• Mass of nucleus = 2.01355 u
• Mass of proton = 1.00728 u  

(i)

Calculate the mass of the helium nucleus, in standard units

 [3]

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%.

(i)

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

[3]

(ii)

Determine the mass of which undergoes fission in one day.

[2]

One of the waste products of the reaction is xenon−140, . Xenon−140 is radioactive, decaying through decay.

The graph shows the variation with time of the mass of 1kg of xenon−140 remaining in the sample.

An alternative nuclear fuel to the traditionally used uranium-235 is thorium-232. When thorium-232 is exposed to neutrons, it will undergo a series of nuclear reactions until it eventually emerges as an isotope of uranium-233, which will readily split and release energy the next time it absorbs a neutron.

Part of the thorium fuel cycle is shown below.

Once the uranium-233 nucleus absorbs a neutron, it undergoes fission, releasing energy and two neutrons and forming the fission products Xenon and Strontium as in parts a-c. Any isotopes of uranium-233 which do not undergo fission decay through a chain ending with a stable nucleus of thallium-205 . 

Show that 12 particles, not including neutrons, are emitted during this combination of decay chains. Explain your reasoning.