(A) When a Neutron Collides with a Nucleus of Uranium-235 (U) the Following Reaction Can Occur

1. This question is about the production of nuclear energy and its transfer to electrical energy.

(a) When a neutron “collides” with a nucleus of uranium-235 (U) the following reaction can occur.

U + n ® Ba + Kr + 2n

(i) State the name given to this type of nuclear reaction.

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(1)

(ii) Energy is liberated in this reaction. In what form does this energy appear?

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(1)

(b) Describe how the neutrons produced in this reaction may initiate a chain reaction.

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(1)

The purpose of a nuclear power station is to produce electrical energy from nuclear energy. The diagram below is a schematic representation of the principle components of a nuclear reactor “pile” used in a certain type of nuclear power station.

The function of the moderator is to slow down neutrons produced in a reaction such as that described in part (a) above.

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(3)

(ii) Explain the function of the control rods.

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(2)

(d) Describe briefly how the energy produced by the nuclear reactions is extracted from the reactor pile and then transferred to electrical energy.

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(4)

(Total 12 marks)

2. This question is about nuclear reactions.

(a) Complete the table below, by placing a tick () in the relevant columns, to show how an increase in each of the following properties affects the rate of decay of a sample of radioactive material.

Property / Effect on rate of decay
increase / decrease / stays the same
temperature of sample
pressure on sample
amount of sample

(2)

Radium-226 (Ra) undergoes natural radioactive decay to disintegrate spontaneously with the emission of an alpha particle (α-particle) to form radon (Rn). The decay constant for this reaction is 4.30 × 10–4 yr–1. The masses of the particles involved in the reaction are

radium: / 226.0254 u
radon: / 222.0176 u
α-particle: / 4.0026 u

(b) (i) Explain what is meant by the statement that the decay constant is 4.30 × 10–4 yr–1.

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(2)

(ii) Calculate the energy released in the reaction.

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(3)

(i) Explain, in terms of the momentum of the particles, why the radon nucleus and the α-particle move off in opposite directions after the reaction.

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(3)

(ii) The speed of the radon nucleus after the reaction is vR and that of the α-particle is vα. Determine the ratio .

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(3)

A college has been using a sample of radium-226 as an α-particle source for 30 years. Initially, the mass of radium was 15.0 μg.

(d) Determine

(i) the initial number of atoms of radium-226 in the sample;

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(ii) the number of atoms of radium-226 in the sample after 30 years;

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(iii) the average activity of the sample during the 30 year period.

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(6)

(e) The α-particle is composed of protons and neutrons. Describe, by reference to the structure of the proton and the neutron, why they are not classed as fundamental particles.

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(3)

Another type of nuclear reaction is a fusion reaction. This reaction is the main source of the Sun’s radiant energy.

(f) (i) State what is meant by a fusion reaction.

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(3)

(ii) Explain why the temperature and pressure of the gases in the Sun’s core must both be very high for it to produce its radiant energy.

High temperature: ......

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High pressure: ......

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(5)

(Total 30 marks)

3. This question is about the radioactive decay of potassium-40.

A nucleus of the nuclide K (potassium-40) decays to a stable nucleus of the nuclide Ar (argon-40).

(a) State the names of the two particles emitted in this decay.

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(2)

(b) A sample of the isotope potassium-40 initially contains 1.5 × 1016 atoms. On average, 16 nuclei in this sample of the isotope undergo radioactive decay every minute.

Deduce that the decay constant for potassium-40 is 1.8 × 10−17 s−1.

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(3)

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(1)

(Total 6 marks)

4. This question is about nuclear reactions.

(a) (i) Distinguish between fission and radioactive decay.

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(4)

A nucleus of uranium-235 () may absorb a neutron and then undergo fission to produce nuclei of strontium-90 () and xenon-142 () and some neutrons.

The strontium-90 and the xenon-142 nuclei both undergo radioactive decay with the emission of β– particles.

(ii) Write down the nuclear equation for this fission reaction.

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(2)

(iii) State the effect, if any, on the mass number (nucleon number) and on the atomic number (proton number) of a nucleus when the nucleus undergoes β– decay.

Mass number: ......

Atomic number: ......

(2)

The uranium-235 nucleus is stationary at the time that the fission reaction occurs. In this fission reaction, 198 MeV of energy is released. Of this total energy, 102 MeV and 65 MeV are the kinetic energies of the strontium-90 and xenon-142 nuclei respectively.

(b) (i) Suggest what has happened to the remaining 31 MeV of energy.

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(2)

(ii) Calculate the magnitude of the momentum of the strontium-90 nucleus.

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(4)

(iii) Explain why the magnitude of the momentum of the strontium-90 nucleus is not exactly equal in magnitude to that of the xenon-142 nucleus.

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(2)

On the diagram below, the circle represents the position of a uranium-235 nucleus before fission. The momentum of the strontium-90 nucleus after fission is represented by the arrow.

(iv) On the diagram above, draw an arrow to represent the momentum of the xenon-142 nucleus after the fission.

(2)

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(2)

(ii) The half-life of strontium-90 is 28.0 years. Deduce that the decay constant of strontium-90 is 7.85 × 10–10 s–1.

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(1)

(d) The decay constant of xenon-142 is 0.462 s–1. Initially, a sample of radioactive waste material contains equal numbers of strontium-90 and xenon-142 nuclei.

(i) Use the values of the decay constants in (c) and (d) to calculate the time taken for the ratio

to become equal to 1.20 × 106.

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(3)

(ii) Suggest why, in the long-term, strontium-90 presents a greater problem then xenon-142 as radioactive waste.

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(2)

(Total 26 marks)

5. This question is about radioactive decay.

Cerium-145 is a radioactive isotope with a half-life of 3.0 minutes. It emits β– particles and also anti-neutrinos.

(a) Give one reason why the existence of the neutrino was postulated in order to explain
β-decay.

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(1)

(b) State the class of particle to which the neutrino belongs.

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(1)

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(2)

(d) Determine the time taken for the activity of a particular sample of Cerium-145 to be reduced to a fraction of its initial activity.

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(2)

(Total 6 marks)

6. A sample of cobalt-60 has an activity of 3.0 × 105 Bq. The half-life of cobalt-60 is 5.3 years.

(a) Define half-life.

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(1)

(b) Determine the decay constant of cobalt-60.

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(2)

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(2)

(Total 5 marks)

7. This question is in about radioactivity and nuclear energy levels.

(a) Define the following terms.

(i) Radioactive half-life ()

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(1)

(ii) Decay constant (λ)

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(1)

(b) Deduce that the relationship between and λ is

λ = ln2.

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(2)

Thorium-227 (Th-227) undergoes a-decay with a half-life of 18 days to form radium-223 (Ra-223). A sample of Th-227 has an initial activity of 3.2 × 105 Bq.

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(2)

In the decay of a Th-227 nucleus, a g-ray photon is also emitted.

(d) (i) Use the following data to deduce that the energy of the γ-ray photon is 0.667 MeV.

mass of Th-227 nucleus = 227.0278 u
mass of Ra-223 nucleus = 223.0186 u
mass of helium nucleus = 4.0026 u
energy of α-particle emitted = 5.481 MeV
unified atomic mass unit (u) = 931.5 MeVc–2

You may assume that the Th-227 nucleus is stationary before decay and that the Ra-223 nucleus has negligible kinetic energy.

(3)

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(ii) Calculate the frequency of the γ-ray photon.

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(3)

Although in the decay of a Th-227 nucleus, an α-particle and a γ-ray photon are emitted, they may have different energies to those in (d)(i). However, all the α-particles emitted in the decay of Th-227 have discrete energies as do the associated g-ray photons. This provides evidence for the existence of nuclear energy levels. The diagram below represents some of the energy levels of a nucleus of Ra-223 relative to Th-227.

(e) On the diagram above label

(i) the arrows associated with α-particles (with the letter A).

(1)

(ii) the arrows associated with γ-ray photons (with the letter G).

(1)

(iii) the ground state energy level of Ra-223 (with the letter R).

(1)

(f) Use data from (d), to suggest a value for the energy difference between the ground states of a nucleus of Th-227 and the ground state of a nucleus of Ra-223.

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(1)

(Total 16 marks)

8. This question is about nuclear power and thermodynamics.

A fission reaction taking place in the core of a nuclear power reactor is

(i) State one form in which energy is released in this reaction.

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(1)

(ii) Explain why, for fission reactions to be maintained, the mass of the uranium fuel must be above a certain minimum amount.

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(2)

(iii) The neutrons produced in the fission reaction are fast moving. In order for a neutron to fission U-235 the neutron must be slow moving. Name the part of the nuclear reactor in which neutrons are slowed down.

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(1)

(iv) In a particular reactor approximately 8.0 × 1019 fissions per second take place. Deduce the mass of U-235 that undergoes fission per year.

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(3)

(Total 7 marks)

9. This question is about radioactive decay.

A nucleus of the isotope xenon, Xe-131, is produced when a nucleus of the radioactive isotope iodine I-13 decays.

(a) Explain the term isotopes.

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(2)

(b) Fill in the boxes below in order to complete the nuclear reaction equation for this decay.

(2)

The activity A of a freshly prepared sample of the iodine isotope is 6.4 × 105 Bq and its half-life is 8.0 days.

(3)

(d) Determine the decay constant of the isotope I-131

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(2)

The sample is to be used to treat a growth in the thyroid of a patient. The isotope should not be used until its activity is equal to 0.5 × 105 Bq.

(e) Calculate the time it takes for the activity of a freshly prepared sample to be reduced to an activity of 0.5 × 105 Bq

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(2)

(Total 11 marks)

10. This question is about radioactive decay and the age of rocks.

A nucleus of the radioactive isotope potassium-40 decays into a stable nucleus of argon-40.

(a) Complete the equation below for the decay of a potassium-40 nucleus.

(2)

A certain sample of rocks contains 1.2 × 10–6 g of potassium-40 and 7.0 × 10–6 g of trapped argon-40 gas.

(b) Assuming that all the argon originated from the decay of potassium-40 and that none has escaped from the rocks, calculate what mass of potassium was present when the rocks were first formed.

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The half-life of potassium-40 is 1.3 × 109 years.

(i) the decay constant of potassium-40;

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(2)

(ii) the age of the rocks.

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(2)

(Total 7 marks)

11. This question is about collisions and radioactive decay.

(a) (i) Define linear momentum and impulse.

Linear momentum: ......

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Impulse: ......

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(2)

(ii) State the law of conservation of momentum.

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(2)

(iii) Using your definitions in (a)(i), deduce that linear momentum is constant for an object in equilibrium.

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(2)

A stationary radon-220 () nucleus undergoes α-decay to form a nucleus of polonium (Po). The α-particle has kinetic energy of 6.29 MeV.

(b) (i) Complete the nuclear equation for this decay.

® Po +

(2)

(ii) Calculate the kinetic energy, in joules, of the α-particle.

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(2)

(iii) Deduce that the speed of the α-particle is 1.74 × 107 m s–1.

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(1)

The diagram below shows the α-particle and the polonium nucleus immediately after the decay. The direction of the velocity of the α-particle is indicated.

(c) (i) On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay.

(1)

(ii) Determine the speed of the polonium nucleus immediately after the decay.

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(3)

(iii) In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c)(i).

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(2)

The half-life of the decay of radon-222 is 3.8 days and radon-220 has a half-life of 55 s.