[Maximum number: 7]

A2. This question is about radioactive decay.
(a) Describe the phenomenon of natural radioactive decay.
(b) A nucleus of americium-241 (Am-241) decays into a nucleus of neptunium-237 (Np-237) in the following reaction.

{ }_{95}^{241} \mathrm{Am} \rightarrow{ }_{X}^{237} \mathrm{~Np}+{ }_{2}^{4} \alpha

(i) State the value of X.
p
(ii) Explain in terms of mass why energy is released in the reaction in (b).
(iii) Define binding energy of a nucleus.
(iv) The following data are available.

Determine the energy released in the reaction in (b).

[Maximum number: 10]

This question is about the use of radioactive isotopes in medicine.

(a)

Distinguish between the biological half-life and effective half-life of a radioactive isotope.

[ 2 ]

(b)

The radioactive isotope iodine-131 undergoes beta decay to the stable isotope xenon-131 with a physical half-life of 8.0 days. Gamma radiation is also emitted in this decay. Iodine-131 is readily absorbed by the thyroid gland. The biological half-life is 21 days.

[ 5 ]

(i)

Calculate the effective half-life of iodine-131.

[ 2 ]

(ii)

Suggest why iodine-131 is often chosen to treat cancer of the thyroid gland.

[ 3 ]

(c)

Iodine-131 can be used to estimate the total blood volume of a patient.

A small amount of the isotope is dissolved in $8.0 \mathrm{~cm}^{3}$ of a solution. $4.0 \mathrm{~cm}^{3}$ of this solution is injected into the patient. After a few minutes a $5.0 \mathrm{~cm}^{3}$ blood sample is taken. The activity of this sample is measured to be 96 Bq .

The remaining $4.0 \mathrm{~cm}^{3}$ of the solution is mixed with $1000 \mathrm{~cm}^{3}$ of water. The activity of $5.0 \mathrm{~cm}^{3}$ of this solution is measured to be 510 Bq .

Estimate the total volume of blood in the patient.

J1. This question is about quarks.

[ 3 ]

[Maximum number: 5]

B1. This question is about plutonium as a power source.
Plutonium $\left({ }_{94}^{238} \mathrm{Pu}\right)$ decays by alpha emission. The energy of the alpha particle emitted is $8.8 \times 10^{-13} \mathrm{~J}$ . The decay constant of plutonium-238 is $8.1 \times 10^{-3} \mathrm{yr}^{-1}$ .
(a) Define decay constant.
(b) Plutonium-238 is to be used as a power source in a space probe.
(i) Determine the initial activity of plutonium such that the power released by plutonium is 6.0 W .
(ii) The power source becomes useless when the power released decreases to 4.0 W . Determine the time, in years, for which the power source can be used in the space probe.

[Maximum number: 6]

B2. This question is about nuclear energy levels and nuclear decay.
(a) The isotope bismuth-212 undergoes $\alpha$ -decay to an isotope of thallium. In this decay a gamma-ray photon is also produced. The isotope potassium-40 undergoes $\beta^{+}$ decay to an isotope of argon.

Outline how the
(i) $\alpha$ particle spectrum and the gamma spectrum of the decay of bismuth-212 give evidence for the existence of discrete nuclear energy levels.
(ii) $\beta^{+}$ spectrum of the decay of potassium-40 led to the existence of the neutrino being postulated.
(b) The isotope potassium-40 occurs naturally in many rock formations. In a particular sample of rock it is found that, out of the total number of argon plus potassium-40 atoms, 23 % are potassium-40 atoms.

Determine the age of the rock sample. The decay constant for potassium-40 is $5.3 \times 10^{-10} \mathrm{yr}^{-1}$ .

[Maximum number: 7]

This question is about binding energy and mass defect.

(a)

State what is meant by mass defect.

[ 1 ]

(b)

(i)

Data for this question is given below.

Binding energy per nucleon for deuterium $\left({ }_{1}^{2} \mathrm{H}\right)$ is 1.1 MeV .
Binding energy per nucleon for helium- $3\left({ }_{2}^{3} \mathrm{He}\right)$ is 2.6 MeV .
Using the data, calculate the energy change in the following reaction.

{ }_{1}^{2} \mathrm{H}+{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+\gamma

[ 2 ]

(ii)

The cross on the grid shows the binding energy per nucleon and nucleon number A of the nuclide nickel-62.

On the grid, sketch a graph to show how the average binding energy per nucleon varies with nucleon number A.

[ 2 ]

(iii)

State and explain, with reference to your sketch graph, whether energy is released or absorbed in the reaction in (b)(i).
This section consists of three questions: 4,5 and 6.

[ 2 ]

[Maximum number: 9]

This question is about binding energy and mass defect.

(a)

State what is meant by mass defect.

[ 1 ]

(b)

(i)

The nuclear mass of the nuclide helium- $3\left({ }_{2}^{3} \mathrm{He}\right)$ is 3.014931 u . Show that the binding energy per nucleon for the nuclide is about 2.6 MeV .

[ 2 ]

(ii)

The binding energy per nucleon for deuterium $\left({ }_{1}^{2} \mathrm{H}\right)$ is 1.11 MeV . Calculate the energy change in the following reaction.

{ }_{1}^{2} \mathrm{H}+{ }_{1}^{1} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+\gamma

[ 2 ]

(iii)

The cross on the grid shows the binding energy per nucleon and nucleon number A of the nuclide nickel-62.

On the grid, sketch a graph to show how the average binding energy per nucleon varies with nucleon number A.

[ 2 ]

(iv)

State and explain, with reference to your sketch graph, whether energy is released or absorbed in the reaction in (b)(ii).

[ 2 ]

[Maximum number: 10]

This question is about nuclear energy.

The graph shows the variation of binding energy per nucleon with nucleon number. The position for uranium-235 (U-235) is shown.

(a)

State what is meant by the binding energy of a nucleus.

[ 1 ]

(b)

(i)

On the axes, sketch a graph showing the variation of nucleon number with the binding energy per nucleon.

[ 2 ]

(ii)

Explain, with reference to your graph, why energy is released during fission of U-235.

[ 3 ]

(c)

U-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ can undergo alpha decay to form an isotope of thorium (Th).

[ 4 ]

(i)

State the nuclear equation for this decay.

[ 1 ]

(ii)

A sample of rock contains a mass of 5.6 mg of U-235 at the present day.

The half-life of U-235 is $7.0 \times 10^{8}$ years. Determine the initial mass of the U-235 if the rock sample was formed $3.9 \times 10^{9}$ years ago.

[ 3 ]

[Maximum number: 2]

The Feynman diagram shows electron capture.

(a)

Deduce that X must be an electron neutrino.

[ 2 ]

[Maximum number: 3]

This question is about nuclear power production.

(a)

Outline the reason why fuel enrichment is necessary for the fuel used in a commercial nuclear reactor.

[ 3 ]

(a)

(i)

Calculate, in $\mathrm{s}^{-1}$ , the decay constant of Au-198.

[ 1 ]

(ii)

A sample contains 5.0 mg of pure Au-198. Determine the mass of Hg-198 present in the sample after one week.

Gamma photons of the following frequencies are emitted in the decay of Au-198:

[ 2 ]

(b)

Explain how this observation provides evidence that nuclear energy levels are discrete.

[ 2 ]