(i) Determine the diameter that will be required for the turbine blades to achieve the maximum power of 0.75 MW.

(ii) State one reason why, in practice, a diameter larger than your answer to (a)(i) is required.

(iii) Outline why the individual turbines should not be placed close to each other.

(iv) Some members of the community propose that the wind farm should be located at sea rather than on land. Evaluate this proposal.

Currently, a nearby coal-fired power station generates energy for the community. Less coal will be burnt at the power station if the wind farm is constructed.

(i) The energy density of coal is 35 MJ kg^–1. Estimate the minimum mass of coal that can be saved every hour when the wind farm is producing its full output.

(ii) One advantage of the reduction in coal consumption is that less carbon dioxide will be released into the atmosphere. State one other advantage and one disadvantage of constructing the wind farm.

(iii) Suggest the likely effect on the Earth’s temperature of a reduction in the concentration of atmospheric greenhouse gases.

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

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

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

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

(i) State the nuclear equation for this decay.

(ii) Define the term radioactive half-life.

(iii) 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\( \times \)10⁸ years. Calculate the initial mass of the U-235 if the rock sample was formed 2.1\( \times \)10⁹ years ago.

(i) total wind power required \( = \frac{{750000}}{{0.3}}\);

maximum wind power required per turbine, \(P = \frac{{750000}}{{5 \times 0.3}}\left( { = 500{\rm{kW}}} \right)\);

\(d = {\left( {\frac{{8P}}{{\rho \pi {v^3}}} = } \right)^{\frac{1}{2}}}40({\rm{m}})\)

Award [1 max] for an answer of 48.9 (m) as it indicates 5 and 0.3 ignored.
Award [2 max] for 22 (m) as it indicates 0.3 ignored.
Award [2 max] for 89 (m) as it indicates 5 ignored.

(ii) not all kinetic energy can be extracted from wind / losses in cables to community / turbine rotation may be cut off/“feathered” at high or low wind speeds;
Do not allow “wind speed varies” as question gives the average speed.

(iii) less kinetic energy available / wind speed less for turbines behind; turbulence/wake effect; (do not allow “turbines stacked too close”)

(iv) implications: average wind speeds are greater / more space available;
limitations: installation/maintenance cost / difficulty of access / wave damage;
Must see one each for [2].

(i) mass of coal per second (=0.0214 kg);
77.1 (kg);
or
energy saved per hour=0.75×3600 (=2700MJh^-1) ;

mass of coal saved \( = \left( {\frac{{2700}}{{35}} = } \right)77.1({\rm{kg}})\);

Award [2] for a bald correct answer.

(ii) advantage:
energy is free (apart from maintenance and start-up costs) / energy is renewable / sufficient for small community with predominance of wind / supplies energy to remote community / independent of national grid / any other reasonable advantage;
Answer must focus on wind farm not coal disadvantages.

disadvantage:
wind energy is variable/unpredictable / noise pollution / killing birds/bats / large open areas required / visual pollution / ecological issues / need to provide new infrastructure;

(iii) greenhouse gas molecules are excited by/absorbed by/resonate as a result of infrared radiations; { (must refer to infrared
not “heat”)
this radiation is re-emitted in all directions;
less greenhouse gas means less infrared/heat returned to Earth; { (consideration of return direction is essential for mark)
temperature falls (to reach new equilibrium);

energy released when a nucleus forms from constituent nucleons / (minimum) energy needed/work done to break a nucleus up into its constituent nucleons;
Award [0] for energy to assemble nucleus.
Do not allow “particles” or “components” for “nucleons”.
Do not accept “energy that binds nucleons together” OWTTE.

(i) generally correct shape with maximum shown, trending down to U-235;
maximum shown somewhere between 40 and 70;
Award [0] for straight line with positive gradient from origin.
Award [1] if maximum position correct but graph begins to rise or flatlines beyond or around U-235.

(ii) identifies fission as occurring at high nucleon number / at right-hand side of graph;
fission means that large nucleus splits into two (or more) smaller nuclei/nuclei to left of fissioning nucleus (on graph);
(graph shows that) fission products have higher (average) binding energy per nucleon than U-235;
energy released related to difference between initial and final binding energy;
Award [2 max] if no reference to graph.

(i) \({}_{92}^{235}{\rm{U}} \to {}_{90}^{231}{\rm{Th}} + {}_2^4\alpha \); (allow He for \(\alpha \); treat charge indications as neutral)

(ii) time taken for number of unstable nuclei/(radio)activity to halve;
Accept atom/isotope.
Do not accept mass/molecule/amount/substance.

(iii) three half-lives identified;
45 (mg);
Award [2] for bald correct answer.