| Date | May 2014 | Marks available | 5 | Reference code | 14M.2.SL.TZ1.5 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Define, Determine, and Draw | Question number | 5 | Adapted from | N/A |
Question
This question is in two parts. Part 1 is about nuclear reactions. Part 2 is about thermal energy transfer.
Part 1 Nuclear reactions
Part 2 Thermal energy transfer
(i) Define the term unified atomic mass unit.
(ii) The mass of a nucleus of einsteinium-255 is 255.09 u. Calculate the mass in MeVc–2.
When particle X collides with a stationary nucleus of calcium-40 (Ca-40), a nucleus of potassium (K-40) and a proton are produced.
\[{}_{20}^{40}{\rm{Ca + X}} \to {}_{19}^{40}{\rm{K + }}{}_1^1{\rm{p}}\]
The following data are available for the reaction.
(i) Identify particle X.
(ii) Suggest why this reaction can only occur if the initial kinetic energy of particle X is greater than a minimum value.
(iii) Before the reaction occurs, particle X has kinetic energy 8.326 MeV. Determine the total combined kinetic energy of the potassium nucleus and the proton.
Potassium-38 decays with a half-life of eight minutes.
(i) Define the term radioactive half-life.
(ii) A sample of potassium-38 has an initial activity of 24×1012Bq. On the axes below, draw a graph to show the variation with time of the activity of the sample.
(iii) Determine the activity of the sample after 2 hours.
(i) Define the specific latent heat of fusion of a substance.
(ii) Explain, in terms of the molecular model of matter, the relative magnitudes of the specific latent heat of vaporization of water and the specific latent heat of fusion of water.
A piece of ice is placed into a beaker of water and melts completely.
The following data are available.
Initial mass of ice = 0.020 kg
Initial mass of water = 0.25 kg
Initial temperature of ice = 0°C
Initial temperature of water = 80°C
Specific latent heat of fusion of ice = 3.3×105J kg–1
Specific heat capacity of water = 4200 J kg–1K–1
(i) Determine the final temperature of the water.
(ii) State two assumptions that you made in your answer to part (f)(i).
Markscheme
one twelfth of the mass of a carbon-12 atom/ \({}_6^{12}{\rm{C}}\);
Do not allow nucleus.
255.09×931.5 = 237600(MeVc−2 );
Award [1] for a bald correct answer.
energy must be given to supply this extra mass;
energy required for reaction=0.573(MeV);
kinetic energy=(8.326-0.573=)7.753(MeV);
Award [3] for a bald correct answer.
smooth curve through points;
=7.3×108(Bq)
Award [2] for a bald correct answer.
of liquid freezes (to become solid) at constant temperature / of solid melts (to become liquid) at constant temperature;
potential energy change is greater for vaporization than fusion / more energy is required to break bonds than to weaken them;
SLH vaporization is greater than SLH fusion;
Only award third marking point if first marking point or second marking point is awarded.
\(0.020 \times 3.3 \times {10^5} + 0.020 \times 4200 \times \left( {T - 0} \right) = 0.25 \times 4200 \times \left( {80 - T} \right)\);
T=68(°C);
Allow [3] for a bald correct answer.
Award [2] for an answer of T=74°(C) (missed melted ice changing temperature).
no energy absorbed by beaker;
no evaporation of water;
Examiners report
i) The definition of the unified atomic mass unit relates to the mass of the carbon 12 atom. Few candidates made this reference.
ii) Almost all were able to convert the mass unit into MeVc-2.
i) This was well answered with the majority of candidates identifying the neutron.
ii) Few could relate the mass defect to the energy required to initiate the reaction.
iii) Many were able to calculate the mass defect but did not realize that in this reaction it is the energy needed to initiate the reaction. This is why the products have more combined mass than the reactants.
i) The definition of radioactive half-life was often poorly done with few appreciating that half the radioactive nuclei decay into a more stable form. Those that explained that the activity of the sample would halve were more successful.
ii) Almost all were able to draw the decay curve.
iii) This was well answered with responses split between those that successfully found the number of half-lives elapsed in 2 hours and going on to find the activity of the sample and those that took the decay constant route. At SL, most successfully found the number of half lives elapsed in 2 hours and were able to find the corresponding activity of the sample.
i) The majority related the latent heat to the energy required for a change of state but few successfully completed the definition by explaining that fusion is the change of state between a solid and liquid at constant temperature.
ii) This explanation was poorly done with few gaining full marks. Few could relate the change in potential energy during a change of state to fusion and vaporization.
i) Of those candidates that established a relevant energy transfer equation, many did not include the heat gained by the ice once it had melted.
ii) Few could state two sources of energy loss that were not included in their energy equation.
