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EXEMPLIFYING EXAMINATION PERFORMANCE

GCE Physics

Introduction

These materials illustrate aspects of performance from the 2018 summer A2 examination series of CCEA’s revised GCE Specification in 2016.

Students’ grade A responses are reproduced verbatim and accompanied by commentaries written by senior examiners. The commentaries draw attention to the strengths of the students’ responses and indicate, where appropriate, deficiencies and how improvements could be made.

It is intended that the materials should provide a benchmark of candidate performance and help teachers and students to raise standards.

For further details of our support package, please visit our website at www.ccea.org.uk

Best wishes

Gavin Gray

Education Manager, Physics

Email: [email protected]

Telephone: 028 9026 1200 ext. 2270

http://www.ccea.org.uk/

mailto:[email protected]

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CCEA EXEMPLIFYING EXAMINATION PERFORMANCE

GCE: A2 Physics

Grade: A Exemplar

APH11: Momentum, Thermal Physics, Circular Motion, Oscillations and

Atomic and Nuclear Physics

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Q1a The graph in Fig. 1.1 shows how the binding energy per nucleon varies with the number of nucleons in the nucleus. Complete Fig. 1.1 by adding appropriate numerical values to the axes of the graph. [2]

Student’s response

Examiner’s comments

The majority of Grade A boundary candidates added the correct numerical values to the axes. Mark awarded: 2.

4


Q1b Describe the principles of fission and fusion. By referring to Fig. 1.1, explain how each process can lead to energy being released. [5]


Fusion is when two lighter nuclei of less binding energy per nucleus join to form a heavier nucleus with more binding energy per nucleon. The charge in binding energy per nuclea releases energy in the process. This occurs on the left side of the peak valve, 56. To the right side of the peak fission occurs. This is when a larger, unstable nucleus with less binding energy per nucleon decays into the lighter, more stable nuclei with more binding energy per nucleon. This change in binding energy per nucleon causes a release of energy with the process. Both fusion and fission release energy when the binding energy per nucleon increases.


The majority of Grade A boundary candidates gave correct descriptions of fission and fusion and explained energy release in terms of binding energy per nucleon. Reference to the graph was usually there but at times vague. Mark awarded: 5.

Q1c(i) Equation 1.1 shows an incomplete equation to describe a fission reaction. The number of neutrons that are released has been omitted.

How many neutrons are released in the reaction? Number of neutrons = ______________________ [1]


2

5


Q1c(ii) Equation 1.2 is another example of a fission reaction.

The mass of each nucleus and a neutron are given in Table 1.1.

Table 1.1 Nucleus Mass / u U-235 235.0439 Zr-94 93.9063 Te-139 138.9347 n 1.0086

Calculate the number of U-235 nuclei that need to undergo fission by the reaction in Equation 1.2 to produce 1 joule of energy.

Number of nuclei = ___________________ [5]


Number of nuclei = 3.60x1010


Grade A boundary candidates had no problem deducing the correct number of neutrons released in the reaction. The familiar calculation in (ii) was also well done by Grade A boundary candidates. Mark awarded: 1, 5.

6


Q2a Quality of written communication will be assessed in part (a) of this question.

The control rods and the moderator are two components of a fission reactor. State a material from which each component can be made and describe how they function to produce nuclear power in a safe manner. [6]


The control rods of the rector are made out of boron – coated steel, this is because boron is efficient at absorbing neutrons. The role of the control rods is to vary the rate of the fission reactions. To do this the rods are raised or lowered into the rector at different levels, this varies the number of neutrons which are being absorbed, and hence the number of neutrons available to carry out further fission reactions with other fuel particles. They also prevent an uncontrollable chain reaction occurring as if something goes wrong or is damaged the control rods drop and separate the sections of the fuel rods, stopping all fission reactions. The moderator, made usually from graphite, slows down the neutrons released from the fission reactions so that they have the correct energy to react with more 235 U particles causing further fission 92 When neutrons are released from fission reactions they are too fast to react further with U-235 and so during collisions with the graphite some of their kinetic energy is converted to heat energy and their speed is reduced So they can react with the U-235 causing fission.


Grade A boundary candidates in general gave detailed answers and knew the theory of the fission reactor well. They usually worked systematically through the parts of the question to achieve full marks. Mark awarded: 6.

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Q2b The use of fossil fuels in power stations causes considerable environmental pollution due to the gases produced. The government is considering several alternative sources of power.

State one advantage and one disadvantage that nuclear power has over the other alternatives to fossil fuel power. Advantage: Disadvantage: [2]


Advantage: It doesn’t rely on the elements to create power, so electricity can be generated everyday.

Disadvantage: An accident in a fission reactor could damage the local environment.


Most Grade A boundary candidates scored at least one mark here. Some were vague in their response, as this candidate, resulting in the loss of one mark. Mark awarded: 1.

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Q3a Gold foil was used in the historic alpha particle scattering experiment conducted by Geiger and Marsden. Gold has atomic number 79 and mass number 199. Calculate the radius of the nucleus of a gold atom. State your answer in metres. (r0 = 1.2 fm) Radius of gold atom = m [2]


Radius of gold atom = 7.01 x 10-15 m


Grade A boundary candidates usually answered this question confidently without the power error creeping in that was common in candidates below the boundary. Mark awarded: 2.

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Q3b(i) Fig. 3.1 shows an overhead view of part of the apparatus used in the alpha particle scattering experiment.

Complete Fig. 3.1 by drawing and labelling any additional apparatus that was used when Geiger and Marsden carried out the experiment. [2]


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Q3b(ii) Indicate, with the letter P, the position in which most alpha particles were detected in the experiment. [1]


Q3b(iii) Explain why the diameter of the container can be larger than 5 cm even though the range of alpha particles in air is less than 5 cm [1].


As the alpha particles caused the container walls to light up when they come into contact it was made of zinc sulfide.


The diagram was completed well by Grade A boundary candidates and most were awarded full marks here in all parts. Mark awarded: 1, 1, 1.

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Q3c Fig. 3.2 shows the path of an alpha particle as it approaches a nucleus.

The nucleus is replaced with one with a larger atomic number. On Fig. 3.2, sketch the new path taken by the alpha particle. [2]



It was typical of Grade A boundary candidates to realise that the bend would be greater but the bend was not shown starting earlier along the path. Mark awarded: 1.

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Q4a(i) Fig. 4.1 shows a fairground carousel where the horses move in a horizontal circle at a constant speed.

A 136 kg horse on the outside of the carousel travels in a circle of diameter 12.0 m. It takes 42 seconds for the horse to complete one full rotation. Use the definition of acceleration to explain why there must be a resultant force on the horse. [3]


Acceleration is the rate of change of velocity, however since the direction of the horse is continually changing and so even though it as constant speed, its velocity is continually changing. This means the acceleration is acting at right angles to the direction of the linear velocity of the horse and so acts towards the centre of the circle. This is part of the resultant force on the horse. The force is required to prevent the horse moving off at a tangent to the circle.


Grade A boundary candidates correctly defined acceleration and then usually discussed the change in direction causing a velocity change but often didn’t add to what was given in the stem of the question to achieve the third mark. Mark awarded: 2.

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Q4a(ii) Calculate the magnitude of the resultant force on the horse.

Force = ____________________ N [3] Student’s response

Force = 18.3 N


This calculation was usually correctly answered by Grade A boundary candidates. Mark awarded: 3.

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Q4b(i) On another fairground ride, the rollercoaster, a carriage and passengers of combined mass 1200 kg approaches a vertical circular section as shown in Fig. 4.2. The diameter of the circle is 38 m.

What is the minimum speed of the rollercoaster carriage for the passengers to feel weightless at the top of the loop? Speed = ______________________m s-1 [2]


Speed = 13.7 m s -1

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Q4b(ii) Describe what happens to the rollercoaster carriage if the speed is less than that calculated in (i). [1]


The carriage won’t make it round the loop.

Q4b(iii) If the rollercoaster carriage has fewer passengers and therefore less mass than in (i), how will the speed at which weightlessness is experienced be affected? [1]


It won’t be affected. It will remain 13.7 ms-1 as mass is indepent to the velocity of the carriage.


Again, the circular motion calculation was well done by most Grade A boundary candidates and they achieved full marks in (i). Many confused the minimum speed to cause weightlessness with the minimum speed to complete the loop and did not get the mark in (ii). Most answered (iii) well. Mark awarded: 2, 0, 1.

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Q5a(i) Equation 5.1 shows the relationship between the number of radioactive nuclei N left after time t. λ is the decay constant and N0 is the initial number of radioactive nuclei.

One isotope of copper, Cu-62, can be used for medical imaging. The isotope is injected into the bloodstream and then a scan is carried out to detect the gamma rays emitted. Fig. 5.1 shows a graph of the natural logarithm, Ln, of the percentage of radioactive Cu-62 nuclei remaining with time.

What is meant by the half-life of a radioactive source and why is it important to consider the half-life when a source is used for medical imaging? [3]

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the half life of a radioactive source is the time taken for the number of radioactive nuclei in a sample to decrease to half the original value. This is important in medical imaging to ensure the patient does not contain a high radioactive source for an extended time but the source has an appropriate half life to decay quickly and disintegrate without harming the body with unnecessary radiation levels.

Q5a(ii) Use Fig. 5.1 to calculate the half-life of Cu-62.

Half-life = _______________ minutes [3] Student’s response

Half-life = 9.6 minutes


Grade A boundary candidates usually correctly explained half-life and considered at least one of the factors that should be considered when using a source for medical imaging. The calculation in (ii) was well done by Grade A boundary candidates using a variety of methods. Mark awarded: 2, 3.

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Q5b After two hours the activity of the source has dropped to 0.46 Bq. Calculate the initial activity of the source.

Initial Activity = __________________ Bq [2]


Initial Activity = 2601 Bq


This calculation was very well done by most Grade A boundary candidates who can correctly deal with the ln function. Mark awarded: 2.

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Q6a The Young modulus is an important property of the material from which contact lenses are made. Comfortable wearing of a lens is achieved using a more flexible contact lens that drapes easily over the cornea, but a high degree of flexibility can be a disadvantage when trying to achieve optimum vision. The Young modulus of two types of contact lens is shown in Table 6.1.

Table 6.1

Contact Lens Young modulus / MPa Type 1 1.1 Type 2 0.49

Which contact lens would be most comfortable for the user?

Explain your answer. [1]


Type 2, as it has a lower Young modulus and is therefore described as being less stiff, and so more flexible.


Grade A boundary candidates correctly identified the correct type of lens and related the Young modulus to the flexibility. Mark awarded: 1.

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Q6b(i) To find a value for the Young modulus of a lens material, lenses made from the same material with powers ranging from −8.0 D to +4.0 D were tested.

What was the range of focal lengths of the lenses tested in centimetres? Focal lengths range from ______________ to cm ______________ [3]


Focal lengths range from 12.5 to -25 cm

Q6b(ii) Complete Table 6.2 for lenses with positive and negative power. [4]

Table 6.2

Power Type of lens Defect in vision that the lens is used to correct

negative positive


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Q6b(iii) In the test, a sample of the lens material that had a width of 2.5 mm and length of 12.0 mm, as shown in Fig. 6.1, was used. The Young modulus of one of the lenses tested was found to be 1.5 MPa. A force F of 4.2 mN in the direction shown produced a strain of 0.04.

Calculate the thickness t of the sample.

Thickness = ______________ m [5] Student’s response

Thickness = 2.8x10-8 m


Grade A boundary candidates usually correctly quoted the equation for power though some sign or 10n errors appeared in the answer to part (i). In part (ii) most scored at least 2 of the available marks. The calculation in part (iii) was very well done by most grade A boundary candidates who worked methodically through clear steps to reach the correct answer. Mark awarded: 1, 2, 2, 5.

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Q7a Describe an experiment to determine the specific heat capacity of a metal block. Include in your answer: • a diagram of the apparatus used that will ensure an accurate result, • the electrical circuit, • the measurements taken, • how the specific heat capacity is determined from the measurements.

[8]


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Measure the mass of the block. Cover the block with insulation so it is completely lagged. Measure the initial temperature. Turn on the heater and start the timer. Once the temperature rises by 20°C, turn off the heater. Record the time and temperature only when the block reaches the highest temperature. The oil improves the thermal conductivity between the block and the thermometer. Record values for Current and Voltage using the ammetre and voltmetre.

Q = McΔθ

Calculate energy transferred using Q = Current x voltage x time

Calculate the temperature change, Δθ, by subtracting the initial temperature from the final.

Clse C = Q to calculate the specific heat capacity MΔθ


Grade A boundary candidates drew well labelled diagrams showing the main apparatus. In their descriptions most key points were included but often the recording of the highest temperature after the stopclock was stopped was omitted or their descriptions were confused. Mark awarded: 7.

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Q7b A kettle with a 2700 W heating element is used to boil 750 cm3 of water. The water is initially at a temperature of 18 °C. Calculate the time taken for the water to boil if the heating element has an efficiency of 75%.

The specific heat capacity of water is 4.187 J g-1 °C-1 and its density is 1 g cm-3. Time = ________________ s [6]


Time = 95.4 s


Most Grade A boundary candidates coped well with the stages of this calculation but at times omitted one step, such as the efficiency, or used the 0.75 incorrectly. Mark awarded: 5.

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Q8a(i) A 0.25 kg mass on the end of a spring is pulled down a distance of 3 cm below equilibrium position and released so that it oscillates with simple harmonic motion. A graph of how the displacement of the mass varies with time is shown in Fig. 8.1.

Explain what is meant by simple harmonic motion. [2] Student’s response

The acceleration of a particle is directly proportional to it displacement from a fixed point and is directed towards that fixed point.

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Q8a(ii) Calculate the displacement of the mass at a time of 12.5 seconds and state whether the mass is above or below the equilibrium position at this time.

Displacement = _______________ m Position relative to equilibrium position = ________________ [6]


Displacement = 8.21x10-3 m

Position relative to equilibrium position = above equilibrium position

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Q8a(iii) Calculate the maximum strain energy stored in the spring.

Energy = _______________ J [4] Student’s response

Energy = 6.15x10-3 J


Simple harmonic motion was adequately explained by Grade A boundary candidates and few lost marks in part (i). The calculation in part (ii) was also usually correct with most boundary candidates also getting the position correct. Grade A boundary candidates found the calculation in (iii) more challenging, with many achieving 2 marks because they ignored the initial stretching of the spring when the load was applied. Mark awarded: 2, 6, 2.

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Q8b Describe how the maximum velocity of the mass could be determined from Fig. 8.1. [3]


The velocity could be determined from the displacement time graph by taking the gradient when the displacement is 0, since that is when velocity is greatest during SHM.


Grade A candidates answered this well, realizing that the gradient was required and identifying the point at which the velocity is maximum. Some did not mention drawing a tangent and lost one mark. Mark awarded: 2.

Q8c(i) Describe how the mass on the spring could be forced to resonate. [1] Student’s response

If the mass was oscillated at its natural frequency.

Q8c(ii) How can you tell that the mass on the spring is resonating? [1] Student’s response

The system will have a large amplitude.


Some descriptions of how the system could be forced to resonate from Grade A boundary candidates were weak and while they knew the term natural frequency they often ignored the forced oscillation requirement in (i). In part (ii) the idea of largest was often missing. Mark awarded: 0, 0.

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Q9a(i) What is the difference between the internal energy of a real gas and the internal energy of an ideal gas? [2]


the internal energy of a gas is equal to the sum of the kinetic and potential energies. However in an ideal gas there are no forces of attraction between the atoms and therefore there is no kinetic energy so the internal energy of an ideal gas is entirely kinetic energy.

Q9a(ii) For a real gas to behave more like an ideal gas how should the

pressure of the gas be adjusted? [1] Student’s response

Pressure should be reduced/decreased


Most Grade A candidates were correctly able to describe the difference between the internal energy of a real gas and an ideal gas in (i) and understood that the pressure should be lowered in (ii). Mark awarded: 2, 1.

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Q9b(i) Fig. 9.1 shows an airship with an envelope containing helium gas at a pressure of 1.03 × 105 Pa.

The envelope of the airship has a volume of 8230 m3. If the temperature of the gas is 14 °C, calculate the mass of helium in the envelope of the airship. The molar mass of helium = 4.003 × 10−3 kg mol−1. Mass of helium = kg [3]


Mass of helium = 1420 kg

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Q9b(ii) Calculate the root mean square speed of the helium gas atoms in the envelope of the airship.

Root mean square speed = _________________ m s-1 [3]


Root mean square speed = 1340 m s-1


The calculations in both (i) and (ii) proved straightforward for most Grade A boundary candidates and many got both parts correct despite their working out showing some confusion in (ii). Mark awarded: 3, 3.

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33


GCE: A2 Physics

Grade: A Exemplar

APH21: Fields, Capacitors and Particle Physics

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35


Q1a(i) The time constant of a resistor–capacitor (R–C) circuit can be determined using the circuit shown in Fig. 1.1.

Define the term time constant. [1] Student’s response

The time constant of a capacitor is the time taken for the voltage across the plates to reduce to 1 of its original value. e

Q1a(ii) Describe how the circuit in Fig. 1.1 could be used to obtain results that would allow the time constant to be determined. The capacitor is initially uncharged. [3]


Set the switch to position 1 to charge the capacitor up to the supply voltage. Using a stop clock set the switch to position 2 and start the clock. Obtain values for the voltage across the capacitor at 10s intervals. Plot a graph of time (x-axis) against voltage y-axis. Find 1/e = 0.368 of the intial voltage at this time will be the time constant τ


The majority of Grade A boundary candidates gave correct definitions of the time constant in part (i) and in part (ii) were able to correctly describe how the circuit could be used to obtain the required results. Mark awarded: 1, 3.

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Q1b(i) The results obtained in (a) (ii) can be used to plot a non-linear graph from which the time constant can be obtained. Label the axes on Fig. 1.2 and sketch the shape of the graph that you would expect to obtain. [2]


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Q1b(ii) Explain fully how you would use your graph to obtain a reliable value for the time constant of the circuit. [3]


Take the initial voltage Vo => y-interupt and find 1/e x Vo. At this voltage v1 this time on the x-axis is equal to τ Find 1/e2 x Vo and thus 2nd voltage V2 = 2τ. Take one more reading off the graph at 1/e3 x Vo and this is equal to 3τ for each point and average the three results.


Grade A boundary candidates usually drew the curve correctly in (i) and used the word reliable to prompt them to repeat and average readings from the graph to get the time constant in part (ii). Very few Grade A boundary candidates lost any marks in this question. Mark awarded: 2, 3. Q2a State Newton’s law of universal gravitation in words. [3] Student’s response

The force between two masses is directly proportional to the product of the masses and inversely proportional to the square of their separation.


Grade A boundary candidates scored at least 2 marks out of the possible 3 for stating Newton’s law. Some omitted the attractive nature of the force. Mark awarded: 2.

38


Q2b(i) CloudSat is a satellite orbiting Earth. It was launched by NASA in April 2006 to study the vertical structure of clouds and quantify their ice and water content.

Use the information in Table 2.1 to calculate the orbital height h of CloudSat above the Earth’s surface.

Table 2.1

Mass of Earth / kg 5.98 x 1024 Radius of Earth / km 6.37 x 103 Gravitational field strength at orbital height h / N kg-1 7.97

Orbital height h = _____________________________ m [4]


Orbital height h = 7.07 x 106 m

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Q2b(ii) Calculate the orbital period of CloudSat at this height. Give your answer in hours.

Orbital period = ________________________ hours [6]


Orbital period = 1.64 hours

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Q2b(iii) State, giving a reason, if CloudSat is a geostationary satellite. [1]


No – its orbital period is not equal to the period of rotation of earth (re 1.64 ≠ 24 hrs)


Most Grade A boundary candidates scored at least 3 marks in the calculation in part (i), often failing to do the subtraction at the end to get the height above the surface of the earth. Part (ii) was usually very well answered by Grade A boundary candidates, they had few problems with this calculation. Most got part (iii) correct and included the 24 hr reference. Mark awarded: 2, 3, 6, 1.

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Q3a(i) The Standard Model of particle physics is a theory concerning the four fundamental forces in nature and is used to classify all known subatomic particles that exist.

Complete Table 3.1 by naming the four fundamental forces in nature and their corresponding exchange particles. [4]

Fundamental force Exchange particle


Fundamental force Exchange particle

Gravitational Graviton

Strong nuclear force Gluon

Weak nuclear force W+, W- or ƻ bosons

Electrostatic Photon

Q3a(ii) Subatomic particles can be classified as hadrons or leptons. State two differences between hadrons and leptons. [2]


Leptons are fundamental particles with no internal structure whilst hadrons are non-fundamental with a quark structure. Hadrons experience the strong nuclear force whilst leptons do not.

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Q3a(iii) State the quark structure of a neutron. [1] Student’s response

udd

Q3a(iv) State the equations which describe β− decay in terms of quarks. Include the virtual exchange particle emitted. [2]



Grade A boundary candidates usually knew the forces and their corresponding exchange particles in part (i) but some lost a mark for errors in the naming of the force, using electrostatic in place of electromagnetic for example. In (ii) most managed to state two correct differences and the quark structure of a neutron was well known by these candidates inn part (iii). Many lost a mark in (iv) or gained no credit, the equations were known by some Grade A candidates but many of the boundary candidates made errors. Mark awarded: 3, 2, 1, 0.

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Q3b Consider two appropriate conservation laws to determine whether the hadron reaction described in Equation 3.1, which produces a pi-minus meson, can occur. Show your working clearly in the space below.

Can this reaction occur? _________________________ [3] Student’s response

Can this reaction occur? No


The correct conservation laws were chosen by most Grade A boundary candidates and they usually managed to deduce that the reaction would not occur and were convincing in their explanations. Mark awarded: 3.

44


Q4a A magnetic field exists around a conductor carrying an electric current. Sketch the shape of the field and indicate its direction due to the current carrying conductor shown in Fig. 4.1. The direction of the current is indicated by the arrow. [2]



Grade A boundary candidates usually correctly drew the shape of the field and identified the direction to get both marks. Mark awarded: 2.

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Q4b Two identical magnets, with opposite poles facing, are placed on a top pan balance. A wire is fixed so that it is parallel to the magnets and connected to a circuit as shown in Fig. 4.2a.

On Fig. 4.2a, draw an arrow to show the direction of the force on the wire when switch S is closed. [1]



Most grade A boundary candidates were able to use FLHR to correctly identify the direction of the force on the wire. Mark awarded: 1.

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Q4c(i) Before the switch was closed, an initial balance reading was taken. The switch was then closed and the readings on the ammeter and balance recorded. These readings are shown in Table 4.1.

Table 4.1

I / A m / g F / N

0 76.83

4.24 76.30

Complete the column headed F / N in Table 4.1 to determine the magnitude of the force exerted on the wire for a current of 4.24 A. [2]


I / A m / g F / N

0 76.83

4.24 76.30 0.7485

Q4c(ii) Determine the flux density of the magnets. The length of the magnets L, as shown in Fig. 4.2b, is 5.00 cm.

Flux density T _____________________________ [3]


Flux density 3.53 T

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Q4c(iii) A voltmeter is placed in parallel across the wire between points A and B and reads 0.41 V when the current through the wire is 4.24 A. Calculate the resistivity of the wire if its diameter is 0.18 mm.

Resistivity = ____________________________ Ω m [4]


Resistivity = 4.92 x 10-8 Ωm


Some grade A boundary candidates struggled to correctly calculate F, losing at least one mark for a 10n error or not calculating the difference in the balance readings in (i). Part (ii) was very well done by grade A boundary candidates using their answer to (i) and the calculation in (iii) also proved straightforward for most of these candidates. Mark awarded: 0, 3, 4.

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Q5a(i) Quality of written communication will be assessed in (a)(ii) of this question.

Fig. 5.1 is a simplified diagram of the National Grid. T1 and T2 are transformers.

What type of transformers are T1 and T2? Transformer T1: Transformer T2: [1]

Describe how a transformer is constructed.[2]


Transformer T1: step-up

Transformer T2: step-down

Describe how a transformer is constructed Primary and secondary coils of wire linked by a soft iron core.

49


Q5a(ii) Explain how transformer T2 works in order to produce an appropriate output voltage to our homes. [6]


The primary coil in T2 has many more turns in the wire compared to the secondary coil. The primary and secondary coil are linked by a soft iron core. An a.c. supply is attached to the primary coil, which produces a constantly alternating magnetic field where the secondary coil cuts the flux, an electromotive force is induced that goes on the supply voltage to our homes.


Grade A boundary candidates could correctly identify transformers T1 and T2 and described the construction of the transformer well to get full marks in part (i). In part (ii) they often lost some marks in their explanations which were at times vague or had key points missing. Mark awarded: 1, 2, 3.

Q5b Explain why high voltage transmission lines are necessary for energy to be transmitted across the country efficiently. [2]


Stepping up the voltage means stepping down the current (P = 1V). Lesser current means less energy loss since energy loss is given by the equation Ploss =12R.


This explanation was well written by most Grade A boundary candidates and the majority quoted the power lost equation in their answer. Mark awarded: 2.

50


Q6a Define electric field strength. [2] Student’s response

Electric field strength is the force acting per unit charge in an electric field.


Grade A boundary candidates knew the definition of electric field strength well and had no problem being awarded both marks. Mark awarded: 2

Q6b(i) Fig. 6.1 shows two point charges Q1 and Q2 of +25μC and +15μC placed a distance of 2 m apart in a vacuum.

Calculate the magnitude and direction of the force exerted on the +25μC charge. Force = ____________________ N Direction = _________________ [3]


Force = 0.84 N

Direction = Left

51


Q6b(ii) The resultant electric field strength is zero at point Z, a distance x from Q1.

Calculate the magnitude of x.

x = ____________________ m [4]


x = 1.13 m


Grade A boundary candidates usually correctly knew and applied the equation in part (i) and were able to deduce the direction. The calculation in part (ii) proved challenging for those below the Grade A boundary but most boundary candidates managed the mathematics of it to achieve full marks. Mark awarded: 3. 4.

52


Q7a(i) Fig. 7.1 shows the basic structure of a synchrotron. A synchrotron is an accelerator used to progressively increase the speed of particles as they travel in a circular path of fixed radius.

Describe how the circular path of fixed radius is achieved. [2] Student’s response

Electro-Magnets as the outside of the evacuated chamber contain the charged particles at progressively higher velocities by increasing their strength (voltage supplied) over time.

Q7a(ii) In this synchrotron the magnetic field is maintained using superconducting electromagnets.

Explain why superconductors are used to create the magnetic field and how the superconducting state is achieved. [4]


Superconducters have no resistance of extremely low temperatures. The magnets are thus cooled to extremely low temperature and then supplied with a high voltage. As the resistance is negligible the current flow is very high and hence a strong magnetic field is created which can contain the charged particlars even at very high velocities.

53


Q7a(iii) The acceleration cavities are connected to a high frequency alternating voltage. The frequency of this voltage is increased as the speed of the particles increases. Why is this necessary? [1]


In order to achieve synchronous acceleration the frequency of the AC current accelerating the particles must equal its frequency travelling from one cavity to the next. Hence AC current frequency is varied as the particle speeds up.

Q7a(iv) The particles can be accelerated until their speed approaches the speed of light. Explain how the particles can continue to gain kinetic energy but no longer increase their speed. [1]


As they approach the speed of light the increase in energy is in the form of an increase in mass rather than velocity. (Ke = ½ mv2 , ke oc M)


Grade A boundary candidates usually gained at least one mark in part (i) for the idea that the field strength needed to increase. The centripetal force was often omitted and the first mark not awarded. In part (ii) Grade A boundary candidates had most of the points but may have omitted one or two, usually either the method of cooling or the fact that a large magnetic field was required. The term synchronous acceleration was often used by Grade A boundary candidates in (iii) rather than explanations of what synchronous acceleration is. Most boundary candidates realized that an increase in mass caused the increase in kinetic energy and got part (iv) correct. Mark awarded: 1, 3, 1, 1.

54


Q7b Protons are accelerated through the accelerator complex at CERN in various stages before being transferred to the synchrotron known as the Large Hadron Collider (LHC) with an initial energy of 0.45 TeV. The LHC has 8 cavities each with a potential difference of 2 MV which accelerate the protons.

How many orbits of the LHC must a proton complete to reach a final energy of 7 TeV?

Number of orbits = _____________________ [5]


Number of orbits = 4.094 x 105


Grade A boundary candidates coped well with this challenging calculation and many managed to reach the correct answer although may not have used the steps described in the mark scheme. Mark awarded: 5.

55


Q8a(i) State Faraday’s law of electromagnetic induction. [1] Student’s response

The induced emf is equal to the rate of change of magnetic flux linkage.

Q8a(ii) A circular coil of wire is placed with its plane perpendicular to a magnetic field. The magnetic flux φ through the coil changes with time t as shown in Fig. 8.1.

Draw a graph to show how the e.m.f. E induced in the coil changes with time on the blank set of axes in Fig. 8.2. [4]



Faraday’s Law was well stated by Grade A boundary candidates and few lost the mark in part (i). It was common in part (ii) for Grade A boundary candidates to score 3 out of the 4 available marks, often having the e.m.f. reversed in sign or ignoring the relative amplitudes. Mark awarded: 1, 3.

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Q8b(i) A coil of wire with 340 turns, each of area 65 cm2, is placed within a uniform magnetic field of 55 mT. The coil is rotated through 500 revolutions per minute, inducing an alternating e.m.f. within the coils as shown in Fig. 8.3.

The e.m.f. induced in the coil is 0 V at times t1 and t2. By making reference to the position of the coil within the field explain why it is zero at these times. [3]


It is zero at these times as these are points where the coil is parallel to the field and is therefore producing no flux cutting, so no emf is induced.

Q8b(ii) Calculate the frequency of the alternating output.

Frequency = ___________________ Hz [1] Student’s response

Frequency = 8.33 Hz

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Q8b(iii) Calculate the maximum value of e.m.f.

Maximum e.m.f. = ______________________________ V [2] Student’s response

Maximum e.m.f = 6.36 V


Grade A boundary candidates often lost marks in part (i) and did not seem to understand the concept well. 1 mark was often awarded for ‘no flux being cut’ but the position of the coil was incorrect and the detail of the mark scheme missing. The calculations in parts (ii) and (iii) were very well done by Grade A boundary candidates. Mark awarded: 1, 1, 2.

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Q9a(i) A beam of electrons travelling horizontally enters a uniform magnetic field midway between two horizontal metal plates, in a vacuum. The plates are 175 mm long and have a separation of 30 mm. The potential difference applied across the plates is increased to 1.5 kV so that the electron beam just emerges past the end of the lower plate as shown in Fig. 9.1.

Determine the electric field strength between the plates. Electric field strength = __________________________ V m−1 [2]


Electric field strength = 50000 V m-1

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Q9a(ii) Determine the force on the electron beam due to the electric field.

Force = _______________________ N [2] Student’s response

Force = 8 x 10-15 N

Q9a(iii) Calculate the acceleration of an electron in the beam due to the electric field.

Acceleration = _______________________ m s−2 [1]


Acceleration = 8.78 x 1015 m s-2


The calculations in this question were very well done by most Grade A boundary candidates and they no problem achieving full marks in all three parts. Mark awarded: 2, 2, 1.

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Q9b(i) For this electron beam that just emerges past the end of the lower plate, calculate the time spent by the beam in the electric field.

Time = ______________________ s [3]


Time = 1.85x10-9 s

Q9b(ii) Calculate the initial speed of the electrons as they enter the field.

Initial speed = m s−1 [1]


Initial speed = 9.47 x 107 m s-1


Again, the calculations in both (i) and (ii) proved straightforward for most Grade A boundary candidates and many got both parts correct. Mark awarded: 3, 1.

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GCE: A2 Physics

Grade: A Exemplar

APH31: Practical Techniques and Data Analysis

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63


Q1a In this experiment you will investigate the oscillation of a bifilar pendulum. The arrangement consists of a half-metre rule suspended horizontally and symmetrically by two vertical threads of fixed length. The rule can be made to oscillate about a vertical axis through the centre of the rule.

Aims The aims of the experiment are: • to measure the time period of the oscillation of the bifilar

arrangement about a vertical axis, for various distances D; • to analyse the results and plot a linear graph; • to use the graph to find unknown constants.

Apparatus You are provided with a bifilar pendulum arrangement, made of two half-metre rules arranged horizontally, with a fixed vertical separation. The distance D between the suspension threads can be varied by moving the loops along the rules. The upper rule should remain securely clamped. Fig. 1.1 is a diagram of the arrangement.

The lower rule can be set into oscillation about the vertical axis, as shown in Fig. 1.2.

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This is best achieved by holding the rule lightly at its centre between finger and thumb and twisting gently. When you release the rule, it will execute horizontal oscillations of small angular amplitude about the central vertical axis.

Procedure Use the stop-clock provided to determine an accurate value of the period T of oscillation of the lower rule. The first distance D has been set at 14.0 cm, with the thread loops at 18.0 cm from each end of both upper and lower rules. Repeat the procedure for four further D values to a maximum of about 38.0 cm. Ensure that the threads are always at equal distances from each end of the rules, so the arrangement is symmetrical about the axis of oscillation. Record all your results in Table 1.1. Label and use the second column as necessary. [4]

Table 1.1

D /cm T /s 14.0


D /cm Time taken for 5 oscillations/s

T /s log10 (T/S) log10 (Dkm) 1 2 Average

14.0 11.03 11.34 11.2 224 0.35 1.15

18.0 8.84 8.69 8.77 1.75 0.24 1.26

24.0 6.57 6.72 6.65 1.33 0.12 1.38

28.0 5.72 5.78 5.75 1.15 0.06 1.45

38.0 4.81 4.78 4.80 0.96 - 0.01 1.58


Grade A boundary candidates usually had an adequate range of values D and were able to correctly obtain 5 sets of values recorded correctly. Some allowed the total time to drop to too low a value and lost a mark. Mark awarded: 3

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Q1b(i) Analysis

The period of this bifilar pendulum is described by Equation 1.1.

T = k D b Equation 1.1

where k and b are constants. Show that a graph of log10 T against log10 D will result in a straight line graph from which values of k and b can be determined. [2]


T = k D6

log10 T = log10 k + b log10 D

log10 T = b log10 D + log10 k

y = m x + c

Q1b(ii) State how b may be determined from the graph of log10 T against log10 D. [1]


B equal the gradient of the line of best fit


In part (i), Grade A boundary candidates had no problem correctly taking logs of the equation and mapping to the equation of a straight line. This usually lead to a correct answer in part (ii). Mark awarded: 2, 1.

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Q1c To draw the graph, it is necessary to calculate additional quantities from your results. Complete the final two blank columns of Table 1.1 with appropriate headings and values recorded to 2 decimal places. [4]


D /cm Time taken for 5 oscillations/s

T /s Log10 (T/S) Log10 (Dkm) 1 2 Average

14.0 11.03 11.34 11.2 224 0.35 1.15

18.0 8.84 8.69 8.77 1.75 0.24 1.26

24.0 6.57 6.72 6.65 1.33 0.12 1.38

28.0 5.72 5.78 5.75 1.15 0.06 1.45

38.0 4.81 4.78 4.80 0.96 -0.01 1.58


Grade A boundary candidates correctly headed the table, calculated the values and followed the instruction to record the values to 2 decimal places. Mark awarded: 4.

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Q1d Plot the graph of log10 T against log10 D on the grid of Fig. 1.3 below and draw the best fit straight line. [5]

The above question could not be exemplified as the candidate’s permission could not be obtained. Q1e Use your graph to determine the value of the constant b. Value of b: _________________ [4] Student’s response

grad = _ 0.25 − 0.025 0 1.48 − 1.25

grad = − 0.97826 …

b = gradp

b = −0.98

Value of b: −0.98


Grade A boundary candidates recognized that b was the gradient of the graph. They used suitable points to calculate the gradient and usually included the negative. Mark awarded: 4.

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Q2a In this experiment, you are provided with an illuminated object, a screen and a converging lens. When the screen and object are a suitable distance apart, there are two positions of the lens which will produce a sharp image on the screen. You will locate the two positions of the lens which give sharp images for different separations between the object and the screen.

Aims The aims are: • to adjust the position of the lens so that focussed images are formed; • to take measurements using the optical bench arrangement; • to plot an appropriate graph and use it to determine the focal length of a

converging lens. Apparatus Fig. 2.1 shows an illuminated object and a screen, separated by a distance y. The light box and metre rule are secured to the desk, and the lens holder and screen can be moved along the ruler. The distance x is the separation of the two positions of the lens at which sharp images are formed on the screen.

The relationship between x, y and the focal length of the lens f is given by Equation 2.1.

y2 − x2 = 4fy Equation 2.1

Procedure Place the screen at a distance of 640 mm from the object, this is the initial value of y. Place the lens between the object and screen and move it until a sharp image of the object is seen on the screen. Record this initial position of the lens (1) in Table 2.1. Move the lens along the metre rule until a second sharp image of the object is seen and record this second position of the lens (2) in Table 2.1.

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Calculate and record the distance x between these two positions. Repeat for four further values of y between 640 mm and 800 mm. [4]

Table 2.1

y /mm Lens position /mm

x /mm 1 2

640



x /mm x2/mm2 𝒙𝒙𝒙𝒙𝒚𝒚

/mm 1 2

640 279 373 94 8840 13.8

690 255 440 185 34200 49.6

740 232 513 281 79000 107

775 227 555 328 108000 139

800 220 584 364 132000 165


Grade A boundary candidates had no problem achieving full marks in this part. They correctly recorded the values to the nearest mm throughout. Mark awarded: 4.

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Q2b(i) Analysis

Use Equation 2.1 to show that a graph of y against will result in a straight line graph from which a value of the focal length can be determined. [2]


y2 – x2 = 4fy

x2 = – (4fy – y2)

x2 = – y2 – 4fy

x2 = – y(y – 4f)

y – 4f =

y = + 4f

y = mx + c

Q2b(ii) State how the value of f can be determined from the graph of

y against [1] Student’s response

4f = y- intercept of graph so find y- intercept and divide by 4 to get f

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Q2b(iii) Calculate any additional values needed to allow you to draw the linear graph described in (b) (i) and record these values in the blank columns of Table 2.1. Head any columns that you use with the appropriate quantity and unit. [2]



x /mm x2/mm2 𝒙𝒙𝒙𝒙𝒚𝒚

/mm 1 2

640 279 373 94 8840 13.8

690 255 440 185 34200 49.6

740 232 513 281 79000 107

775 227 555 328 108000 139

800 220 584 364 132000 165


The equation proved difficult to rearrange for many candidates below the boundary but most Grade A boundary candidates managed to get it correct in part (i) leading to a correct answer in part (ii) for how the value of f can be determined. In (iii) these candidates headed the table correctly and usually recorded the values to the correct significance. Mark awarded: 2.

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Q2c(i) Use the grid of Fig. 2.2 to plot the graph of y against .

The vertical axis has been labelled and a scale added for you. Label the horizontal axis and select a suitable scale starting from zero. Plot the values from Table 2.1. Draw the best fit straight line for the points plotted. [5]

The above question could not be exemplified as the candidate’s permission could not be obtained. 2c(ii) Use your graph to calculate a value for the focal length f of

the lens.

f = _________________ mm [3] Student’s response

y – intercept = 627.5 = 4f

f =

f = 156.875

= 157 mmp

f = 157 mm

627.5 4

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Sf

f

Q2c(iii) Use the points on your graph to calculate the percentage uncertainty in f.

% uncertainty in f = ___________________ % [3]


645 – 627.5 = 17.5 mm

% f = x 100

= x 100

627.5p

= 11.14%

% uncertainty in f = 11.1 %


Some may have lost a mark for a poorly chosen best fit line. The value of the focal length was usually correct and within the acceptable range to be awarded the quality mark in part (ii). There was sometimes confusion in calculating the percentage uncertainty between using the intercept values and the focal length values. Mark awarded: 3, 2.

17.5

157

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75


GCE: A2 Physics

Grade: A Exemplar

APH32: Practical Techniques and Data Analysis

76


77


Q1a(i) The electrical resistance R of a component may be determined by measuring the potential difference across the component and the current flowing through it. In one experiment, the component was connected across a fixed 4.5 V d.c. supply, and an ammeter and a voltmeter were placed in the circuit, as in Fig. 1.1 below.

The analogue voltmeter display is shown in Fig. 1.2 below. It has a dual scale facility, which means that by connecting across one pair of terminals, the meter reads up to a maximum of 10 volts (the upper scale) and by connecting across the other pair of terminals, the meter reads up to a maximum of 5 volts (the lower scale). The correct scale must be chosen before deciding on the voltage measurement.

Using all the information you have been given, decide which scale was being used in this case. Give a reason for your choice. Scale (10 volt or 5 volt): ________________ Reason _____________________________ [1]

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Scale (10 volt or 5 volt): 5 volt

Reason the supply is fixed 4.5V so using the 5 volt allows for more accurate readings with smaller 0.1 divisions compared to 10 volt having 0.2 division

Q1a(ii) Using the scale you have chosen, state the voltage reading and the absolute uncertainty associated with the reading.

Voltage __________ ± __________ V [2]


Voltage 4.0 ± 0.1 V


Grade A boundary candidates often chose the correct scale but did not give the correct reason, focusing on the accuracy of the scale rather than the values on the ammeter. Most correctly quoted the voltage to 0.1 V and gave the uncertainty. Mark awarded: 0, 2.

Q1b(i) A digital ammeter was used, and it gave a reading of 0.23 amps.

What is the absolute uncertainty associated with this reading? Uncertainty in current = ± __________ A [1]


Uncertainty in current = ± 0.01 A

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Q1b(ii) Use the voltage and current readings to calculate a value for the resistance of the component and the absolute uncertainty in this value.

Resistance = ________ ± __________ Ω [4]


Resistance = 17.4 ± 1.2 Ω

Q1b(iii) Why is it better to refer to an ‘uncertainty’ rather than an ‘error’

associated with this reading? [2] Student’s response

Error implies the value is wrong. Uncertainty implies the value is accurate to with a certain range.


In part (i), Grade A boundary candidates had no problem stating the uncertainty in the current. Calculating the resistance was correctly done by these candidates although answers weren’t always given to the correct number of significant figures. The uncertainty was also usually correct. In part (iii) most Grade A boundary candidates correctly identified the difference between an error and an uncertainty. Mark awarded 1, 4, 2.

80


Q1c The fixed d.c. supply is replaced with a variable d.c. supply. Explain how you would use this and why it ensures your value for the resistance of the component is both reliable and accurate. [3]


You would adjust the supply voltage on the variable power pack and record different I and V values for different supply voltages. By repeating, multiple values of R can be calculated, and averaged, to find an accurate and reliable value for R.


Grade A boundary candidates usually obtained at least 2 out of the 3 available marks. They described the use of the variable d.c. supply to obtain a series of results and averaged but sometimes omitted the identification and discarding of anomalous results. Mark awarded: 2.

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Q2a(i) A pendulum undergoes simple harmonic motion after it has been displaced to one side and allowed to swing freely. A motion sensor is used, so that a graph of displacement s against time t for two complete oscillations can be displayed. An example of such a graph is shown in Fig. 2.1.

By finding the gradient of a tangent to the curve, use Fig. 2.1 to determine the size of the maximum velocity of the pendulum. State one time at which this maximum value of velocity occurs. Maximum velocity = __________ cm s−1 occurs at s __________ [3]


Maximum velocity = 80 cm s-1

Occurs at 1.5 s

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Q2a(ii) Determine the minimum velocity of the pendulum. State one time at which this occurs.

Minimum velocity = __________ cm s−1 occurs at __________ s [2]


Minimum velocity = 0 cm s−1

occurs at 2 s


Most Grade A boundary candidates correctly drew a gradient in part (i) and were able to calculate the maximum velocity. The time was usually identified correctly. In part (ii) these candidates usually identified the minimum velocity as zero and knew when it would occur. Mark awarded: 3, 2.

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Q2b(i) The same pendulum is set in motion a second time, with a smaller initial displacement than before.

On Fig. 2.1, sketch the graph of displacement s against time t for this new motion. [2]


Q2b(ii) How will the magnitude of maximum velocity for this second motion of the pendulum compare to the maximum velocity of the original motion shown in Fig. 2.1? [1]


It will be smaller


The sketch of the graph was correctly done by Grade A boundary candidates in part (i) and they correctly identified that the maximum velocity would be reduced to achieve the mark in part (ii). Mark awarded: 2, 1.

84


Q3(i) A cathode ray oscilloscope, CRO, is used to measure the frequency of sound waves produced by a vibrating tuning fork. The signal from a microphone is connected across the y-input of the CRO.

Fig. 3.1 shows the display from the CRO screen while the tuning fork is sounding.

From the CRO display, determine the frequency of tuning fork being used. The screen is 10 cm wide. The timebase is set to 1.5 ms cm−1. Frequency = __________ Hz [4]


Frequency = 0.5 Hz

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Q3(ii) The y-sensitivity is set at 2 mV cm−1. What is the peak voltage of the display?

Voltage = __________ mV [1]


Voltage = 7 mV

Q3(iii) How would you expect the display to change over time, as the tuning fork continues to sound? [1]


The time period would increase, meaning the waves would be more spread out across the screen.

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Q3(iv) On Fig. 3.2 sketch the display you would see if the timebase is switched off. [2]



Grade A boundary candidates were familiar with the calculation in part (i) but often made a 10n error and lost one mark. Part (ii) was well answered with most boundary candidates reading the scale correctly. In part (iii) the Grade A boundary candidate sometimes discussed a changed in period or frequency and were not awarded this mark. Part (iv) was well answered by Grade A boundary candidates who understood the function of the timebase. Mark awarded: 3, 1, 0, 2.

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Q4a(i) Geiger and Nuttall proposed a theory relating the half-life t 12 in seconds of an alpha emitting nuclide to the energy E in MeV of the emitted alpha particle. The theory is expressed in Equation 4.1.

State what the unit abbreviation MeV stands for. [1] Student’s response

Mega electron volts

Q4a(ii) State the unit of each of the constants A and B in Equation 4.1. If they do not have a unit write ‘no unit’.

Unit of A = __________ Unit of B = __________ [2]


E -½

0

MeV -½ Ñ MeV -½

Unit of A = MeV ½

Unit of B = no unit


Grade A boundary candidates were usually able to correctly state what MeV stood for in part (i). Part (ii) proved more challenging, candidates below the Grade A boundary often included seconds in their answers. The Grade A boundary candidates usually did manage to get to the correct unit. Mark awarded: 1, 2.

MeV 1

run rise

MeV -½ no unit

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Q4b(i) Table 4.1 gives experimental values of E and t ½ for some alpha emitting nuclides. Values for E−½/MeV−½ and log10(t½/s) have been calculated.

Table 4.1

Nuclide E/McV t½/s E-½/MeV-½ log10(t½/s)

238U 4.20 1.4 x 1017 0.488 17.15

234U 4.82 7.7 x 1012 0.455 12.89

229Th 5.42 6.0 x 107 0.430 7.78

208Rn 6.14 1.5 x 103 0.404 3.18

212Po 7.39 1.8 x 10-3 0.368 -2.74

Have the values of E−½/MeV−½ been recorded correctly in Table 4.1? Explain your answer. [1]


Yes, they have been given to 3 significant figures, the same accuracy as the E/MeV values.

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Q4b(ii) On the graph grid of Fig. 4.1 draw a graph of log10(t½/s) against E−½/MeV−½. Scale the axes appropriately, plot the points and draw the best fit line. [6]



In part (i) Grade A boundary candidates knew that the number of significant figures was correct and gave the correct reason. Graphs were usually well drawn in part (ii) and best fit lines appropriate. Mark awarded: 1, 6.

90


Q4c(i) Table 4.2 gives two values of E.

Table 4.2

E/MeV E-½ /MeV-½ Log10(t½/s)

4.53

7.20

Enter the corresponding values for E− 12 in the second column of Table 4.2. [2]



4.53 0.470

7.20 0.373

Q4c(ii) According to the Geiger and Nuttall proposed theory in Equation 4.1,

A = 148 and B = 53.5. Use these values and Equation 4.1 to calculate the Geiger and Nuttall theoretical values for log10(t½/s).

Enter the values in the third column of Table 4.2. [2]



4.53 16.06

7.20 1.70

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Q4c(iii) On the graph grid of Fig. 4.1 plot the two theoretical points from Table 4.2 and join the points by a straight line. Label this line GN. This line is a graphical representation of the Geiger–Nuttall law. [2]



In part (i) Grade A boundary candidates usually calculated the values correctly and were awarded both marks. Likewise in part (ii) these candidates had no problems using the equation to calculate the log t values. Points were plotted correctly in part (iii) and the GN line drawn accurately. Mark awarded: 2, 2, 2.

92


Q4d(i) You should find that your line from the experimental results is not in very good agreement with the line GN. The values of A and B do not work well for the nuclides listed.

Use your graph to determine a numerical value for A which corresponds with the experimental data in Table 4.1. A = __________ [3]

Student’s response=

A = grad

= 17 – 0 0 0.48 – 0.38

= 170

A = 170

Q4d(ii) Determine the percentage difference in the numerical value for A that corresponds to the experimental data in Table 4.1 and the numerical value of 148 proposed by Geiger and Nuttall.

Percentage difference = __________ % [2]


170 – 148 = 22

% A = 22 2 14.86%

= 14.8649%

Percentage difference = 14.9 %


Grade A boundary candidates correctly identified the gradient as a value for A and were able to use their graph to get a value within the acceptable range in part (i).

% A = X 100

93


These candidates had no problem with part (ii), the percentage difference calculation being familiar to them and helped by the fact that comparison to either 148 or their gradient value was acceptable in this case. Mark awarded: 3. 2.

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