IBPhysicsDPSLExam QuestionsSynoptic AssessmentSynoptic Exam Questions (Paper 2)

Synoptic Exam Questions (Paper 2) (DP IB Physics: SL): Exam Questions

2 hours5 questions
1a
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The radioactive isotope uranium−238 decays in a decay series to the stable lead−206. 

The half−life of U presubscript 92 presuperscript 238 is 4.5 × 109 years, which is much larger than all the other half−lives of the decays in the series.

A rock sample, when formed originally, contained 6.0 × 1022 atoms of U presubscript 92 presuperscript 238 and no Pb presubscript 82 presuperscript 206 atoms. At any given time, most of the atoms are either straight U presubscript 92 presuperscript 238 or Pb presubscript 82 presuperscript 206 with a negligible number of atoms in other forms in the decay series.

Sketch on the axes below the variation of number of U presubscript 92 presuperscript 238 atoms and the number of Pb presubscript 82 presuperscript 206 atoms in the rock sample as they vary over a period of 1.0 × 1010 years from its formation. Label the lines U and Pb.

7-1-ib-sl-hard-sqs-q4a-question

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1b
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A certain time, t, after its formation, the sample contained twice as many U presubscript 92 presuperscript 238 atoms as Pb presubscript 82 presuperscript 206 atoms. 

Show that the number of straight U presubscript 92 presuperscript 238 atoms in the rock sample at time t was 4.0 × 1022.

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1c4 marks

Lead−214 is an unstable isotope of lead−206. It decays by emitting a beta to the power of minus particle to form bismuth−214 (Bi) 

Bismuth is also unstable and has two decay modes: 

  • Emitting an α particle to form thallium−210 (Tl) + energy

  • Emitting a β particle to form polonium−214 (Po) + energy

(i) Write decay equations for the decay chain of lead−214 to thallium−210 and to polonium−214.

[3]

(ii) Outline the nature of the energy released during this process.

[1]

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1d3 marks

Natural uranium consists of 99.3% straight U presubscript 92 presuperscript 238 and 0.7% straight U presubscript 92 presuperscript 235.

To be used as fuel in a nuclear reactor, natural uranium must be enriched and enclosed in sealed metal containers. The process of enrichment involves increasing the amount of fissile uranium.

Suggest why

(i) natural uranium is not suitable for use as nuclear fuel

[1]

(ii) enrichment is favoured over chemically separating the isotopes from each other.

[2]

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1e
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When a uranium–235 nucleus undergoes fission, one of the possible reactions is: 

straight U presubscript 92 presuperscript 235 space plus space straight n presubscript 0 presuperscript 1 rightwards arrow Xe presubscript 54 presuperscript 139 space plus space Sr presubscript 38 presuperscript 95 space plus space 2 straight n presubscript 0 presuperscript 1 space left parenthesis plus energy right parenthesis

The binding energy per nucleon, E, is given in the table below: 

Nuclide

E / MeV

straight U presubscript 92 presuperscript 235

7.60

Xe presubscript 54 presuperscript 139

8.39

Sr presubscript 38 presuperscript 95

8.74

A 1500 MW nuclear reactor, operating at 27% efficiency, uses enriched fuel containing 3% uranium–235 and 97% uranium–238. The molar mass of uranium−235 is 0.235 kg mol–1.

Estimate the total mass of original fuel required per year in the nuclear reactor. 

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1f
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Determine the number of fission reactions per day in the nuclear reactor assuming the production of power is continuous. 

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1g
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A nuclear fusion power station uses water as a coolant in its primary cooling circuit. The water enters the reactor core at a temperature of 280°C and absorbs thermal energy from the fusion reactions. The water has a mass flow rate of 2500 kg s-1 and exits the reactor core at 320°C before entering a heat exchanger.

Diagram of a nuclear power plant showing the flow from reactor pressure vessel through steam generator, turbine, electric generator, and cooling tower.

In the steam generator, the water from the primary circuit cools from 320 °C back to 280 °C, and is used to convert secondary circuit water at 25 °C into steam at 100 °C. The specific heat capacity of water is 4200 J kg-1 K-1, and the specific latent heat of vaporisation of water is 2.26 × 106 J kg-1.

Determine the mass of steam that can be produced per second.

Assuming that all the thermal energy from the primary circuit water is transferred to the secondary circuit water, and no thermal energy is lost to the surroundings.

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2a
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A ballistic pendulum is used to determine the speed of a projectile. A projectile of mass m space equals space 0.050 space kg is fired into a large block of wood of mass M space equals space 2.50 space kg, which is suspended by a light wire of length 2.00 space straight m. The projectile embeds itself in the block, and the combined system swings upwards.

Diagram showing two stages of a ballistic pendulum collision; left: a mass m moving towards block M at speed v, right: combined mass M+m moving at speed V, swinging to height h.

(i) The collision between the projectile and the block is inelastic.

State what is meant by an inelastic collision and explain why momentum is conserved, but kinetic energy is not.

[3]

(ii) Immediately after the collision, the combined block and projectile system moves with a common speed V. The projectile's initial speed was v.

Show that V space equals space fraction numerator m v over denominator m space plus space M end fraction​.

[2]

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2b
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After the collision, the system swings up to a maximum vertical height h.

The swing can be assumed to be frictionless.

(i) By considering the conservation of energy after the collision, derive an expression for the speed V in terms of g and h.

[2]

(ii) The system swings through an angle theta space equals space 25.0 degree to reach the maximum height h.

Determine the height of the swing.

[2]

(iii) Calculate the initial speed of the projectile.

[3]

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2c3 marks

The following graph shows the velocity of the oscillation as a function of time if the pendulum system were to oscillate in simple harmonic motion.

Graph of sinusoidal wave showing velocity in metres per second against time in seconds. Peaks at Vmax, with labelled points at t0, 2t0, 3t0, and 4t0.

On the axes below, sketch the graph for the acceleration of the pendulum system as a function of time, assuming simple harmonic motion.

Graph with labelled axes. Y-axis: Acceleration (m/s^2), 0 to a_max. X-axis: Time (s), 0 to 4t₀. Vertical and horizontal grid lines are present.

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2d5 marks

In reality, the pendulum system would not oscillate in simple harmonic motion. Use the idea of damping to explain why this is the case.

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3a3 marks

An experiment to determine the charge of an electron is shown.   

ib-sl-5-1-sq-4a-question

Oil drops are sprayed into a chamber above two parallel metal plates which are separated by a distance d. The oil drops become charged before entering the region between the plates.

A potential difference V is applied between the plates.

(i) Explain why the oil drops become charged.

[1]

(ii) Draw the electric field lines between the plates.

[2]

ib-practice-paper-2-set-a-question-9a

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3b4 marks

An oil drop is observed to be stationary between the plates when the potential difference is V subscript 1. When the potential difference is increased to V subscript 2, the drop is observed to move upwards with a constant velocity v.

(i) State the sign of the charge on the oil drop.

[1]

(ii) Draw the forces acting on the oil drop when V space equals space V subscript 1 and when V space equals space V subscript 2.

[3]

ib-practice-paper-2-set-a-question-9b

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3c3 marks

Show that the electric charge on the oil drop is given by

q space equals space fraction numerator 6 straight pi eta r v d over denominator V subscript 2 minus V subscript 1 end fraction

where eta is the viscosity of air and r is the radius of the oil drop.

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3d
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The following measurements are made for the oil drop:

  • V subscript 1 space equals space 115 space straight V

  • V subscript 2 space equals space 715 space straight V

  • v space equals space 0.220 space mm space straight s to the power of negative 1 end exponent

  • r space equals space 1.29 space straight mu straight m

The viscosity of air between the plates is eta space equals space 1.8 cross times 10 to the power of negative 5 end exponent space Pa space straight s and the separation of the plates is d space equals space 6.0 space mm.

Deduce, using the equation in part (c), whether the value of the charge for the oil drop is consistent with the currently accepted value of the elementary charge.

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3e
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The voltage supply connected to the parallel plates is switched off. The oil drop falls with a constant velocity v subscript 0.

Show that v subscript 0 over v is about 0.2.

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3f2 marks

The oil drop collides with another oil drop of charge +14e, where e is the elementary charge.

Deduce the net charge on each oil drop after the collision.

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4a4 marks

When scientists develop climate models for planets other than Earth, the value of the solar constant S must be adjusted.

(i) Explain why S is a constant and how it can be adjusted for different planets in the Solar System.

[2]

(ii) Outline two assumptions made in the calculation of solar constant.

[2]

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4b5 marks

Different climate models consider the energy absorbed by the Earth with and without an atmosphere.

(i) Explain why the average power absorbed per unit area of the Earth is less than S in both models.

[2]

(ii) Draw an energy balance diagram to illustrate the model in which Earth has no atmosphere. 

[2]

 

ib-practice-paper-2-set-b-question-9b

(iii) Discuss one limitation of this model in terms of the greenhouse effect.

[1]

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4c6 marks

A simplified energy balance model of the Earth with an atmosphere is shown in the diagram.

VZ_axXLP_ib-practice-paper-2-set-b-question-9c

In this model, the Earth's surface is assumed to be a black body radiator at constant temperature T subscript S. It receives both solar radiation and radiation emitted from the atmosphere. The atmosphere is modelled as a body with albedo alpha and average equilibrium temperature T subscript A space equals space 242 space straight K.

(i) Draw arrows to show the energy exchanges between the Earth's atmosphere and surface.

[1]

(ii) Determine the value of alpha used in this model.

[1]

(ii) Calculate the average equilibrium temperature of the Earth's surface T subscript S. 

[4]

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4d3 marks

Carbon dioxide and water vapour are both known to be greenhouse gases.

Compare and contrast the roles of carbon dioxide and water vapour in the greenhouse effect. 

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4e2 marks

Suggest why the burning of fossil fuels may lead to an increase in global warming by the enhanced greenhouse effect.

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5a4 marks

In a comparison of two stars, A and B, the following data was collected

Surface temperature of star A = 25 000 K

Surface temperature of star B = 4300 K

The radius of star B was determined to be 1.1 × 105 times larger than the radius of star A.

(i) Outline what is meant by the luminosity of a star.

[1]

(ii) Calculate the ratio of the luminosity of star B to the luminosity of star A.

[3]

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5b
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Determine the wavelengths of light for which the maximum rate of emission occurs from stars A and B.

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5c4 marks

The graph shows the variation of rate of emission against wavelength for the Sun.

25-1-3d-m-25-1-wien-displacement-graph-sun-star-a-b-cie-ial-sq

On the graph, sketch the variation of rate of emission against wavelength for stars A and B.

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5d
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Under the right conditions, four hydrogen nuclei can fuse to make a helium nucleus in a process known as the proton–proton cycle.    

Nuclei

Mass/ u

straight H presuperscript 1

1.0078

He presuperscript 4

4.0026

Show that 4 × 10–12 J of energy is released as a result of the fusion of four hydrogen nuclei.

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5e2 marks

Fusion occurs naturally in the core of stars.

Explain why very high densities of matter and very high temperatures are needed to bring about and maintain nuclear fusion in stars.

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5f
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While on the main sequence, the Sun maintains a constant luminosity of 3.86 × 1026 W. It is predicted that the Sun will spend a total of 1010 years in this phase of its evolutionary cycle. 

Show that the Sun will convert a total mass of 2 × 1029 kg of hydrogen into helium during its time on the main sequence. 

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5g3 marks

One day, the Sun will leave the main sequence and move on to the next stage of its evolutionary cycle.

Discuss what will happen to the Sun.

In your answer, you should outline

  • the conditions that will initiate this change

  • the nuclear processes that will occur 

  • the physical changes that the Sun will undergo.

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