P4.3 · Nuclear equations and half-lives
Explain — 4 marks
A hospital uses Technetium-99m (Tc-99m) as a radioactive tracer in medical imaging. Tc-99m has a half-life of 6 hours. A patient is injected with an initial activity of 800 MBq at 09:00. The medical team needs to understand how the activity changes over time to plan when scans should be performed and when it is safe to discharge the patient.
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(a) Define what is meant by the half-life of a radioactive isotope.
[1 mark]
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(b) Calculate the activity of Tc-99m remaining in the patient's body at 21:00 (12 hours later). Show your working.
[2 marks]
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(c) Explain why Tc-99m is suitable for use as a medical tracer, considering its half-life and the type of radiation it emits (Tc-99m undergoes gamma decay).
[1 mark]
Show mark scheme
- (a) The time taken for the activity/number of radioactive nuclei to decrease to half its original value
- (b) Correct identification that 12 hours = 2 half-lives (6 hours each)
- (b) Correct calculation: 800 ÷ 2 ÷ 2 = 200 MBq (or equivalent working showing halving twice)
- (c) Half-life of 6 hours is long enough to allow time for imaging/diagnosis but short enough to minimize radiation dose to the patient / Gamma radiation is penetrating so it can be detected outside the body but less ionizing than alpha/beta, reducing harm to healthy tissue
P7.2 · The motor effect
Describe — 5 marks
An electric toothbrush contains a small DC motor that drives the brush head. The motor consists of a rectangular coil of wire mounted on an axle, positioned between the poles of a permanent magnet. A split-ring commutator and carbon brushes allow current to flow through the coil as it rotates.
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(a) Describe the direction of the force acting on each side of the coil relative to the magnetic field and the current.
[2 marks]
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(b) Describe how the commutator and brushes enable the coil to rotate continuously in the same direction.
[3 marks]
Show mark scheme
- (a) Force is perpendicular to both the magnetic field and the current
- (a) Forces on opposite sides of the coil act in opposite directions (creating a couple/turning effect)
- (b) Commutator reverses the current direction in the coil every half rotation
- (b) Brushes maintain electrical contact between the power supply and the rotating commutator
- (b) Current reversal ensures the force keeps the coil rotating in the same direction (rather than oscillating)
P2.5 · Static electricity
State — 4 marks
A student rubs a polythene rod with a duster. The rod becomes negatively charged and is then brought near to small pieces of paper on a desk. The paper pieces are attracted to the rod even though they are initially uncharged.
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(a) State what happens to electrons in the polythene rod during the rubbing process.
[1 mark]
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(b) State the type of charge induced on the surface of the paper pieces that face the negatively charged rod.
[1 mark]
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(c) State two reasons why the paper pieces are attracted to the rod despite being initially uncharged.
[2 marks]
Show mark scheme
- (a) Electrons are transferred from the duster to the polythene rod / electrons move onto the polythene rod (1 mark)
- (b) Positive charge is induced on the surface of the paper facing the rod (1 mark)
- (c) The negatively charged rod repels electrons in the paper, leaving a positive charge on the near surface (1 mark)
- (c) Opposite charges attract, so the positive charge on the paper is attracted to the negative charge on the rod (1 mark)
P5.8 · Newton's Laws
Show — 4 marks
A delivery driver pushes a 25 kg box across a warehouse floor. The box accelerates from rest to 2 m/s in 4 seconds. The driver applies a constant horizontal force, and friction acts against the motion.
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(a) Calculate the acceleration of the box.
[1 mark]
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(b) Show that the resultant force acting on the box is 12.5 N. (You may assume friction is negligible.)
[2 marks]
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(c) In reality, friction acts on the box with a force of 37.5 N. Show that the driver must apply a force of 50 N to achieve the same acceleration as calculated in part (a).
[1 mark]
Show mark scheme
- (a) a = Δv / Δt = 2 / 4 = 0.5 m/s² (1 mark)
- (b) Use F = ma (1 mark)
- (b) F = 25 × 0.5 = 12.5 N (1 mark)
- (c) Applied force − friction = resultant force; F − 37.5 = 12.5; F = 50 N (1 mark)
P4.2 · Isotopes and nuclear radiation
Show — 2 marks
Carbon-14 dating is used by archaeologists to determine the age of organic materials. Carbon-14 is a radioactive isotope of carbon that undergoes beta decay. A sample of wood from an ancient artefact contains carbon-14. The half-life of carbon-14 is 5730 years.
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Show that after three half-lives, the activity of a carbon-14 sample is reduced to one-eighth of its original activity.
[2 marks]
Show mark scheme
- {'mark': 1, 'description': 'After one half-life, activity = ½ × original activity (or equivalent working for subsequent half-lives)'}
- {'mark': 1, 'description': 'After three half-lives, activity = ½ × ½ × ½ × original activity = 1/8 × original activity (or 0.125 × original activity)'}
P2.4.2 · Energy transfers
Define — 4 marks
Smoke detectors in homes contain a small amount of americium-241, a radioactive isotope that emits alpha particles. The alpha particles ionise air molecules inside the detector, allowing a small electric current to flow. When smoke enters the detector, the smoke particles absorb the alpha radiation, causing the current to drop and triggering the alarm.
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(a) Define what is meant by the term "isotope".
[2 marks]
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(b) Americium-241 has a half-life of 432 years. Define what is meant by the term "half-life".
[2 marks]
Show mark scheme
- (a) atoms of the same element
- (a) with the same number of protons but different numbers of neutrons (or different mass number)
- (b) the time taken
- (b) for half of the radioactive nuclei to decay (or for the activity to halve)
P2.1.3 · Current, potential difference and resistance
Show — 4 marks
An electric heater is connected to a 230 V mains supply. The heating element has a resistance of 12 Ω when operating at full power.
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(a) Calculate the current flowing through the heating element when it is operating at full power. Show your working.
[2 marks]
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(b) The heating element is replaced with one that has a greater resistance. Explain why this causes a smaller current to flow from the same 230 V supply. Show your reasoning using the equation V = I × R.
[2 marks]
Show mark scheme
- (a) Use of the equation I = V ÷ R or equivalent rearrangement
- (a) Correct substitution: I = 230 ÷ 12
- (a) Correct answer: 19.2 A (accept 19.17 A or 19 A)
- (b) Reference to V = I × R (or I = V ÷ R)
- (b) Recognition that V remains constant (at 230 V)
- (b) Explanation that when R increases, I must decrease (for constant V)
- (b) Consequence: smaller current flows through the heating element
P2.3 · Domestic uses and safety
Explain — 4 marks
A portable electric heater has a metal outer case and is fitted with a 3-pin plug containing a fuse. During use, the live wire inside the heater works loose and touches the metal case.
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(a) Explain how the earth wire and fuse work together to prevent anyone touching the case from receiving an electric shock.
[2 marks]
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(b) The heater is replaced with a new model that has a plastic case and is marked 'double insulated'. Explain why this new heater does not need an earth wire.
[2 marks]
Show mark scheme
- (a) The earth wire provides a low resistance path to ground (accept: earth)
- (a) A large current flows through the earth wire causing the fuse to melt / blow (accept: break the circuit)
- (b) Plastic is an insulator / does not conduct electricity
- (b) So current cannot flow through the case / the case cannot become live
P8.1 · Our solar system and the life cycle of a star
Evaluate — 3 marks
An astronomy student is researching the life cycle of stars. She reads two statements online: Statement A claims that all stars eventually become black holes, and Statement B claims that the Sun will eventually expand into a red giant and then become a white dwarf. The student wants to evaluate which statement is more accurate based on stellar physics.
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(a) Evaluate Statement A. Is it correct that all stars become black holes? Explain your answer.
[1 mark]
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(b) Evaluate Statement B by describing the actual life cycle of the Sun and explaining why the Sun's fate differs from that of the most massive stars.
[2 marks]
Show mark scheme
- (a) Statement A is incorrect; only the most massive stars (much more massive than the Sun) can become black holes / most stars do not have sufficient mass to form black holes
- (b) Statement B is correct: the Sun will become a red giant (when hydrogen fusion ends and helium fusion begins in the core) and then become a white dwarf (after shedding its outer layers)
- (b) The Sun's fate differs because it does not have enough mass to undergo further fusion stages or collapse into a black hole; only very massive stars have sufficient gravitational force to continue fusion and eventually form black holes
P1.1 · Energy changes in a system
Calculate — 2 marks
A student uses an electric kettle to boil water for a cup of tea. The kettle contains 0.8 kg of water. The specific heat capacity of water is 4200 J/kg°C. The water is heated from 15°C to 100°C.
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(a) Calculate the temperature change of the water.
[1 mark]
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(b) Calculate the energy transferred to the water. Use the equation: energy transferred = mass × specific heat capacity × temperature change
[1 mark]
Show mark scheme
- (a) 85 (°C)
- (b) 0.8 × 4200 × 85
- (b) 285600 (J) OR 286000 (J) OR 2.86 × 10^5 (J)
P5.5.1 · Pressure in a fluid
State — 5 marks
A student is investigating the energy transfer in a household kettle. When switched on, the kettle's heating element becomes very hot and transfers energy to the water inside. The student observes that the rate of temperature change is faster when the kettle is first switched on compared to when the water is nearly boiling.
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(a) State the form of energy that is transferred to the water by the heating element.
[1 mark]
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(b) State two reasons why the rate of temperature change decreases as the water gets hotter.
[2 marks]
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(c) State what happens to the thermal energy of the water molecules as the water temperature approaches 100°C, and explain why the temperature remains constant once boiling begins.
[2 marks]
Show mark scheme
- (a) Thermal energy (or heat energy / internal energy)
- (b) The temperature difference between the heating element and the water decreases, so the rate of energy transfer decreases (or smaller temperature gradient)
- (b) More thermal energy is lost to the surroundings as the water temperature increases / heat loss to the environment increases
- (c) The thermal energy of the water molecules increases (or internal energy increases / molecules move faster and vibrate more)
- (c) At 100°C, the energy supplied is used to break intermolecular bonds / overcome forces between molecules to change state from liquid to gas, rather than increasing the temperature
P3.3.1 · Particle model and pressure
Calculate — 2 marks
A student is investigating the heating effect of an electric current. They pass a current through a resistor immersed in water and measure the temperature change. The resistor has a resistance of 12 Ω and operates at a potential difference of 6 V for 30 seconds.
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(a) Calculate the current flowing through the resistor using the equation V = IR.
[1 mark]
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(b) Using your answer from part (a), calculate the power dissipated by the resistor using the equation P = VI.
[1 mark]
Show mark scheme
- (a) Correct rearrangement and calculation: I = V ÷ R = 6 ÷ 12 = 0.5 A (accept 0.5 A or equivalent working)
- (b) Correct calculation using current from part (a): P = V × I = 6 × 0.5 = 3 W (accept 3 W or equivalent working with their value from part a)
GCSE Perfect