A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Charged Oil Droplets and Millikan's Experiment — mark scheme explained
The short answer
In the early 20th century, Robert Millikan conducted a series of experiments to measure the charge of an electron. His work involved studying charged oil droplets between oppositely charged parallel plates. This experiment not only provided crucial evidence for the quantisation of electric charge but also demonstrated fundamental principles in physics.
The question
An oil droplet with a mass of 1.5 × 10 -14 kg is held stationary in an electric field by applying a potential difference of 300 V across two parallel plates separated by 2 cm. Calculate the charge on the droplet.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
Marks are typically awarded for correct use of formulae, accurate substitution of values, and clear reasoning. Ensure that all steps in your calculations are shown and that units are consistent throughout.
What the command words demand
- Calculate
- Perform a numerical calculation using the given data and appropriate formulae.
- Derive
- Show how a formula or equation can be derived from first principles or other known equations.
- Explain
- Provide a clear and detailed description of a concept, process, or phenomenon.
- Discuss
- Consider multiple aspects of a topic, including its significance and implications.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 5-7 minutes per question to ensure you have enough time to carefully read the question, perform necessary calculations, and check your work.
- Use the condition for holding the droplet stationary: QV = mgd1 mark
- Substitute the given values into the equation: Q × 300 V = (1.5 × 10 -14 kg) × 9.81 m/s 2 × 0.02 m1 mark
- Solve for Q: Q = (1.5 × 10 -14 kg × 9.81 m/s 2 × 0.02 m) / 300 V1 mark
- Calculate the charge: Q ≈ 9.81 × 10 -18 C1 mark
Final answer: Q ≈ 9.81 × 10 -18 C
Work through every step correctly and you earn all 4 marks.
Another worked example
An oil droplet of mass 1.5 × 10 -14 kg is observed to fall at a terminal velocity of 2 mm/s in air with a viscosity of 1.81 × 10 -5 Pa·s. Calculate the radius of the droplet.
- Use Stokes' Law for viscous drag force: F = 6πηrv1 mark
- At terminal velocity, the gravitational force equals the viscous drag force: mg = 6πηrv1 mark
- Substitute the given values into the equation: (1.5 × 10 -14 kg) × 9.81 m/s 2 = 6π × 1.81 × 10 -5 Pa·s × r × 2 × 10 -3 m/s1 mark
- Solve for r: r = (1.5 × 10 -14 kg × 9.81 m/s 2 ) / (6π × 1.81 × 10 -5 Pa·s × 2 × 10 -3 m/s)1 mark
- Calculate the radius: r ≈ 2.14 × 10 -7 m1 mark
Final answer: r ≈ 2.14 × 10 -7 m
Work through every step correctly and you earn all 5 marks.
Common mistakes
Forgetting to convert units when using the formula QV = mgd.
Why it happens: Students often forget to ensure that all units are consistent, leading to incorrect calculations.
Fix: Always check and convert units before substituting values into equations. For example, ensure that distance is in meters and potential difference is in volts.
Using the wrong formula for gravitational force.
Why it happens: Students may confuse the gravitational force with other forces or use incorrect formulas.
Fix: Always use F g = mg, where m is the mass of the droplet and g is the acceleration due to gravity (9.81 m/s 2 ).
Forgetting to use Stokes' Law for viscous drag force.
Why it happens: Students may not recognize when to apply Stokes' Law, leading to incorrect calculations of terminal velocity or droplet radius.
Fix: Use F = 6πηrv for the viscous drag force. Ensure that all variables are correctly identified and substituted into the equation.
Incorrectly identifying the charge on the oil droplet as continuous rather than quantised.
Why it happens: Students may not fully understand the concept of charge quantisation, leading to incorrect interpretations of Millikan's results.
Fix: Understand that electric charge is quantised and always a multiple of the elementary charge (e ≈ 1.6 × 10 -19 C).
Forgetting to balance forces when analyzing the motion of a falling oil droplet.
Why it happens: Students may not consider all forces acting on the droplet, leading to incorrect analysis of its motion.
Fix: Always identify and balance all forces acting on the droplet. At terminal velocity, the gravitational force (mg) equals the viscous drag force (6πηrv).
Using incorrect values for physical constants.
Why it happens: Students may use approximate or incorrect values for constants like the acceleration due to gravity or the viscosity of air, leading to significant errors in calculations.
Fix: Always use standard values for physical constants. For example, g ≈ 9.81 m/s 2 and η (viscosity of air) ≈ 1.81 × 10 -5 Pa·s at room temperature.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Charge | Balance electric and gravitational forces on a droplet to find its charge. | 4 |
| Calculate Droplet Radius | Use Stokes' law and terminal velocity to find the radius of a falling oil droplet. | 5 |
| Millikan Oil Drop | Balance electric force against gravity to find the mass of a charged droplet. | 4 |
| Stokes' Law Calculation | Use terminal velocity and Stokes' law to find the mass of a falling droplet | 5 |
| Millikan Oil Drop | Balance electric force against gravity to find the mass of a stationary charged droplet. | 4 |
| Total across these question types | 22 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.