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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Use the condition for holding the droplet stationary: QV = mgd
- S2
Substitute the given values into the equation: Q × 300 V = (1.5 × 10 -14 kg) × 9.81 m/s 2 × 0.02 m
- S3
Solve for Q: Q = (1.5 × 10 -14 kg × 9.81 m/s 2 × 0.02 m) / 300 V
- S4
Calculate the charge: Q ≈ 9.81 × 10 -18 C
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Use the condition for holding the droplet stationary: QV = mgd
- S2
Substitute the given values into the equation: Q × 300 V = (1.5 × 10 -14 kg) × 9.81 m/s 2 × 0.02 m
- S3
Solve for Q: Q = (1.5 × 10 -14 kg × 9.81 m/s 2 × 0.02 m) / 300 V
- S4
Calculate the charge: Q ≈ 9.81 × 10 -18 C
Final answer: Q ≈ 9.81 × 10 -18 C
Common mistakes
- Forgetting to convert units when using the formula QV = mgd. — 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. — 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. — 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. — 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. — 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. — 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
- Full worked solution (all marking points)4 marks