AQA A-Level Physics Paper 3 (3BA), June 2025: Question 1

5 marks · Medium difficulty · Short Answer

Sketch a black-body radiation curve using Wien's displacement law, suggest the absolute magnitude of a Sun-like star, and describe a difficulty in detecting Earth-like exoplanets.

Practise this question

Question

Question 01 consists of three parts. Part 01.1 provides the temperature of star HIP 56948 as 5800 K at a distance of 210 ly and asks to sketch its black-body curve on Figure 1, labeling the wavelength axis with a suitable scale and unit. Figure 1 shows axes for intensity versus wavelength. Part 01.2 states HIP 56948 has the same diameter as the Sun and asks to suggest a value for its absolute magnitude. Part 01.3 asks to suggest one difficulty in detecting an Earth-like planet around HIP 56948.
Question text

01 HIP 56948 is a star with a black-body temperature of 5800 K. The star is at a

distance of 210 ly from the Sun.

01.1 Sketch, on Figure 1, the black-body curve for HIP 56948.

Label the wavelength axis with a suitable scale and unit.

[3 marks]

Figure 1

01.2 The diameter of HIP 56948 is the same as the diameter of the Sun.

Suggest a value for the absolute magnitude of HIP 56948.

[1 mark]

absolute magnitude =

01.3 Astronomers study HIP 56948 in their search for Earth-like exoplanets because

HIP 56948 is similar to the Sun.

Suggest one difficulty in detecting an Earth-like planet around HIP 56948.

[1 mark]

Mark scheme

Show the mark scheme Mark scheme for Question 01 detailing 5 marks. For 01.1 (3 marks): evidence of lambda max = 500 nm or 0.5 micrometres, correct asymmetrical peak shape with steeper left-hand side, and wavelength scale showing lambda max at peak with consistent unit. For 01.2 (1 mark): value of 5 (accept answers that round to 5). For 01.3 (1 mark): recognition that the planet is much smaller than the star, leading to very small variation of a measured quantity linked to a named/described detection method.

Question Answers Additional comments/Guidance Mark AO

01.1 Evidence of λmax = 500 nm / 0.5μm etc. (seen in calculation or No sf penalty 3 1 × AO1

graph)

MP1 value consistent with their unit (can be 1 × AO2

Shape correct i.e. shown as calculation)

1 × AO3

MP2: Single peak shown with clearly steeper

LHS than RHS AND correct shape on RHS

MP3: scale shown with indication of λmax. Allow

Scale with their λmax at their peak zero on axis.

and unit shown on scale consistent with value

01.2 5 accept answers that round to 5 1 AO2

601.3 (Idea that the planet is much smaller than the star Mark as list. 1 AO3

and therefore):

Answer must refer to a method of detecting

variation of quantity AND named/described method of

exoplanets

measurement

Treat comments about direct observations of

the planet as neutral

Total 5

How to answer it

Black-Body Radiation, Absolute Magnitude & Exoplanets

What this question tests
  • Wien's Displacement Law: Calculating peak wavelength (λmax) from temperature and plotting an accurate black-body curve.
  • Stellar Properties & Absolute Magnitude: Applying knowledge that stars with solar temperature and radius share the Sun’s absolute magnitude (M ≈ +5).
  • Exoplanet Detection Methods: Understanding limitations and difficulties in detecting Earth-sized exoplanets via transit and radial velocity methods.
Question 01.1 • 3 Marks

Sketching the Black-Body Curve for HIP 56948

Wien's Law, Axis Scaling, and Spectral Curve Geometry

📐 Step-by-Step Peak Calculation

  1. Identify Wien's Law:
    λmax × T = 2.9 × 10⁻³ m K
  2. Substitute given values:
    T = 5800 K
    λmax = (2.9 × 10⁻³) / 5800 = 5.0 × 10⁻⁷ m
  3. Convert to common units:
    λmax = 500 nm (or 0.5 μm )

✅ What Full Marks Look Like

  • Mark 1 (Working / Value): Clear evidence of λmax = 500 nm (or 5.0 × 10⁻⁷ m ) either written out or marked on the axis.
  • Mark 2 (Curve Shape): Single smooth peak with an asymmetric profile: noticeably steeper slope on the short-wavelength (left) side, longer tail approaching the axis asymptotically on the right.
  • Mark 3 (Axis & Alignment): Axis labelled with unit (e.g. / nm or / 10⁻⁷ m ) with the peak of the sketched curve aligning vertically with 500 nm.
How to draw the sketch: Label the horizontal axis unit as wavelength / nm . Put regular increments such as 0, 250, 500, 750, 1000 nm. Start your curve at or very near the origin, rise steeply to a single crest directly above 500, then decrease much more gradually toward the right, leveling off above zero intensity without curling upwards or touching the axis prematurely.

🧠 Exam Technique

  • Always check the unit prompt! The question gives wavelength / _____ . If you write nm , write numbers like 500, 1000. If you write m , use values like 5 × 10⁻⁷.
  • Never draw a symmetric bell curve or Gaussian distribution. Black-body curves are strictly asymmetric.

❌ Common Errors

  • Symmetric curve: Drawing a standard normal distribution (loses the shape mark).
  • Missing unit on axis: Leaving the axis blank or omitting powers of ten.
  • Misaligned peak: Calculating 500 nm correctly, but sketching the apex at a completely different position on the scale.
Mark Breakdown: 1 mark for calculating λmax ≈ 500 nm • 1 mark for correct asymmetric shape (steeper LHS, asymptotic RHS) • 1 mark for correct unit and alignment of peak with scale.
Question 01.2 • 1 Mark

Absolute Magnitude of a Solar Twin

Stefan-Boltzmann Law & Solar Comparison

✅ Correct Value

5 (Accept any value rounding to 5, e.g. 4.8 to 5.0)

Because absolute magnitude is dimensionless, no unit is required.

💡 Key Knowledge

  • Luminosity is given by Stefan-Boltzmann: L = 4πr²σT⁴ .
  • HIP 56948 has the same temperature (5800 K) and the same diameter (hence same radius r ) as the Sun.
  • Therefore, its total power output (luminosity) is identical to the Sun: Lstar ≈ L☉ .
  • Absolute magnitude ( M ) depends solely on luminosity. The absolute magnitude of the Sun is standard specification knowledge: M☉ ≈ +4.83 ≈ 5 .

❌ Common Trap: Distance Confusion

Students often attempt an elaborate calculation using the distance d = 210 ly . This distance is a distractor for this question part! Distance is needed only to relate apparent magnitude ( m ) to absolute magnitude ( M ). The question does not provide m , so you must recognise the star is an exact solar twin.

Mark Breakdown: 1 mark for stating 5 (or any value in the range 4.8 – 5).
Question 01.3 • 1 Mark

Difficulties in Detecting Earth-like Exoplanets

Transit Method vs. Radial Velocity Method

✅ Acceptable Answers (Need Method + Effect)

  • Transit Method: The fractional dip in brightness / light intensity is extremely small because an Earth-sized planet has a tiny cross-sectional area compared to the star.
  • Radial Velocity (Doppler) Method: The wobble / variation in radial velocity (Doppler shift of spectral lines) is extremely small because the mass of an Earth-like planet is tiny compared to the star.

🧠 Mark Scheme Constraint: Two Parts Required

To secure the mark, the scheme requires:

Named / described detection method + Identification of the tiny change in measured quantity

Simply saying "the planet is too small" scores 0 marks. You must state what measurement becomes difficult as a consequence.

❌ Examiner Commentary & Uncredited Answers

  • Direct observation: Writing "it is hard to see with a telescope because it's too dim/far away" is treated as neutral and scores no marks. Exoplanets are almost never detected by direct imaging.
  • Vague responses: "The signal is too weak" without specifying light intensity / brightness / velocity shift loses the mark.
Mark Breakdown: 1 mark (AO3) for naming an exoplanet detection technique AND clearly stating which quantity has an extremely small variation due to the planet's small size/mass.

Topics

Optional topics · 3.9 Astrophysics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 3 (3BA), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.