AQA A-Level Physics Paper 1, June 2025: Question 22

AQA A-Level Physics • Particles and Radiation

This multiple-choice question evaluates your ability to apply Einstein's photoelectric equation to solve for an unknown metal work function (ϕ):

Recalling and rearranging Einstein's photoelectric equation: hf = ϕ + E_k(max) .
Calculating maximum kinetic energy from electron velocity using E_k = ½mv² .
Locating and applying the electron rest mass ( m_e = 9.11 × 10⁻³¹ kg ) from the formula booklet.
Handling powers of 10 accurately under timed multiple-choice conditions.

B: 3.5 × 10⁻¹⁹ J

Mark Scheme: 1 mark for option B (AO2 – application of physics principles to calculate work function).

Photon Energy ( E = hf ): Provided directly as 3.8 × 10⁻¹⁹ J .
Photoelectric Equation:
hf = ϕ + E_k(max)
Rearranged for work function:
ϕ = hf - E_k(max)
Kinetic Energy: E_k(max) = ½ m_e v_max²
Electron Mass: m_e = 9.11 × 10⁻³¹ kg (from the AQA Data Booklet).

Calculate the maximum kinetic energy (E_k(max)) of the emitted electron:
E_k(max) = ½ × m_e × v_max²
E_k(max) = 0.5 × (9.11 × 10⁻³¹ kg) × (2.5 × 10⁵ m s⁻¹)²
E_k(max) = 0.5 × (9.11 × 10⁻³¹) × (6.25 × 10¹⁰) = 2.847 × 10⁻²⁰ J
Convert to standard base power of 10⁻¹⁹ J to make subtraction easy:
E_k(max) = 0.285 × 10⁻¹⁹ J
Subtract E_k(max) from the incident photon energy (hf) to find ϕ:
ϕ = hf - E_k(max)
ϕ = (3.8 × 10⁻¹⁹ J) - (0.285 × 10⁻¹⁹ J)
ϕ = 3.515 × 10⁻¹⁹ J ≈ 3.5 × 10⁻¹⁹ J (Option B)

Choosing A ( 0.29 × 10⁻¹⁹ J ): This is the value of the kinetic energy E_k(max) , not the work function! Always read carefully what value the question asks for.
Choosing D ( 4.1 × 10⁻¹⁹ J ): Result of mistakenly adding the kinetic energy rather than subtracting: 3.8 × 10⁻¹⁹ + 0.29 × 10⁻¹⁹ = 4.09 × 10⁻¹⁹ J . Conservation of energy requires work function to be less than the incident photon energy if electrons are released.
Choosing C ( 3.8 × 10⁻¹⁹ J ): Assuming zero kinetic energy or assuming photon energy equals work function (threshold condition).
Forgetting to square speed: Calculating ½mv instead of ½mv² .

Eliminate impossible answers immediately: If electrons are emitted with kinetic energy, the work function ϕ must be strictly smaller than the incident photon energy ( 3.8 × 10⁻¹⁹ J ). This instantly eliminates C and D without any math!
Spot the distractors: Multiple-choice options frequently include intermediate calculation steps (like E_k in option A) and sign errors (like addition in option D).
Speed tip: Match powers of ten before subtracting: writing 2.85 × 10⁻²⁰ J as 0.29 × 10⁻¹⁹ J allows simple mental subtraction: 3.8 - 0.29 = 3.51 .

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