AQA A-Level Physics: Anode Voltage and Microscopes in Atomic Physics — mark scheme explained

The question

Calculate the anode voltage needed to produce a de Broglie wavelength of 0.1 nm. [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 de Broglie equation: λ = h / p

• S2

  Find the momentum: p = h / λ = (6.63 × 10 -34 ) / (1 × 10 -10 ) = 6.63 × 10 -24 kg·m/s

• S3

  Use p = √(2m e eV), rearranged to V = p 2 / (2m e e)

• S4

  Substitute values: V = (6.63 × 10 -24 ) 2 / (2 × 9.11 × 10 -31 × 1.60 × 10 -19 )

• S5

  Simplify: V = (4.40 × 10 -47 ) / (2.92 × 10 -49 )

• S6

  Calculate V: V ≈ 151 V

• S7

  This is of the order of 150 V — wavelength comparable to atomic size

• S8

  Therefore the anode voltage required is V ≈ 150 V

Model answer

Worked through, with each step tagged to the mark it earns.

1. S1

   Use the de Broglie equation: λ = h / p

2. S2

   Find the momentum: p = h / λ = (6.63 × 10 -34 ) / (1 × 10 -10 ) = 6.63 × 10 -24 kg·m/s

3. S3

   Use p = √(2m e eV), rearranged to V = p 2 / (2m e e)

4. S4

   Substitute values: V = (6.63 × 10 -24 ) 2 / (2 × 9.11 × 10 -31 × 1.60 × 10 -19 )

5. S5

   Simplify: V = (4.40 × 10 -47 ) / (2.92 × 10 -49 )

6. S6

   Calculate V: V ≈ 151 V

7. S7

   This is of the order of 150 V — wavelength comparable to atomic size

8. S8

   Therefore the anode voltage required is V ≈ 150 V

9. Final answer: V ≈ 150 V

Common mistakes

• Using the wrong value for Planck's constant (h) or the mass of an electron (m). — Always double-check the values of constants and use the correct units.
• Forgetting to convert units when necessary (e.g., from nm to m). — Ensure all units are consistent before performing any calculations.
• Misinterpreting the role of electromagnetic lenses in TEM. — Review the function of each component in the TEM, focusing on the role of electromagnetic lenses.
• Confusing the principles of operation between TEM and STM. — Clearly differentiate between the principles of TEM (transmitted electrons) and STM (tunnelling current).
• Failing to explain the importance of the feedback loop in STM. — Emphasize the function of the feedback loop and its importance in creating accurate topographic maps.
• Not providing specific examples of applications for TEM and STM. — Practice giving specific examples of how TEM and STM are used in material science and surface science.

Where the marks go

• Full worked solution (all marking points)6 marks

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