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Radius and speed of the electron in the nth orbit sheet
3-mark answer frame

Derive an expression for the radius of the nth Bohr orbit of the hydrogen atom.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write the force balance. mvₙ²/rₙ = (1/4πε₀)(Ze²/rₙ²) ... (i)
  2. 2 · Write Bohr's quantum condition. mvₙrₙ = nh/2π ... (ii)
  3. 3 · Eliminate the speed. Multiply (i) by mrₙ³ and use the square of (ii): n²h²/4π² = mZe²rₙ/(4πε₀).
  4. 4 · Make rₙ the subject. rₙ = n²h²ε₀/(πmZe²).
  5. 5 · Draw the orbits. [Diagram: nucleus at the centre; circles for n = 1, 2, 3 with radii a₀, 4a₀, 9a₀; electron with v along the tangent and F towards the centre]
  6. 6 · Close in one line. So, rₙ ∝ n²; for hydrogen r₁ = a₀ = 0.53 Å.

Scoring tip: Number your equations and say which one goes into which. Box the final formula.