Describe Rutherford's nuclear model of the atom. Show that the total energy of the electron in a hydrogen atom is −e²/(8πε₀r), and state two limitations of the model.

1. 1 · State the model in one line. A tiny positive nucleus holds nearly all the mass; electrons revolve round it, held by electrostatic attraction.
2. 2 · Draw the picture. [Diagram: nucleus +e at centre, electron −e on a circle of radius r, velocity v along the tangent, force F towards the centre]
3. 3 · Write the force balance and kinetic energy. mv²/r = (1/4πε₀)(e²/r²), so K = (1/2)mv² = e²/(8πε₀r).
4. 4 · Write the potential energy and add. U = −e²/(4πε₀r), so E = K + U = −e²/(8πε₀r). Negative means the electron is bound.
5. 5 · State two limitations.
   • An accelerated electron radiates and should spiral into the nucleus: unstable atom
   • It predicts a continuous spectrum, but atoms give line spectra
6. 6 · Real life. If an atom were a cricket stadium, the nucleus would be a mustard seed at the centre.
7. 7 · Close in one line. So, Rutherford found the nucleus, but his model cannot explain why atoms are stable or why they give line spectra.

Scoring tip: Show the sign of U clearly. Many students lose a mark by writing the potential energy as positive.