Atomic line spectra and energy levelsEdexcel A-Level Physics: Subtopic test

1. 1
   Hydrogen gas at low pressure is excited in a discharge tube. A hydrogen atom has energy levels of −13.6 eV (n = 1, the ground state), −3.40 eV (n = 2), −1.51 eV (n = 3) and −0.85 eV (n = 4).

   (a)

   Which transition emits the photon of highest frequency?

   [1 mark]

   • An = 4 to n = 3
   • Bn = 3 to n = 2
   • Cn = 2 to n = 1
   • Dn = 3 to n = 1

   (b)

   What is the energy, in joules, of the photon emitted when an electron falls from n = 3 to n = 2? (e = 1.60 × 10⁻¹⁹ C)

   [1 mark]

   • A1.9 J
   • B3.0 × 10⁻¹⁹ J
   • C1.2 × 10¹⁹ J
   • D7.9 × 10⁻¹⁹ J

   (c)

   Explain why the light from the discharge tube gives a line spectrum rather than a continuous spectrum.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   White light is passed through cool mercury vapour and then into a spectrometer. A mercury atom has energy levels of −10.4 eV (the ground state), −5.5 eV, −3.7 eV and −1.6 eV, and the atoms in the vapour are all in the ground state.

   (a)

   Which statement best explains the dark lines in the spectrum of the light that has passed through the vapour?

   [1 mark]

   • AMercury atoms absorb photons of any energy but re-emit only some of them.
   • BOnly photons with energy greater than 10.4 eV are absorbed by the vapour.
   • CPhotons whose energy equals the difference between two energy levels are absorbed, and are re-emitted in random directions.
   • DThe vapour emits dark light at certain frequencies.

   (b)

   What is the frequency of the radiation absorbed when a mercury atom moves from the ground state to the −5.5 eV level? (h = 6.63 × 10⁻³⁴ J s, e = 1.60 × 10⁻¹⁹ C)

   [1 mark]

   • A1.2 × 10¹⁵ Hz
   • B2.5 × 10¹⁵ Hz
   • C1.3 × 10¹⁵ Hz
   • D7.4 × 10³³ Hz

   (c)

   A photon of energy 5.0 eV passes through the vapour. State and explain whether it is absorbed by the mercury atoms.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An atom of element X has its lowest three energy levels at −6.0 eV (the ground state), −2.4 eV and −1.0 eV. A cool gas of X atoms, all in their ground state, is illuminated with photons of several different energies.

   (a)

   Calculate the frequency of the radiation emitted when an electron in an X atom falls from the −2.4 eV level to the ground state. (h = 6.63 × 10⁻³⁴ J s, e = 1.60 × 10⁻¹⁹ C)

   [3 marks]

   (b)

   The gas is illuminated with photons of energy 3.0 eV, 3.6 eV, 4.2 eV and 5.0 eV. Deduce which of these photons can be absorbed and explain why the others cannot. Calculate the frequency of the highest-energy photon that can be absorbed.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A low-pressure sodium street lamp produces almost entirely yellow light of wavelength 589 nm. In a sodium atom the ground-state energy level is −5.14 eV, and the yellow light is emitted when an electron falls to the ground state from the next level above it.

   (a)

   Explain how the line emission spectrum of an element such as sodium provides evidence that electrons in atoms have discrete energy levels.

   [6 marks]

   (b)

   Calculate the frequency of the yellow light, the energy of one photon in J and in eV, and the energy of the upper level involved in the transition. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

   [6 marks]

   Total for question 4: 12 marks

End of questions