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Quantum Phenomena - discrete energy levels for electrons

Q7. In a discharge tube a high potential difference is applied across hydrogen gas contained in the tube. This causes the hydrogen gas to emit light that can be used to produce the visible line spectrum as shown below.

The visible line spectrum above has been used to predict some of the electron energy levels in a hydrogen atom.

The energy levels predicted from the visible line spectrum are those between 0 and –3.40 eV in the energy level diagram.

(a) Some of the predicted energy levels are shown below:

(i) Calculate the energy, in eV, of a photon of light that has the lowest frequency in the visible hydrogen spectrum shown in the diagram.

[3 marks]

(ii) Identify the state of an electron in the energy level diagram labelled 0.

[1 mark]

(iii) Identify the state of an electron that is in the energy level labelled –13.6 eV.

[1 mark]

(iv) Explain why the energy levels are negative.

[1 mark]

(b) Discuss how the discharge tube is made to emit electromagnetic radiation of specific frequencies. In your answer you should:

explain why there must be a high potential difference across the tube

discuss how the energy level diagram predicts the visible line spectrum.

show how one of the wavelengths of light is related to two of the energy levels in the energy level diagram.

[6 marks]

(Total 12 marks)