Question 1

Paper 2Hard10 marks

A gas is studied using an emission spectrum and an absorption spectrum. For the absorption measurement, the atoms are initially in their lowest energy state. Figure 1 shows the resolved line positions; each line-centre wavelength has an uncertainty of ±2 nm\pm 2\ \text{nm}

Assume each line corresponds to a photon transition. Take the lowest atomic energy to be 0 eV0\ \text{eV} and use hc=1240 eV nmhc=1240\ \text{eV nm}

Relative intensityEmission00.51415 nm620 nm1240 nmRelative intensityAbsorption00.51415 nm1240 nm3504004505005506006507007508008509009501000105011001150120012501300Wavelength / nm
(a)

State the feature of the emission spectrum that provides evidence for discrete atomic energy levels.

[1]
(b)

Calculate the energy of a photon corresponding to the emission line at 415 nm415\ \text{nm}

[2]
(c)

Calculate the energy gap corresponding to the absorption line at 1240 nm1240\ \text{nm}

[1]
(d)

Using the results from (b) and (c) and the information in Figure 1, determine the minimum number of energy levels needed to account for all the displayed lines. Draw an energy-level diagram, with levels labelled relative to the lowest energy state, and show the transitions corresponding to every displayed emission and absorption line.

[4]
(e)

Explain why the absence of a 620 nm620\ \text{nm} absorption line does not contradict the 620 nm620\ \text{nm} emission line. State the initial state required for absorption of a 620 nm620\ \text{nm} photon.

[2]

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