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Quantum Phenomena - discrete energy levels for electrons

Q2. Some energy levels of an atom of a gas are shown in diagram 1.

Diagram 1

When a current is passed through the gas at low pressure, a line spectrum is produced. Two of these lines, which correspond to transitions from levels B and C respectively to the ground state, are shown in diagram 2.

Diagram 2

(a) Describe what happens to an electron in an atom in the ground state in order for the atom to emit light of wavelength 4.0 × 10–7 m.

The ground state electron needs to be excited/promoted to a higher energy level/orbit. This is achieved by the interaction of a high energy electron with the electron in the ground state (OR irradiation by elecromagnetic energy) When the excited electron relaxes/is de-excited/falls back to a lower energy state a photon of electromagnetic radiation is emitted. The photon has an energy that corresponds to the energy jump between the levels. The photon's wavelength is related to that energy by the equation E = hf = hc/λ

(3 MAX marks)

(b) Determine the energy, in J, of

(i) the photons responsible for each of the two lines shown in diagram 2.

The diagram shows wavelengths - big wavelength means low frequency and energy and vice versa - so the 400 nm line is the lower energy line!

E = hf = hc/λ

400 nm line

E = 6.63 x 10-34 x 3.0 x 108/4.0 × 10–7 m

E = 4.95 x 10-19 J

E = 5.0 x 10-19 J

200 nm line

E = 6.63 x 10-34 x 3.0 x 108/2.0 × 10–7 m

E = 9.9 x 10-19 J

 

(ii) the energy of each of levels B and C in Figure 1.

In figure 1 the ground state is given as 12.0 × 10–18 J - so we need to work in '× 10–18 J'

Transition from A to B is 5.0 x 10-19 J = 0.5 x 10-18 J

Therefore the energy of level B (which is a higher energy level - less negative than the ground state) =- (2.0 + 0.5) x 10-18 = – 1.5 × 10–18 J

Transition from A to C is 10.0 x 10-19 J = 1.0 x 10-18 J

Therefore the energy of level C =- (2.0 + 1.0) x 10-18 = – 1.0 × 10–18 J

(5 marks)

(Total 8 marks)