QuestionSome of the energy levels of a hydrogen atom are: n = 1: −13.6 eV, n = 2: −3.40 eV, n = 3: −1.51 eV.(a) Explain why the energy levels have negative values. (1)
(b) An electron falls from n = 2 to n = 1. Calculate the wavelength of the photon emitted and state the region of the electromagnetic spectrum it is in. (4)
(c) State how many different photon energies can be emitted by electrons de-exciting from n = 3 to the ground state. (1)Answer(a) Zero energy is defined as an electron that is free of the atom. Energy must be supplied to free a bound electron, so a bound electron has less than zero energy. (1)(b) ΔE = −3.40 − (−13.6) = 10.2 eV (1)ΔE = 10.2 × 1.60 × 10-19 = 1.63 × 10-18 J (1)λ = hc / ΔE = (6.63 × 10-34 × 3.00 × 108) ÷ 1.63 × 10-18 = 1.22 × 10-7 m
(1)This is 122 nm, which is in the ultraviolet region. (1)(c) Three: 3 → 1, 3 → 2 and 2 → 1. (1)Examiner tips- The photon energy is always the positive difference between the two levels. Take care with the minus signs.
- Convert eV to J before using λ = hc / ΔE.
- Visible light is roughly 400 nm to 700 nm. In hydrogen, falls to n = 1 give ultraviolet photons, while falls to n = 2 give mainly visible light.
(b) An electron falls from n = 2 to n = 1. Calculate the wavelength of the photon emitted and state the region of the electromagnetic spectrum it is in. (4)
(c) State how many different photon energies can be emitted by electrons de-exciting from n = 3 to the ground state. (1)Answer(a) Zero energy is defined as an electron that is free of the atom. Energy must be supplied to free a bound electron, so a bound electron has less than zero energy. (1)(b) ΔE = −3.40 − (−13.6) = 10.2 eV (1)ΔE = 10.2 × 1.60 × 10-19 = 1.63 × 10-18 J (1)
(1)This is 122 nm, which is in the ultraviolet region. (1)(c) Three: 3 → 1, 3 → 2 and 2 → 1. (1)Examiner tips- The photon energy is always the positive difference between the two levels. Take care with the minus signs.
- Convert eV to J before using λ = hc / ΔE.
- Visible light is roughly 400 nm to 700 nm. In hydrogen, falls to n = 1 give ultraviolet photons, while falls to n = 2 give mainly visible light.