22.4. Energy levels in atoms and line spectra
A subsection of Physics, 9702, through 22. Quantum physics
Listing 10 of 16 questions
State what is meant by a photon. Light in a beam has a continuous spectrum that lies within the visible region. The photons of light have energies ranging from 1.60 eV to 2.60 eV. The beam passes through some hydrogen gas. It then passes through a diffraction grating and an absorption spectrum is observed. All of the light absorbed by the hydrogen is re-emitted. Explain why dark lines are still observed in the absorption spectrum. Some of the energy levels of an electron in a hydrogen atom are illustrated in . –0.54 –0.85 –1.51 –3.40 –13.60 energy / eV (not to scale) The dark lines in the absorption spectrum are the result of electron transitions between energy levels. On , draw arrows to show the initial electron transitions between energy levels that could give rise to dark lines in the absorption spectrum. Calculate the shortest wavelength of the light in the beam. wavelength = m
9702_m17_qp_42
THEORY
2017
Paper 4, Variant 2
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A beam of white light passes through a cloud of cool gas. The spectrum of the transmitted light is viewed and contains a number of dark lines. Explain why these dark lines occur. Some energy levels for the electron in an isolated hydrogen atom are illustrated in . energy n = 6 n = 5 n = 4 n = 3 n = 2 Table 7.1 shows the wavelengths of photons that are emitted in the transitions to n = 2 from the other energy levels shown in . Table 7.1 wavelength / nm The energy associated with the energy level n = 2 is – 3.40 eV.
9702_m23_qp_42
THEORY
2023
Paper 4, Variant 2
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shows the lowest four energy levels of an electron in an isolated atom. increasing energy n = 4 n = 3 n = 2 n = 1 shows the lines in the emission spectrum of the atom that correspond to the transitions of the electron from n = 3 to n = 1 and from n = 4 to n = 1. increasing frequency Explain, with reference to photons, why there is a single frequency of electromagnetic radiation that corresponds to each of these transitions. On , draw a line that corresponds to the transition of the electron from n = 2 to n = 1. Label this line A. On , draw a line that corresponds to the transition of the electron from n = 3 to n = 2. Label this line B. The frequency of radiation represented by line A is fA. The frequency of radiation represented by line B is fB. The energy of the ground state (n = 1) is E1. Determine an expression, in terms of fA, fB, E1 and the Planck constant h, for the energy E3 of the energy level n = 3. E3 =
9702_s23_qp_42
THEORY
2023
Paper 4, Variant 2
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State three pieces of evidence provided by the photoelectric effect for a particulate nature of electromagnetic radiation. 1. 2. 3. Briefly describe the concept of a photon. Explain how lines in the emission spectrum of gases at low pressure provide evidence for discrete electron energy levels in atoms. Three electron energy levels in atomic hydrogen are represented in . increasing energy The wavelengths of the spectral lines produced by electron transitions between these three energy levels are 486 nm, 656 nm and 1880 nm. On , draw arrows to show the electron transitions between the energy levels that would give rise to these wavelengths. Label each arrow with the wavelength of the emitted photon. Calculate the maximum change in energy of an electron when making transitions between these levels. energy = J
9702_w08_qp_4
THEORY
2008
Paper 4, Variant 0
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Explain how a line emission spectrum leads to an understanding of the existence of discrete electron energy levels in atoms. Some of the lines of the emission spectrum of atomic hydrogen are shown in . wavelength / nm The photon energies associated with some of these lines are shown in . wavelength / nm photon energy / 10–19 J 4.85 4.58 …………… 3.03 Complete by calculating the photon energy for a wavelength of 486 nm. Energy levels of a single electron in a hydrogen atom are shown in . –21.80 –5.45 –2.42 –1.36 –0.87 –0.60 energy / 10–19 J (not to scale) Use data from to show, on , the transitions associated with each of the four spectral lines shown in . Show each transition with an arrow.
9702_w09_qp_42
THEORY
2009
Paper 4, Variant 2
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State an effect, one in each case, that provides evidence for the wave nature of a particle, the particulate nature of electromagnetic radiation. Four electron energy levels in an atom are shown in . electron energy –0.87 × 10–19 J –1.36 × 10–19 J –2.42 × 10–19 J –5.44 × 10–19 J (not to scale) An emission spectrum is associated with the electron transitions between these energy levels. For this spectrum, state the number of lines, calculate the minimum wavelength. wavelength = m
9702_w10_qp_41
THEORY
2010
Paper 4, Variant 1
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State an effect, one in each case, that provides evidence for the wave nature of a particle, the particulate nature of electromagnetic radiation. Four electron energy levels in an atom are shown in . electron energy –0.87 × 10–19 J –1.36 × 10–19 J –2.42 × 10–19 J –5.44 × 10–19 J (not to scale) An emission spectrum is associated with the electron transitions between these energy levels. For this spectrum, state the number of lines, calculate the minimum wavelength. wavelength = m
9702_w10_qp_42
THEORY
2010
Paper 4, Variant 2
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Questions Discovered
16