Energy levels and line spectraAQA A-Level Physics: Subtopic test

1. 1
   A neon sign glows when a current passes through low-pressure neon gas. When its light is viewed through a diffraction grating, a few bright coloured lines are seen against a dark background instead of a continuous band of colours.

   (a)

   What does a line spectrum provide evidence for?

   [1 mark]

   • AAtoms emit photons of every wavelength
   • BElectrons in atoms have discrete energy levels
   • CElectrons in atoms can have any energy
   • DLight is emitted by the nuclei of atoms

   (b)

   An atom has energy levels E₁ (the lowest), E₂, E₃ and E₄ (the highest). Which transition emits the photon with the greatest frequency?

   [1 mark]

   • AE₂ → E₁
   • BE₃ → E₂
   • CE₄ → E₃
   • DE₄ → E₁

   (c)

   Explain why the spectrum is made of separate lines and not a continuous band.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Some of the energy levels of a hydrogen atom are: n = 1 at −2.18 × 10⁻¹⁸ J, n = 2 at −5.45 × 10⁻¹⁹ J and n = 3 at −2.42 × 10⁻¹⁹ J.

   (a)

   An electron in a hydrogen atom falls from n = 3 to n = 2. What is the energy of the photon emitted?

   [1 mark]

   • A7.87 × 10⁻¹⁹ J
   • B1.94 × 10⁻¹⁸ J
   • C3.03 × 10⁻¹⁹ J
   • D−3.03 × 10⁻¹⁹ J

   (b)

   What is the frequency of the photon emitted in the transition from n = 3 to n = 2?

   [1 mark]

   • A4.57 × 10¹⁴ Hz
   • B2.19 × 10⁻¹⁵ Hz
   • C2.01 × 10⁻⁵² Hz
   • D6.56 × 10⁻⁷ Hz

   (c)

   A photon of energy 1.0 × 10⁻¹⁸ J passes through hydrogen gas with all the atoms in the ground state, and is not absorbed. Explain why.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Astronomers study the light from a cloud of hydrogen gas. Some of the energy levels of a hydrogen atom are: n = 1 at −13.6 eV, n = 2 at −3.40 eV, n = 3 at −1.51 eV and n = 4 at −0.85 eV.

   (a)

   Calculate the wavelength of the photon emitted when an electron falls from n = 3 to n = 2.

   [3 marks]

   (b)

   Calculate the frequency of the photon emitted when an electron falls from n = 2 to n = 1, and state which region of the electromagnetic spectrum it is in.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student views a hydrogen discharge lamp through a diffraction grating and measures three visible lines, at wavelengths of 656 nm, 486 nm and 434 nm. Some of the energy levels of a hydrogen atom are: n = 1 at −13.60 eV, n = 2 at −3.40 eV, n = 3 at −1.51 eV, n = 4 at −0.85 eV and n = 5 at −0.54 eV.

   (a)

   Explain how the line spectrum of the lamp provides evidence for discrete energy levels in atoms.

   [6 marks]

   (b)

   Evaluate whether the three measured wavelengths support the energy levels given for hydrogen.

   [6 marks]

   Total for question 4: 12 marks

End of questions