1. 1
   In a hydrogen discharge tube, collisions with fast-moving electrons excite hydrogen atoms from the ground state (n = 1) to the n = 4 level. The excited atoms then return to the ground state, some directly and some by way of intermediate levels. The atoms are described using the Bohr model.

   (a)

   What is the energy of the photon emitted when an atom returns directly from n = 4 to n = 1?

   [1 mark]

   • A0.85 eV
   • B12.1 eV
   • C12.8 eV
   • D13.6 eV

   (b)

   What is the angular momentum of the electron in the n = 4 orbit according to the Bohr model?

   [1 mark]

   • A$\frac{2h}{\pi}$
   • B$\frac{h}{2\pi}$
   • C$\frac{h}{8\pi}$
   • D$4h$

   (c)

   Calculate the wavelength of the photon emitted when an atom drops from n = 4 to n = 3.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A physicist compares two stable nuclides: carbon-12, $^{12}_{6}\mathrm{C}$, and lead-208, $^{208}_{82}\mathrm{Pb}$. The mass of each nucleus may be taken as its nucleon number multiplied by the unified atomic mass unit.

   (a)

   How many neutrons are in a nucleus of $^{208}_{82}\mathrm{Pb}$?

   [1 mark]

   • A82
   • B126
   • C208
   • D290

   (b)

   What is the ratio $\frac{\text{radius of lead-208 nucleus}}{\text{radius of carbon-12 nucleus}}$?

   [1 mark]

   • A0.39
   • B17
   • C4.2
   • D2.6

   (c)

   Show that the density of nuclear matter does not depend on the nucleon number, and estimate its value.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Alpha particles with a kinetic energy of 5.0 MeV are fired at a gold foil ($^{197}_{79}\mathrm{Au}$), and the numbers scattered at each angle agree with Rutherford's prediction, which assumes only an electrostatic force between the alpha particle and the nucleus. When the experiment is repeated with aluminium foil ($^{27}_{13}\mathrm{Al}$) using alpha particles of increasing kinetic energy, the number scattered through angles close to 180° agrees with Rutherford's prediction up to about 7 MeV, but above this energy it falls increasingly below the prediction.

   (a)

   Determine the distance of closest approach for a 5.0 MeV alpha particle moving head-on towards a gold nucleus, and compare it with the radius of the gold nucleus.

   [3 marks]

   (b)

   Explain the deviation from Rutherford's prediction for aluminium above 7 MeV, and evaluate whether it is consistent with the expected size of the aluminium nucleus.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The four visible lines in the emission spectrum of atomic hydrogen have measured wavelengths of 656.3 nm, 486.1 nm, 434.0 nm and 410.2 nm. They are produced by transitions that end on the n = 2 level. The emission spectrum of neutral helium, whose atoms each have two electrons, contains lines at 587.6 nm, 501.6 nm and 447.1 nm; no formula of the form E = −k/n² reproduces the helium lines.

   (a)

   Explain how the Bohr model accounts for the discrete energy levels of hydrogen and for its line spectrum.

   [6 marks]

   (b)

   Evaluate the Bohr model in the light of these data.

   [6 marks]

   Total for question 4: 12 marks

End of questions