1. 1
   Electrons are fired one at a time at a pair of narrow slits. Each electron is recorded as a single dot at one point on a detector screen. After several thousand electrons have arrived, the dots build up a pattern of alternating bright and dark fringes. The experiment is repeated with slow neutrons of mass 1.67 × 10⁻²⁷ kg travelling at 2.0 × 10³ m s⁻¹ through slits of suitable width, and a similar fringe pattern builds up.

   (a)

   Which conclusion is best supported by these observations?

   [1 mark]

   • AElectrons are waves only; the dots are produced by the screen, not by the electrons
   • BElectrons are particles only; the fringes are caused by electrons repelling each other in the beam
   • CEach electron is detected as a localised particle, but where electrons arrive is governed by wave interference
   • DThe fringes are formed by photons emitted when the electrons pass through the slits

   (b)

   What is the de Broglie wavelength of the neutrons?

   [1 mark]

   • A2.0 × 10⁻¹³ m
   • B2.0 × 10⁻¹⁰ m
   • C3.6 × 10⁻⁷ m
   • D5.0 × 10⁹ m

   (c)

   A student claims that a cricket ball of mass 0.16 kg moving at 30 m s⁻¹ through a gap between two fielders should also produce interference fringes. Suggest why no such effect is ever observed.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In an electron diffraction tube, electrons are accelerated from rest through a potential difference of 2.0 kV and directed at a thin layer of polycrystalline graphite. A set of concentric bright rings appears on a fluorescent screen beyond the graphite. The spacing between neighbouring planes of carbon atoms in graphite is of the order of 10⁻¹⁰ m.

   (a)

   The accelerating potential difference is increased from 2.0 kV to 8.0 kV. What happens to the de Broglie wavelength of the electrons and to the radii of the rings?

   [1 mark]

   • AWavelength halves and the rings become smaller
   • BWavelength halves and the rings become larger
   • CWavelength falls to a quarter and the rings become smaller
   • DWavelength doubles and the rings become larger

   (b)

   The electrons are replaced by protons with the same kinetic energy. How does the de Broglie wavelength of the protons compare with that of the electrons?

   [1 mark]

   • AAbout 43 times larger
   • BThe same, because the kinetic energy is the same
   • CAbout 1840 times smaller
   • DAbout 43 times smaller

   (c)

   Calculate the de Broglie wavelength of the electrons.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   X-rays of wavelength 71.0 pm are directed at a graphite block. A detector measures the wavelength of the X-rays scattered at different angles θ from the original direction. At θ = 45° the scattered peak is at 71.7 pm, at θ = 90° it is at 73.4 pm and at θ = 135° it is at 75.1 pm. At every angle a second, weaker peak is also detected at the original wavelength of 71.0 pm.

   (a)

   Use the measurement at θ = 135° to determine a value for the Planck constant.

   [3 marks]

   (b)

   Explain how these results provide evidence for the particle nature of light, and suggest why the peak at 71.0 pm is detected at every angle.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student illuminates a clean sodium surface in an evacuated photocell with monochromatic light and measures the maximum kinetic energy Emax of the emitted photoelectrons. The results are: frequency 6.0 × 10¹⁴ Hz, Emax = 0.21 eV; 7.0 × 10¹⁴ Hz, 0.62 eV; 8.0 × 10¹⁴ Hz, 1.04 eV; 9.0 × 10¹⁴ Hz, 1.45 eV. At 5.0 × 10¹⁴ Hz no photoelectrons are emitted, however intense the light. At 8.0 × 10¹⁴ Hz, doubling the light intensity doubles the photocurrent but leaves Emax unchanged, and even at very low intensity emission begins with no measurable delay.

   (a)

   Determine, using the data, the Planck constant and the work function of sodium in eV, and evaluate whether the data are consistent with Einstein's photoelectric equation.

   [6 marks]

   (b)

   Discuss how the observations in this experiment contradict the wave model of light and are explained by the photon model.

   [6 marks]

   Total for question 4: 12 marks

End of questions