Rutherford scattering and nuclear radiusAQA A-Level Physics: Subtopic test

1. 1
   In an alpha particle scattering experiment, a narrow beam of alpha particles from a radioactive source is fired at a thin gold foil inside an evacuated chamber. A detector counts the alpha particles scattered through different angles. Almost all the particles pass through the foil, but about 1 in 8000 is scattered through an angle greater than 90°.

   (a)

   What can be concluded from the observation that almost all the alpha particles pass through the foil with little or no deflection?

   [1 mark]

   • AThe nucleus carries a negative charge
   • BAtoms are solid spheres of uniform positive charge
   • CMost of the volume of an atom is empty space
   • DElectrons are more massive than alpha particles

   (b)

   What can be concluded from the small number of alpha particles scattered through angles greater than 90°?

   [1 mark]

   • AAlmost all the mass and positive charge of the atom are concentrated in a very small nucleus
   • BThe electrons in the atom are positively charged
   • CAlpha particles are attracted to the nucleus
   • DAtoms contain neutrons

   (c)

   The gold foil used is only a few hundred atoms thick. Explain why a much thicker foil would make the results difficult to interpret.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An alpha particle of kinetic energy 7.7 MeV is fired directly towards the centre of a stationary gold nucleus, which has proton number 79. The alpha particle is brought momentarily to rest at a distance r from the centre of the nucleus before it is repelled. The gold nucleus can be assumed to remain at rest.

   (a)

   Which statement is correct about the alpha particle at the point of closest approach?

   [1 mark]

   • AIts kinetic energy has been transferred to the gold nucleus
   • BIts kinetic energy is zero and its initial kinetic energy is stored as electric potential energy
   • CIts electric potential energy is zero
   • DIts kinetic energy is at a maximum

   (b)

   The initial kinetic energy of the alpha particle is doubled. How does the distance of closest approach r change?

   [1 mark]

   • AIt doubles
   • BIt is divided by four
   • CIt stays the same
   • DIt is halved

   (c)

   The distance of closest approach for this alpha particle is 3.0 × 10⁻¹⁴ m. Explain why this gives only an upper limit for the radius of the gold nucleus.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A beam of electrons of kinetic energy 420 MeV is directed at a thin target of carbon-12 nuclei. The scattered electrons are detected at different angles and the intensity shows a diffraction pattern, with the first minimum at 40° to the original direction. For these electrons, use E = pc. The first minimum occurs when sin θ = 1.22λ/D, where λ is the electron wavelength and D is the diameter of the nucleus.

   (a)

   Calculate the wavelength of the electrons.

   [3 marks]

   (b)

   Calculate the radius of the carbon-12 nucleus from this pattern, and explain why electrons of such high energy are needed to measure the size of a nucleus.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Physicists have learnt about the nucleus by scattering particles from it. In the early 1900s alpha particles were fired at thin gold foil, and later in the century beams of high-energy electrons were scattered from nuclei. Measurements show that the radius R of a nucleus depends on its nucleon number A according to R = R₀A^(1/3), where R₀ = 1.2 fm.

   (a)

   Describe how the results of the alpha particle scattering experiment led to the nuclear model of the atom, and how later scattering experiments have extended our knowledge of the nucleus.

   [6 marks]

   (b)

   Show that the equation implies that all nuclei have the same density, calculate the density of nuclear matter, and calculate the radius of a ²⁰⁸Pb nucleus. Take the mass of one nucleon to be 1.66 × 10⁻²⁷ kg.

   [6 marks]

   Total for question 4: 12 marks

End of questions