AQA A Level Physics

Revision Notes

8.3.7 Nuclear Density

Constant Density of Nuclear Material

  • Assuming that the nucleus is spherical, its volume is equal to:

  • Where R is the nuclear radius, which is related to mass number, A, by the equation:

  • Where R0 is a constant of proportionality
  • Combining these equations gives:

  • Therefore, the nuclear volume, V, is proportional to the mass of the nucleus, A
  • Mass (m), volume (V), and density (ρ) are related by the equation:

  • The mass, m, of a nucleus is equal to:

m = Au

  • Where:
    • A = the mass number
    • u = atomic mass unit
  • Using the equations for mass and volume, nuclear density is equal to:

  • Since the mass number A cancels out, the remaining quantities in the equation are all constant
  • Therefore, this shows the density of the nucleus is:
    • Constant
    • Independent of the radius
  • The fact that nuclear density is constant shows that nucleons are evenly separated throughout the nucleus regardless of their size

Nuclear Density

  • Using the equation derived above, the density of the nucleus can be calculated:

  • Where:
    • Atomic mass unit, u = 1.661 × 10–27 kg
    • Constant of proportionality, R0 = 1.05 × 10–15 m
  • Substituting the values gives a density of:

  • The accuracy of nuclear density depends on the accuracy of the constant R0, as a guide nuclear density should always be of the order 1017 kg m–3
  • Nuclear density is significantly larger than atomic density, this suggests:
    • The majority of the atom’s mass is contained in the nucleus
    • The nucleus is very small compared to the atom
    • Atoms must be predominantly empty space

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