Nuclear size and density

Physics > Nuclear size and density

Find out what are core size and density… Read how to use radius, gold foil experiment, nucleus density formula, atom emission spectra.

The size of the nucleus is calculated from its radius, and the density is derived from the size.

Learning challenge

  • Derive the relationship between nuclear radius, density and size.

Key points

The first estimate of the radius was made by G. Geiger and E. Marsden in 1909 in an experiment with gold foil.

There is an empirical relationship between the radius, charge, and mass number for heavier nuclei (A> 20), where r is an empirical constant (1.2-1.5 fm).

Core density formula:


  • Alpha particles are two protons and two neutrons combined with a particle corresponding to a helium nucleus.
  • Atomic spectra are emission or absorption lines that appear when an electron passes from one energy level to another.
  • The nucleus is the massive central part of an atom with a positive charge. Consists of protons and neutrons.

The core size is calculated from the radius. It can be measured by scattering electrons in the nucleus. Determining the radius of an atomic nucleus resembles the problem with calculating the atomic radius, since they simply do not have clear boundaries. But the nucleus of an atom can be modeled as a sphere with a positive charge to interpret electron scattering experiments: there is no clear boundary and electrons “see” a range of cross sections for which an average value can be taken. The nuclear cross section is proportional to the square of the radius, which determines the scattering of electrons.

The first estimate of the radius in 1909 was made by G. Geiger and E. Marsden. They own the famous experiment with gold foil, where some particles were scattered at an angle of more than 90 °, due to which they returned to the same side as the alpha source. Rutherford was able to determine the upper limit of the radius of the gold nucleus 34 fm.

In later studies, it was possible to reveal an empirical relationship between the radius and mass number for heavier nuclei (A> 20): R ≈ r⋅A1/3 (r is an empirical constant, 1.2-1.5 fm). Hence, the radius for the gold core (A = 197) is 7.5 fm.

The nuclear density is approximately 4 ⋅ 1017 kg / m3… It can be determined by its size:

Physics Section

  • Nuclear size and density
  • Nuclear stability
  • Energy and nuclear forces
  • Natural radioactivity
  • Radiation detector
  • Radioactive decay series
  • Alpha decay
  • Beta decay
  • Gamma decay
  • Carbon-14
  • Calculations with half-lives
Quantum tunneling and conservation laws
  • Quantum tunneling
  • Conservation of the nucleon number and other laws
Applications of nuclear physics
  • Medical imaging and diagnostics
  • Dosimetry
  • Biological effects of radiation
  • Therapeutic uses of radiation
  • Radiation from food
  • Tracer
  • Thermonuclear reaction
  • Nuclear fission in reactors
  • Emission tomography
  • Nuclear weapon
  • Computed tomography and MRI

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