Density of Neutron Star

Density of Neutron Star

The densest material found on earth is the metal osmium, but its density pales by comparison to the densities of exotic astronomical objects such as white dwarf stars and neutron stars.

A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist and they are rotating extremely rapidly. A neutron star is basically a giant atomic nucleus about 11 km in diameter made especially of neutrons. It is believed that under the immense pressures of a collapsing massive stars going supernova it is possible for the electrons and protons  to combine to form neutrons via electron capture, releasing a huge amount of neutrinos. Since they have some similar properties as atomic nuclei, neutron stars are sometimes described as giant nuclei. But be careful, neutron stars and atomic nuclei are held together by different forces.  A nucleus is held together by the strong force, while a neutron star is held together by gravitational force.

Density of neutron star is enormous. They are so dense that one teaspoon of its material would have a mass over 5.5×1012 kg. It is assumed they have densities of 3.7 × 1017 to 6 × 1017 kg/m3, which is comparable to the approximate density of an atomic nucleus of 2.3 × 1017 kg/m3.

Density of Nuclear Matter

Nuclear density is the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since atomic nucleus carries most of atom’s mass and atomic nucleus is very small in comparison to entire atom, the nuclear density is very high.

The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and from its mass. Typical nuclear radii are of the order 10−14 m. Assuming spherical shape, nuclear radii can be calculated according to following formula:

r = r0 . A1/3

where r0 = 1.2 x 10-15 m = 1.2 fm

For example, natural uranium consists primarily of isotope 238U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of 238U isotope (238.03u). Its radius of this nucleus will be:

r = r0 . A1/3 = 7.44 fm.

Assuming it is spherical, its volume will be:

V = 4πr3/3 = 1.73 x 10-42 m3.

The usual definition of nuclear density gives for its density:

ρnucleus = m / V = 238 x 1.66 x 10-27 / (1.73 x 10-42) = 2.3 x 1017 kg/m3.

Thus, the density of nuclear material is more than 2.1014 times greater than that of water. It is an immense density. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

See above:

Density