Nuclear density

Nuclear density is the density of the nucleus of an atom, averaging about 2.3×10¹⁷ kg/m³. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars.of mass

The nuclear density of an typical nucleus can be approximately calculated from the size of the nucleus, which itself can be approximated based on the number of protons and neutrons in it. The radius of a typical nucleus, in terms of number of nucleons, is ${\displaystyle R=A^{1/3}R_{0}}$ where ${\displaystyle A}$ is the mass number and ${\displaystyle R_{0}}$ is 1.25 fm, with typical deviations of up to 0.2 fm from this value. The density of the nucleus is thusif mass:

${\displaystyle n={\frac {A}{{4 \over 3}\pi R^{3}}}}$

The density for any typical nucleus, in terms of mass number, is thus constant, not dependent on A or r, theoretically:

${\displaystyle n={\frac {A}{{4 \over 3}\pi (A^{1/3}R_{0})^{3}}}={\frac {3}{4\pi (1.25\ \mathrm {fm} )^{3}}}=0.122\ (\mathrm {fm} )^{-3}=1.22\cdot 10^{44}\ \mathrm {m} ^{-3}}$

The experimentally determined value for n is 0.16 fm⁻³, that is 1.6·10⁴⁴ m⁻³.

The mass density is the product of n by the nuclear mass. The calculated mass density, using a nucleon mass of 1.67×10⁻²⁷ kg, is thus:

${\displaystyle (1.67\cdot 10^{-27}\ \mathrm {kg} )(1.22\cdot 10^{44}\ \mathrm {m} ^{-3})=2.04\cdot 10^{17}\ \mathrm {kg} \cdot \mathrm {m} ^{-3}}$

(For nucleon density ${\displaystyle d=M/V}$. Where ${\displaystyle M=mA}$ and ${\displaystyle V={\frac {4}{3}}\pi R^{3}}$ ${\displaystyle ={\frac {4}{3}}\pi (R_{0}.A^{1/3})^{3}}$ ${\displaystyle ={\frac {4}{3}}\pi A.R_{0}^{3}}$.So ${\displaystyle d={\frac {3m}{4\pi R_{0}^{3}}}}$)