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'''Nuclear density''' is the [[density]] of the [[Atomic nucleus|nucleus]] of an [[atom]], averaging about 2.3&times;10<sup>17</sup> kg/m<sup>3</sup>. The descriptive term ''nuclear density'' is also applied to situations where similarly high densities occur, such as within [[neutron stars]].

The nuclear density of an typical nucleus can be approximately calculated from the [[nuclear size|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 [[nucleon]]s, is
<math>R=A^{1/3}R_0</math>
where <math>A</math> is the [[mass number]] and <math>R_0</math> is 1.25 [[femtometer|fm]], with typical deviations of up to 0.2&nbsp;fm from this value. The density of the nucleus is thus:
:<math>n = \frac{A}{{4\over 3} \pi R^3}</math>
The density for any typical nucleus, in terms of mass number, is thus constant, not dependent on ''A'' or ''r'', theoretically:

:<math>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}</math>

The experimentally determined value for ''n'' is 0.16&nbsp;fm<sup>−3</sup>.

The mass density is the product of ''n'' by the nuclear mass. The calculated mass density, using a [[nucleon]] mass of 1.67×10<sup>−27</sup> kg, is thus:
:<math>(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}</math>

For nuclear density d=M/V.
Where M=mA and V=4/3πR^3=4/3π(R_0A^1/3)=4/3πAR_0^3.
Sod=3m/4πR_0^3

== Applications and extensions ==
The components of an atom and of a nucleus have varying densities. The [[proton]] is not a fundamental particle, being composed of [[quark-gluon matter]]. Its size is approximately 10<sup>−15</sup> meters and its density 10<sup>18</sup> kg/m<sup>3</sup>. The descriptive term ''nuclear density'' is also applied to situations where similarly high densities occur, such as within [[neutron stars]].

Using [[deep inelastic scattering]], it has been estimated that the "size" of an [[electron]], if it is not a point particle, must be less than 10<sup>−17</sup> meters. This would correspond to a density of roughly 10<sup>21</sup> kg/m<sup>3</sup>.

Probing deeper within particles, one finds quarks which appear to be very dense and very hard. There are possibilities for still higher densities when it comes to [[quark matter]], [[gluon matter]], or [[neutrino matter]]. In the immediate future, the highest experimentally measurable densities will likely be limited to [[lepton]]s and [[quark]]s.

== References ==
*{{cite web |url= http://www.cyberphysics.co.uk/topics/atomic/nucleus.htm |title= The Atomic Nucleus |accessdate= 2014-11-18 }} (derivation of equations and other mathematical descriptions)

==See also==
*[[Nuclear matter]]
*[[Quark–gluon plasma]]

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[[Category:Density]]