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| In [[physics]], [[astronomy]], [[chemistry]], [[biology]] and [[geography]] '''number density''' (symbol: ''n'') is an [[intensive quantity]] used to describe the degree of concentration of [[countable]] objects ([[Elementary particle|particle]]s, [[molecules]], [[phonon]]s, [[Cell (biology)|cell]]s, [[galaxy|galaxies]], etc.) in physical [[space]]: [[Three-dimensional space|three-dimensional]] volume number density, [[Two-dimensional space|two-dimensional]] area number density, or [[One-dimensional space|one-dimensional]] line number density. [[Population density]] is an example of areal number density. The term '''number concentration''' (symbol: ''C'') is sometimes used in chemistry for the same quantity, particularly when comparing with other [[concentration]]s.
| | The writer is known as Irwin. For a whilst I've been in South Dakota and my mothers and fathers reside close by. Hiring is my occupation. To gather coins is 1 of the things I adore most.<br><br>My blog post; [http://Bit.do/Lu9u Bit.do] |
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| ==Definition==
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| Volume number density is the number of specified objects per unit [[volume]]:<ref>{{GoldBookRef | file = N04260 | title = number concentration}}</ref>
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| : <math>n = \frac{N}{V} </math> ,
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| where
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| :''N'' is the total number of objects in a volume ''V''.
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| Here it is assumed<ref>{{Citation
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| | author1 = Clayton T. Crowe
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| | author2 = Martin Sommerfeld
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| | author3 = Yutaka Tsuji
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| | title = Multiphase flows with droplets and particles: allelochemical interactions
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| | year = 1998
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| | page = 18
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| | place =
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| | publisher = [[CRC Press]]
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| | url =
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| | doi =
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| | id =
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| | isbn = 0-8493-9469-4}}</ref> that ''N'' is large enough that [[rounding]] of the count to the nearest [[integer]] does not introduce much of an [[Random error|error]], however ''V'' is chosen to be small enough that the resulting ''n'' does not depend much on the [[Volume|size]] or [[shape]] of the volume ''V''.
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| ==Units==
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| In [[SI]] system of units, number density is measured in m<sup>−3</sup>, although cm<sup>−3</sup> is often used. However, these units are not quite practical when dealing with atoms or molecules of [[gas]]es, [[liquid]]s or [[solid]]s at [[room temperature]] and [[atmospheric pressure]], because the resulting numbers are extremely large (on the order of 10<sup>20</sup>). Using the number density of an [[ideal gas]] at 0 [[Celsius|°C]] and 1 [[Atmosphere (unit)|atm]] as a [[yardstick]]: 1 [[amagat]] = [[Loschmidt constant|2.6867774×10<sup>25</sup>]] m<sup>−3</sup> is often introduced as a unit of number density, for any substances at any conditions (not necessarily limited to an ideal gas at 0 °C and 1 atm).<ref>{{Citation
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| | author = Joseph Kestin
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| | title = A Course in Thermodynamics
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| | volume = 2
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| | year = 1979
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| | page = 230
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| | place =
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| | publisher = Taylor & Francis
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| | url =
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| | doi =
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| | id =
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| | isbn = 0-89116-641-6}}</ref>
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| ==Usage==
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| Using the number density as a [[Function (mathematics)|function]] of [[Coordinate system|spatial coordinates]], the total number of objects ''N'' in the entire volume ''V'' can be calculated as
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| : <math>N=\iiint_V n(x,y,z)\;dV </math> ,
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| where
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| :<math>dV=dx\,dy\,dz</math> is a volume element. If each object possesses the same [[mass]] ''m''<sub>0</sub>, the total mass ''m'' of all the objects in the volume ''V'' can be expressed as
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| : <math>m=\iiint_V m_0\, n(x,y,z)\;dV </math> .
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| Similar expressions are valid for [[electric charge]] or any other [[extensive quantity]] associated with countable objects. For example, replacing <math>m\rightarrow q</math> (total charge) and <math>m_0\rightarrow q_0</math> (charge of each object) in the above equation will lead to a correct expression for charge.
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| The number density of [[solution|solute]] molecules in a [[solvent]] is sometimes called [[concentration]], although usually concentration is expressed as a number of [[Mole (unit)|moles]] per unit volume (and thus called [[molar concentration]]).
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| ==Relation to other quantities==
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| ===Molar concentration===
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| For any substance, the '''number density''' ''n'' (in units of m<sup>−3</sup>) can be expressed in terms of its [[molar concentration]] ''c'' (in units of [[Mole (unit)|mole]]/m<sup>3</sup>) as:
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| :<math>n=N_{\rm A}\,c</math> ,
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| where ''N''<sub>A</sub> is the [[Avogadro constant]] ≈ 6.022×10<sup>23</sup> mol<sup>−1</sup>. This is still true if the [[spatial dimension]] unit, metre, in both ''n'' and ''c'' is consistently replaced by any other spatial dimension unit, e.g. if ''n'' is in units of cm<sup>−3</sup> and ''c'' is in units of [[Mole (unit)|mole]]/cm<sup>3</sup>, or if ''n'' is in units of [[Litre|L]]<sup>−1</sup> and ''c'' is in units of [[Mole (unit)|mole]]/[[Litre|L]], etc.
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| ===Mass density===
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| For [[atom]]s or [[molecule]]s of a well-defined [[molecular mass]] ''M'' (in units of [[Kilogram|kg]]/[[Mole (unit)|mole]]), the '''number density''' can be expressed in terms of the mass [[density]] of a substance ''ρ'' (in units of kg/m<sup>3</sup>) as
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| :<math>n=\frac{N_{\rm A}}{M}\rho</math> .
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| Note that the ratio ''M''/''N''<sub>A</sub> is the mass of a single atom or molecule in units of [[Kilogram|kg]].
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| ==Examples==
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| The following table lists common examples of number densities at 1 [[atmosphere (unit)|atm]] and 20 [[Celsius|°C]], unless otherwise noted.
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| {| class="wikitable" align="center" style="text-align:center"
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| |+ Molecular<ref name=mol>For [[Chemical element|elemental]] substances, atomic densities/concentrations are used</ref> number density and related parameters of some materials
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| ! Material !!colspan="2" | Number density (''n'') !! [[Molar concentration]] (''c'') !![[Density]] (<math>\rho</math>) !! [[Molar mass]] (''M'')
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| |-
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| |align="right" | [[Units of measurement|Units]] ||align="center" |(10<sup>27</sup> m<sup>−3</sup>) or<br>(10<sup>21</sup> cm<sup>−3</sup>)||align="center" |([[amagat]])||align="center" |(10<sup>3</sup> [[Mole (unit)|mol]]/m<sup>3</sup>) or ([[Mole (unit)|mol]]/[[Litre|L]])||(10<sup>3</sup> kg/m<sup>3</sup>) or ([[gram|g]]/[[cubic centimeter|cm<sup>3</sup>]])||(10<sup>−3</sup> kg/[[Mole (unit)|mol]]) or ([[gram|g]]/[[Mole (unit)|mol]])
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| |-
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| |align="left"| [[ideal gas]] ||0.02504||0.932||0.04158||41.58×10<sup>−6</sup>×''M''||''M''
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| |-
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| |align="left"| [[Density of air|dry air]] ||0.02504||0.932||0.04158||1.2041×10<sup>−3</sup>||28.9644
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| |-
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| |align="left"| [[Water (data page)|water]] ||33.3679||1241.93||55.4086||0.99820||18.01524
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| |-
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| |align="left"| [[Carbon|diamond]] ||176.2||6556||292.5||3.513||12.01
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| |}
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| ==See also==
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| * [[Columnar number density]]
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| ==References and notes==
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| {{Reflist}}
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| [[Category:Density]]
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| [[Category:Physical quantities]]
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| [[lv:Koncentrācija#Fizikā lietots jēdziens]]
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The writer is known as Irwin. For a whilst I've been in South Dakota and my mothers and fathers reside close by. Hiring is my occupation. To gather coins is 1 of the things I adore most.
My blog post; Bit.do