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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.
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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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| |align="left"| [[ideal gas]] ||0.02504||0.932||0.04158||41.58×10<sup>−6</sup>×''M''||''M''
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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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| |align="left"| [[Water (data page)|water]] ||33.3679||1241.93||55.4086||0.99820||18.01524
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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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Myrtle Benny is how I'm known as and I feel comfortable when people use the complete name. For many years he's been living in North Dakota and his family enjoys it. To collect badges is what her family and her appreciate. My working day job is a librarian.
Also visit my site std home test (visit the next website page)