Particle number

<h2 id="determining-the-particle-number">Determining the particle number</h2>
<p>The concept of particle number plays a major role in <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical</a> considerations. In situations where the actual particle number of a given thermodynamical system needs to be determined, mainly in <a href="/facts/Chemistry/SrNqkGVm">chemistry</a>, it is not practically possible to measure it directly by <a href="/facts/Counting/DsRhH9RT">counting</a> the particles. If the material is homogeneous and has a known <i><a href="/facts/Amount_of_substance/tQVyNLCp">amount of substance</a></i> <i>n</i> expressed in <i><a href="/facts/Mole_(unit)/kCMFwCc0">moles</a></i>, the particle number <i>N</i> can be found by the relation :

N
        =
        n
        
          N
          
            A
          
        
      
    
    {\displaystyle N=nN_{A}}
  
,
where <i>NA</i> is the <a href="/facts/Avogadro_constant/SwajCq22">Avogadro constant</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p>
<h2 id="particle-number-density">Particle number density</h2>
<p>A related <a href="/facts/Intensive_parameter/UcgSh8EG">intensive system parameter</a> is the particle <a href="/facts/Number_density/qtyDnLhz">number density</a> （or particle number concentration PNC), a quantity of kind <a href="/facts/Volumetric_number_density/qtyDnLhz">volumetric number density</a> obtained by dividing the particle number of a system by its <a href="/facts/Volume/aeAXCBUd">volume</a>. This parameter is often denoted by the lower-case letter <i>n</i>.
</p>
<h2 id="in-quantum-mechanics">In quantum mechanics</h2>
<p>In <a href="/facts/Quantum_mechanical/BRc3Mzgr">quantum mechanical</a> processes, the total number of particles may not be preserved. The concept is therefore generalized to the <a href="/facts/Particle_number_operator/XY3bo2I3">particle number operator</a>, that is, the <a href="/facts/Observable/fcBAsBjm">observable</a> that counts the number of constituent particles.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> In <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, the particle number operator (see <a href="/facts/Fock_state/GtFWL7uV">Fock state</a>) is conjugate to the phase of the <i>classical</i> wave (see <a href="/facts/Coherent_state/erY7zuXu">coherent state</a>).
</p>
<h2 id="in-air-quality">In air quality</h2>
<p>One measure of <a href="/facts/Air_pollution/zmk9Dy7S">air pollution</a> used in air quality standards is the atmospheric concentration of <a href="/facts/Atmospheric_particulate_matter/RleGr5E6">particulate matter</a>. This measure is usually expressed in μg/m3 (<a href="/facts/Micrograms/aAHxytph">micrograms</a> per cubic metre). In the current EU emission norms for cars, vans, and trucks and in the upcoming EU emission norm for non-road mobile machinery, particle number measurements and limits are defined, commonly referred to as <i>PN</i>, with units [#/km] or [#/kWh]. In this case, PN expresses a quantity of particles per unit distance (or work).
</p>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Benenson, Walter; Harris, John; Stöcker, Horst (2002). Handbook of Physics. Springer. ISBN 0-387-95269-1. <a href="0-387-95269-1" target="_blank">0-387-95269-1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Benenson, Walter; Harris, John; Stöcker, Horst (2002). Handbook of Physics. Springer. ISBN 0-387-95269-1. <a href="0-387-95269-1" target="_blank">0-387-95269-1</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Schumacher, Benjamin; Westmoreland, Michael (2010). Quantum Processes, Systems, and Information. Cambridge University Press. <a href="/wiki/Cambridge_University_Press" target="_blank">/wiki/Cambridge_University_Press</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Particle number open-in-new

Particle number