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If I have a particle that's size is 0.3 micrometers (µm) at an air concentration of 6000 cubic centimeters (cm³) can I use this information to calculate the Milligram Per Cubic Meter (mg/cm³)? I think that means I'm trying to find the volumetric mass density?

 Sep 8, 2014

Best Answer 

 #2
avatar+33615 
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You need the density of the particles.  If we say this is ρ kg/m3, and we assume the 0.3 μm is the diameter of a particle, then the mass of a particle is

m = ρ*(4/3)*pi*(3*10-7/2)3kg = ρ*pi*(9/2)*10-21kg = ρ*pi*(9/2)*10-15mg

The number density is 6000 particles per cm3, so the volumetric mass density is

  ρ*pi*(9/2)*10-15*6000mg/cm3 =  ρ*pi*27*10-12mg/cm3

 

Can't go any further without knowing the value of  ρ (in kg/m3)

 Sep 9, 2014
 #1
avatar+4473 
+8

I wonder how we would go from micrometers to milligrams...

 Sep 9, 2014
 #2
avatar+33615 
+8
Best Answer

You need the density of the particles.  If we say this is ρ kg/m3, and we assume the 0.3 μm is the diameter of a particle, then the mass of a particle is

m = ρ*(4/3)*pi*(3*10-7/2)3kg = ρ*pi*(9/2)*10-21kg = ρ*pi*(9/2)*10-15mg

The number density is 6000 particles per cm3, so the volumetric mass density is

  ρ*pi*(9/2)*10-15*6000mg/cm3 =  ρ*pi*27*10-12mg/cm3

 

Can't go any further without knowing the value of  ρ (in kg/m3)

Alan Sep 9, 2014

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