Question

non-absorbing particles suspended in air and exposed to daytime radiation have a homogeneous size of 1 μm in diameter with a refractive index of 1.33. The density of the particle is 1.5 g/cm³. The wavelength of light is taken to be 500 nm. What is the concentration in μg/m³ which results in a limit of visibility of 1.5 km?

Answer 1

Since the particles are non absorbing,

the only loss is due to scattering.

The extinction coefficient due to scattering is given by

Where N is the number density of the particle.

D is the diameter of the particle

D = 10^-6 m

and Qsc is the scattering efficiency.

When the particle size is larger than the wavelength of the light,

we take Qsc = 2

Now, the extinction coefficient is defined as

where d is the limit of visibility

So,

d = 1.5 km = 1500 m

So,

The number density of particles is

/m^3

To get the concentration of particles,

we have to find the mass of N particles.

For a single particle,

density = 1.5 g/cm^3 = 1500 kg/m^3

So, mass = 1500*V =

So, total mass of N particles is

In micro gram/m^3,

this is