Question

Absorption and transmission: When a photon of light hits a molecule of gas or a particle in the atmosphere, there are three possibilities: 1) it can be absorbed (the energy is converted to heat), 2) it can be reflected (it continues on but in a different direction), 3) or it can be transmitted. These processes determine our ability to see distant objects (such as the mountains around Los Angeles and Irvine) and the colors in the sky (such as blue sky and red sunsets). When we look at the mountains in the distance, we are looking at sunlight that is reflecting off of the mountain. We will call the total light reflected “lo” and the fraction of the light that get to us (that we can see) is the transmitted fraction which we will call "". 1. The transmitted light (1) can be calculated as | = lo e-oa dx Where dx is the length of the light passes through. Oa is the absorption extinction coefficient. It can be calculated as t Oa = N*ba where N is the concentration of the gas- ba is the absorption cross section (Ca) of the gas which is a property of the gas. Discussion Question #1: What is the fraction of light (I/l.) that would pass through a uniform gas column of 105 cm length if the concentration is N = 1016 molecules cm3 and the absorption cross section of the gas molecule is ba= 10-19 cm2 per molecule?

Answer 1

Answer of 1:

Concentration of gas $\rightarrow N=10^{16}\ molecules\ cm^{-3}$
Absorption cross section of gas molecule $\rightarrow b_{a}=10^{-19}\ cm^{2}\ molecule^{-1}$

We have formula for transmitted light intensity :

$I=I_{0}\cdot e^{-(\sigma_{a}\cdot dx)}$

Where,
Original light intensity
"I

Absorption extinction coefficient $\rightarrow \sigma_{a}=N\cdot b_{a}$
Length of the light passes through $\rightarrow dx=10^{5}\ cm$

$I=I_{0}\cdot e^{-(\sigma_{a}\cdot dx)}$

$\therefore \frac{I}{I_{0}}= e^{-(N\cdot b_{a}\cdot dx)}$

$\therefore \frac{I}{I_{0}}= e^{-(10^{16}\times 10^{-19}\times 10^{5})}$

${\color{Blue} \therefore {I}/{I_{0}}= 3.72\times10^{-44}}$

Therefore, this fraction of amount of light would pass through uniform gas column.

Answer of 2:

When sunlight passes through $NO_{2}$ in the atmosphere, nitrogen oxide becomes nitrogen monoxide by chemical reaction, it mostly absorbs all the wavelengths and transmits red lights considerably.

Answer of 3:

Particle absorption limits the visibility the most on a polluted day.
Particle scattering limits the visibility the most on less-polluted day.
Overall, on a less-polluted day one can see 67.1 km further in atmosphere.

Answer of 4:

If the laws of physics were such that light with long wavelengths were scattered more easily than light with short wavelengths then sky color would be red and sunset would be blue in a polluted atmosphere.