Download The atmosphere is made up of oxygen and nitrogen mostly. Oxygen

The atmosphere is made up of oxygen and nitrogen mostly. Oxygen absorbs some solar radiation, but mostly these two molecules only scatter light to make the sky blue. How do they do this?
To understand how, we need to understand what is known as dipole radiation.
Consider an electric field incident on an atom represented by an electron surrounding a nucleus,
i.e. an electromagnetic “dipole”. The incident electric field can be described by
~ =E
~ 0 eiωt
E
The incident electric field makes the electric field of the atom oscillate. There’s a fair bit of handwaving here, but it makes sense that the amplitude of displacement of electric charge within the
molecule should be proportional to the incident electric field, i.e.
~ =E
~ 0 eiωt
~x (t) = ~x0 eiωt ∝ E
But, now the molecule is vibrating and moving its electric charge back and forth, it generates
its own electric field, distinct from the incident electric field. This is new electromagnetic field
represents what we term the scattered radiation. Remember that force required to accelerate the
charge qe of an electron, which has mass me , is
F = qe E = me a
An electric field is created by the acceleration of the electric charge created by the incident radiation. Therefore the scattered field, or “dipole radiation”, is determined by:
~ dipole (t) ∝ a (t)
E
But we know that acceleration of the electron is simply the second derivative of the displacement
~x (t)
a (t) = ẍ (t) = −ω 2~x0 eiωt
Therefore the scattered electric field - the dipole radiation - is given by
~ dipole ∝ ω 2 E
~0
E
Both the intensity and flux of an electromagnetic wave are proportional to the square of the electric
field. Therefore, because I ∝ E 2 , we can write
I~dipole ∝ ω 4 I~0
In other words, the intensity of scattered dipole radiation is proportional to the intensity of the
incoming radiation, and the fourth power of the frequency of the radiation.
Now, noting that Nitrogen and Oxygen molecules respond as dipoles to incoming solar radiation, we can explain why the sky is blue.
If
I~dipole ∝ ω 4
then, because ω/2π = ν = c/λ, then
I~dipole ∝ 1/λ4
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Blue has a wavelength of 0.4 µm, and red has wavelength of 0.7 µm. Therefore
Iblue /Ired = 0.74 /0.44 = 9
All wavelengths of light are scattered, but blue light is scattered 9 times more effectively than red
light.
Of course, this then begs the question, if short wavelengths are what are favoured, than why is
the sky not violet? To answer this question, we must consider human physiology.
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