Why is the sky never Green?
The sky sometimes IS green; or at least for an instant at sunset, there is a brilliant flash of green; known, naturally as the ‘green flash’. What happens at sunset is that the blue light (and also the violet) has been scattered away, and the red and yellow light of the sunset gets absorbed into the atmosphere. Then, all that is left is the green part of the spectrum; but only for an instant. To see the ‘green flash’, you need to be in an area where the horizon is very low (such as at sea). Also,because the more obtuse the angle of the sun’s rays the better, the green flash lasts longer at higher latitudes and high altitudes. (I have heard that, at the south pole, as the sun gradually sets to bring on months of darkness, the ‘green flash’ can last for a minute or more; turning the horizon a brilliant veridian green). If you are fortunate enough to be in an aircraft as the sun is setting, the green flash may last several seconds. Look up ‘green flash’, and you will find more information
Scattering does not change the wavelength of light. At the one extreme (broad daylight), the light passes through a small amount of air, so you only see the scattered blue light (well, actually it’s mainly violet, but human eyes are more sensitive to blue, so it appears blue to us). At the other extreme (sunset, sunrise), the light is passing through hundreds of miles of air, and all the blue light scatters so much that most of it ends up scattered into (and absorbed by) the ground. I have not done the calculation, but I suspect that for cases in-between, when the light is only passing trough a medium amount of air, the depletion of blue light by scattering into the ground is balanced by the low amount of scattering of red light, yielding a net result of a white or gray sky.