This is a schematic showing how atmospheres form.
Click on image for full size
Image from: The New Solar System
How a planet-to-be sweeps up nearby material to be part of itself
As shown in this picture, while they were forming in the solar nebula, the core of the planets-to-be drew material to themselves from the cloud of gas and dust around them. The bigger planets-to-be were able to draw even more material unto themselves because of gravity.
Big protoplanets such as Neptune were positioned far out in the cloud where there was less gas. That is why Neptune is not as big as Jupiter.
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