Do we know exactly what the atom looks like?

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Also, when an atom emits light when another particle hits it, why does one of the electrons move to the outer shell?
 
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This depends on what you mean by "looks like". Our perception of objects using vision requires trillions of photons coming from an object of relatively large size (compared to atoms). Atoms are so small that if a photon is emitted from an electron on one "side" of an atom, and another from the other "side", we cannot tell the difference. Also, does this really tell us what the atom looks like? Many features of objects that we see depend on the interaction of the material as a whole. Whether it is smooth or rough can make it shiny or dull, things can change colors if you reduce the size of the object far enough (such as gold looks green if you don't have a large enough piece of it, according to a book I have on quantum physics. The scale is something like fractions of millimeters or something.)

At the atomic scale I personally prefer to think of things in terms of how the different forces interact, not how they "look".

Also, when an atom emits light when another particle hits it, why does one of the electrons move to the outer shell?

At first, the electron absorbs energy from the collision, resulting in the electron jumping to a higher (more energetic) orbital shell. The electron then emits a photon and falls back down to the lowest state it can go into. Electrons can only absorb energy in certain amounts that equal the jump from one orbital to another.