Question

How were atomic models developed when no one had seen an atom?

Answer 1

there were experiments done by various scientists for example goldfoil experiment by ernst rutherford gave rotherford model..and many more..

Answer 2

look up the following atomic models:
thomson's plum pudding
rutherford's gold foil
bohr's energy levels

the results of these experiments allowed us to change the model we use to visualize what an atom might look like, even if we've never actually seen one

Answer 3

The first and most important clue to the existence of atoms was chemistry -- the Rules of Constant and Multiple Proportions. It's very hard to explain why water ALWAYS consists of 9 parts (by mass) oxygen to 1 part hydrogen -- unless there is some fundamental "unit" of water that is made from "units" of oxygen and hydrogen. What other way could there be to have exactly and precisely the same recipe followed every time? If the amount of a substance were not quantized -- came in any size chunk you wanted, no matter how large or small -- then why wouldn't water sometimes be 9.0002 parts oxygen to 1 part hydrogen, or 8.884 to 1, or anything in between?

So there is good evidence for atoms just from the nature of chemistry, and this is why organic chemists accepted the existence of atoms in the 19th century, long before there was any direct evidence at all.

The next important piece of evidence was the gas laws. Why does a gas exert a pressure, an why does it increase with temperature the way it does? This is very easy to explain if you think the gas is made of little balls bouncing around mostly empty space -- that is, the gas is made of atoms. It's very hard to explain if a gas is made of some continuous but low-density stuff, like very light foam. Why would it exert a pressure? Why would the pressure change with temperature the way it does?

So experiments with gases also gave evidence for atoms, although understanding the gas laws (which happened in the 17th and 18th centuries) had to wait a while, before the math and physics for dealing with bouncing balls caught up to observation.

Another good piece of evidence was Brownian motion: the obsevation under a microscope that tiny bits of flotsam in water will jiggle around randomly. Why does this happen? Again, it's easy to explain if the water is made of atoms in motion, for they will bombard the stuff unevenly, from moment to moment, like a crowd jostling someone walking through it, and hence it will jiggle randomly. But how can this happen, if the water is not made of atoms?

The final proof of atoms is probably the fact that they were directly imaged by, e.g. STMs in the 1990s. But there was lots of indiret proof before that.