How do we know atoms exist?
My dad is always a curious guy. So he doesn't believe in atoms because we haven't 'seen' them. So what he's asking is how do we know they actually exist. I know they exist -- theories, experiments (e.g. foil experiment), etc. My dad doesn't believe in anything if it's a theory, despite all the evidence. But, hey, I can't make him believe. I can explain to him how they're real, and still not believe.
He also asks a couple questions (you can answer them if you'd like) such as why mercury is liquid, how do we know that quarks exist, how carbon dating works, etc.
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Atoms have been imaged. It takes a tunneling scanning electron microscope to image an atom but it can be done. By the way, an atom is never going to be seen, visible light has a wavelength that is larger than the largest atom.