If you had to explain to a non-scientist why it is that scientists accept the idea that all material things are composed of atoms what evidence would you use?

There are many things that convinced scientists of the existence of atoms,  and it has been accepted for at least 100 years now, examples are the macroscopic behaviour of gases, the light emitted by hydrogen lamps, and more recently it has become possible to see individual atoms with the best microscopes!

Explanation:

There are many reasons why people thought that our material world was composed of atoms. One of the most striking reasons why scientists came to believe in atomic theory was how it could explain phenomena like the behaviour of gases, by assuming that gases were composed of a great number of individual particles moving randomly, scientists like Maxwell and Boltzmann developed a theory that could explain the macroscopic behaviour of gases, this theory is called the Kinetic Theory of Gases.

More convincing maybe is how Quantum mechanics can predict phenomena like the atomic emission spectrum of Hydrogen and many molecules and atoms. That the spectra of different elements can be explained by assuming they are made of atoms and using quantum mechanics to predict the frequency at which these atoms will emit or absorb light is a very convincing argument! The Spectrum of hydrogen can be seen with an hydrogen lamp and a prism to separate the different wavelengths.

Moreover, modern electron microscopes can indeed detect single atoms! That means that one can quite literally see single atoms.

Most of the technological development of humanity for the last century wouldn't have been possible without atomic theory, as it underpin our understanding of the physical world.

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