In the 1800s, one of the statements in john dalton's atomic theory was that atoms are indivisible. later experimental evidence led to the discovery of subatomic particles such as neutrons, electrons, and protons. what happened to the indivisible atom part of dalton's atomic theory, and why?

Dalton's atomic theory was changed by a new atomic theory, because of the discovery of particles in the atom; disproving the  indivisible atom concept.

Explanation:

The first atomic model was the one proposed by Jhon Dalton, according to which it is postulated that:  

"Matter is made up of indivisible, indestructible and extremely small particles called atoms."  

That is, the atom is a solid and indivisible mass.

However, at the end of 19th century the physicist J.J. Thomson began experimenting with cathode ray tubes and found out that atoms contain small subatomic particles with a negative charge (later called electrons).  This means the atom was not indivisible as Dalton proposed. So, Thomson developed in 1904 a new atomic model that was called the raisin pudding atomic model.

Years later other atomic models substituted Thomson's model and currently we have the modern quantum model of the atom, which recognizes more particles in the atom  besides electrons.