1. explain why brownian motion provides evidence for the existence of atoms and molecules

For the answer to the question above, Brownian motion is the random, zigzag motion (with very small steps), produced by air molecules colliding with visible particles of dust or smoke. The visible particles (viewed with a microscope) are responding to the repeated out of balance collisions with the air particles. 

It indicates that gas particles, which are thousands of times smaller than the dust particles and remain invisible even when viewed by the microscope, must be moving at relatively high speeds in random directions to cause the motion we can see in the relatively massive dust particles.