If most of the space within an atom is empty(proved by rutherford's experiment), then when atoms constitute matter there must exist large empty spaces- but this doesn't happen!

I don't think the atoms would come close together because there exists electron -electron repulsion!

how could we account for this???

The diameter of proton is about 10^-15 m, where as the diameter of Hydrogen atom is 0.53 x 10^-10 m. So, there is nothing in between the only proton and the only electron.

Sure, electrons of adjacent atoms repel each other. So, matter is not closely packed spheres one touching each other but, the electron cloud is diffused and atoms may maintain some distance apart. We define atomic radius as half the distance between the centres of the nuclei of two adjacent atoms in a crystal as exactly we donot know how far the electron cloud spreads around nucleus as per Quantum mechanical model of atom.

Approved