can an atom exist without a nucleus

No, it cannot.

what occurs when the atom has no nucleus

there is no atom

just free electrons which disperse or are attracted by some other charged particles

No, an atom cannot exist without a nucleus. The nucleus is a fundamental part of an atom and contains most of its mass. It is made up of positively charged protons and neutral particles called neutrons. The nucleus is surrounded by negatively charged electrons, which orbit the nucleus in specific energy levels or shells.

Essentially, the nucleus holds the atom together by exerting a strong force of attraction on the negatively charged electrons, preventing them from flying away. Without the nucleus, the electrons would disperse, and the atom would lose its structure and stability.

To understand why an atom cannot exist without a nucleus, it is essential to explore the fundamental principles of atomic structure, such as the arrangement of subatomic particles and the forces that bind them together. These concepts are explained by the field of quantum mechanics, which delves into the behaviors and properties of particles at the atomic and subatomic levels.