In the context of atoms, electrons are bound to the nucleus by the electromagnetic force. To completely remove an electron from an atom, it requires energy to overcome the attractive force between the negatively charged electron and the positively charged nucleus.
The energy required to free an electron from an atom is known as the ionization energy. The ionization energy varies depending on the specific atom or molecule involved. In general, electrons can be removed from atoms through various processes such as ionization caused by high-energy radiation, collisions with other particles, or strong electric fields.
However, it's important to note that the speeds at which electrons move within atoms are typically much lower than the speed of light. Electrons in atoms occupy specific energy levels or orbitals, and their motion is governed by quantum mechanics. They exist in quantized states, and their behavior is described by wave functions.
While high-energy processes can cause electrons to gain enough energy to escape the atom, the conditions required for this to happen usually involve external influences such as intense radiation or extreme temperatures. Under normal circumstances, electrons within atoms are bound and do not break free from their associated protons.