In the hydrogen atom, the electron and proton are attracted to each other due to the electromagnetic force, specifically the electrostatic attraction between opposite charges. The proton has a positive charge (+1) and the electron has a negative charge (-1). According to Coulomb's law, opposite charges attract each other.
However, when it comes to the interaction between two electrons, there are additional factors at play. Electrons are fermions and obey the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. This principle applies to electrons in an atom as well.
In the case of the hydrogen atom, each electron occupies its own unique quantum state, defined by a set of quantum numbers such as the principal quantum number, azimuthal quantum number, and magnetic quantum number. These quantum numbers determine the energy, spatial distribution, and orientation of an electron's wavefunction.
Due to the Pauli exclusion principle, two electrons cannot occupy the exact same quantum state, which means that they have different wavefunctions. This leads to a repulsive force between the electrons known as electron-electron repulsion.
While the attractive force between the negatively charged electron and the positively charged proton dominates, the repulsive force between the negatively charged electrons becomes significant as they get closer to each other. This repulsion counteracts the attractive force, making the net force between electrons repulsive.
Therefore, in a hydrogen atom, the electron experiences a strong attraction to the proton but repulsion from another electron due to the combined effect of electrostatic attraction and electron-electron repulsion.