What force of attraction holds the electron in the hydrogen atom?

The force of attraction that holds the electron in the hydrogen atom would be the electromagnetic force. This is not only true for the hydrogen atom but for all atoms in the periodic table. It is the electromagnetic force that maintains the electrons in orbit around the atom. Electrons are known to be negatively charged particles and the nucleus of the atoms is positively charge. This opposite charges between these particles is what holds them together. The electromagnetic force is a manifestation of the opposite charges of the electrons and the nucleus and the magnetic force present in the atom.