What does negative sign in the electronic energy of hydrogen atom convey?

Explanation

The energy of an electron in the atom is lower than the energy of a free electron at rest which is taken as zero. The energy of the electron in a hydrogen atom has a negative sign for all possible orbits. This negative sign means that the energy of the electron in the atom is lower than the energy of a free electron at rest. A free electron at rest means that it is infinitely far away from the nucleus and has negligible attraction towards the nucleus. Thus it is assigned the energy value of zero. Mathematically, this corresponds to setting the orbit 'n' equal to infinity in the energy equation. As the electron gets closer to the nucleus, (as n decreases), En becomes larger in absolute value and more and more negative. The most negative energy value is given by n=1 which corresponds to the most stable orbit. It is called the ground state of an atom.