Negative electron gain energy for hydrogen atom means that

Explanation

The energy of the electron in a hydrogen atom has a negative sign for all possible orbits. What does this negative sign for all posible orbits. What does this negative sign convey? 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 is an electron that is infinitely far away from the nucleus and is assigned the energy value of zero.
As the electron gets closer to the nucleus (as `n` decreases), energy 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. We call this as the ground state.