Question

what does negative sign signify in ground state of hydrogen

Answer 1

The energy level of an electron in a hydrogen atom is - 13.6 eV in ground state. It has a negative sign because we take the energy of a free electron ( at infinite distance from the nucleus of the atom) to be zero, so naturally when the electron approaches the nucleus, it's energy decreases as it gets to a more stable state and thus it attains a negative value. So, the negative sign signifies the relative energy of the electron with respect to a free electron. (similar to how gravitational potential is conventionally taken negative)