What is the formula for the energy of a hydrogen orbital?

The energy of a hydrogen orbital is quantitatively described by the formula E = -13.6 eV * (Z^2/n^2). In this equation:

• The term -13.6 eV represents the ground state energy of hydrogen when Z (the atomic number) is equal to 1. This value is derived from the Bohr model of the hydrogen atom, which effectively describes electron energy levels in hydrogen-like atoms.

• Z denotes the atomic number of the nucleus; for hydrogen, Z is 1, but the formula can be applied to any hydrogen-like atom by substituting the appropriate value of Z.

• n is the principal quantum number, which can take on positive integer values (1, 2, 3, ...), indicating the electron's energy level or shell. When n increases, the energy level is less negative, implying that the electron is further from the nucleus and has higher potential energy.

This formula shows that the energy levels become less negative (closer to zero) as n increases, indicating that electrons in higher orbits have more energy. The factor of Z^2 signifies that as the nuclear charge increases, the attraction between the nucleus and the electron increases, resulting in lower energy (more negative value