Answer to Question #137580 in Physics for Max

Question

Explain energy of hydrogen atom.

Answer 1

The electron in a Hydrogen atom can only have certain energies. These energies are called the Hydrogen's “energy levels”. The different energy levels of Hydrogen are denoted by the quantum number n where n varies from 1 for the ground state (the lowest energy level) to ∞, corresponding to unbound electrons. In practice, electrons with high n (e.g. 100 or more) are so weakly bound that even weak disturbances will pull the electron away.

Because it takes a minimum amount of energy, called the “ionization energy” to strip or ionize a bound electron from the Hydrogen atom, energy levels are usually referred to as being negative quantities. In both classical physics and quantum mechanics the absolute value of energy is irrelevant; only energy differences matter. It is convenient to say that when ionized the electron will have zero binding energy to the proton. With this convention, the different energy levels of a Hydrogen atom are given by the equation:

$$E=-\frac{E_0}{n^2}, E_0=13.6\ eV$$