For atomic hydrogen, the lowest-energy state, with the 0.53 radius orbit, has an energy of = - 313 kcal . Atomic hydrogen in this state is 313 kcal more stable than an ionized atom. This 313 kcal is the ionization energy of atomic hydrogen. Although the numerical value is calculated from first principles in the Bohr theory (using quantities such as Planck's constant and the mass and charge of the electron), it agrees exactly with the measured value of the ionization energy of hydrogen given in Chapter 3. This is the kind of agreement that builds confidence in any theory.
In the n = 2 quantum state, atomic hydrogen has an energy of




This is a higher (less negative) energy than the n = 1 state. In this state, the atom is only 78 kcal more stable than the ion. The higher the quantum number, n, the closer the energy comes to that of the ionized atom. Ionization, or removal of the electron, can be considered as placing the electron in quantum state n = (i.e., the electron is an infinite distance from the nucleus), with energy