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Deduction Balmer's formula from the Bohr atom

comes from: The atomic structure: light and quantum physics
See also: quantization of the orbits of the Bohr atom

The quantization of the orbits of the atom, along with the ad hoc assumption Bohr that an electron does not emit radiation while remains in an orbit, leads naturally to the Balmer formula.

total energy of the electron is the sum of its kinetic energy (due to movement), and potential energy (due to electrostatic attraction with the nucleus)

This equation means that each orbit is associated with a given energy. In particular, the lower orbit has an energy of 13.6 eV (electron volts). The minus sign is interpreted as the electron is inside the atom. The closer to zero this value, it means that is closer to escape the atom. A one electron orbital n = 1 should be 13.6 eV for starting supply of the atom. Other orbital (n = 2, n = 3, etc) require a Enerio E ₀ / 4, E ₀ / 9, E ₀ / 16, ... etc to be uprooted.

The factor E ₀ / h is the constant that appears in Rydbeg formula Balmer. Through the Bohr atom is in theory an expression that had been deduced empirically from previous experiments.