It was Niels Bohr who made the first step in the development of the quantum theory of atoms in 1913. He stated his ideas in the form of three postulates.
1. Each atom has a set of possible energy levels (stable states) . An atom can have an amount of internal energy that is equal to any of these levels, but it cannot have an amount of energy that is intermediate between these levels. In stable states, atoms do not radiate energy.
2. An atom can make a transition from one energy level to another by emitting a quantum of electro-magnetic energy (a photon) . The energy of an emitted or absorbed photon is equal to the energy difference between the levels: hν = En - Em where h = 6.63*10-34 J s (Planck's constant), and ν is the photon's frequency. Both these postulates contradict the laws of classical physics, but experimental data supports them.
3. The third postulate assumes that electrons in an atom revolve in certain circular stable orbits with a quantum angular momentum: mvrn = n(h/2π) where m is the electron's mass, vis its velocity, and rn is the orbit radius. The integer n is the quantum number. Applying Bohr's quantum postulates to circular orbits of the hydrogen atom results in the following equations: The radii of the orbits are: rn = r1n2 where r1 = (ε0h2/(πme2) = 5*10-11 m is the Bohr radius. The total energies of the states are: En = - (1/ε02)*(me4/8h2)*(1/n2) . The state with the least energy (n = 1) is called the ground state. For the hydrogen atom E1 = -21.7*10-19 J = -13.6 eV, this energy is called the ionization energy.