Niels Bohr realized that Rutherford’s model developed by his scattering experiment only explained the scattering effect and did not present an answer to any of these problems:

1.  How are the electrons arranged about the atom?
2.  What keeps the negative electron from falling into a positive nucleus by electrical 
      attraction?
3.  What allows the Balmer formula for hydrogen admission and absorption spectral lines to 
      work?
4.  Of what is the nucleus composed?
5.  What keeps the nucleus from exploding on account of the repulsion of its positive 
     charges?

Niels was able to answer the first three questions in his first model presented 1912-1913.
 
 

The two postulates of this model stated:

1.  Electrons in the atom can exist in stationary states which emit no radiation.
2.  The emission and absorption of radiation is explained by a discontinuous transition 
     between these stationary states.  The frequency of the emitted or absorbed radiation 
     is modeled by the equation hf = Ei - Ef where h is Planck’s constant, f  is the frequency, 
     and Ei and Ef are approximately the energies of the atom in the initial and final stationary
     states.

Bohr calculated an equation for his model that gave simplistic values for the radii at which the electrons could orbit.  The equation was rn = an2 where a is the constant h2/4?2mkqe ( 5 X 10^-11 m ) and n was any integer except zero.  This model now theorized how the electrons were arranged about the atom. 

The first postulate allowed the electron to defy classical physics because old school states that a body such as the electron would radiate energy when moving in a planetary motion, which would cause the electron to be pulled in in less than a second.  Since there is no energy being emitted when the electron is in this “stationary state” it is able to move about like the moon does to earth without crashing into Australia like a space station.  This postulate also supports Robert Millikan’s Oil Drop experiment in that it explains how an atom can exist only in definite amounts of quanta, hence “stationary states.”

The second postulate explains how the atom can have varying values of quanta caused by the absorption or admittance of electromagnetic radiation ( light. )  The transitional stage between the stationary states is discontinuous or non existent.  The overall charge of the atom either increases or decreases to a minimum when the electron jumps from one stationary state to another.  The jump is caused by a quantized radiation that hits the atom and transfers the electron to another stationary state.  This occurrence can be modeled by Bohr’s equation as seen above hf = Ei - Ef . 
The Balmer formula is an empirical relation that determines the wavelength of light from spectral lines emitted by an element or elements.  What is most striking about the Bohr model is that it can be derived into the Balmer formula.  It looks like this

Balmer formula:  1  =  RH  X  1 - 1    Bohr formula:  hf = Ei - Ef 
               n²i  n²f

If the quantum number is n, Ef = 1 E1 and Ei = 1 E1 where E1 is the energy of the atom in the first orbit. 

Substituting each into Bohr’s Formula we get hf = E1 X 1 - 1
                                                                           n²i  n²f

Next substitute c /   for f:  hc = E1 X 1 - 1
                                                   n²i  n²f

Divide both sides by Plank’s constant h times the speed of light c:

      1 = E1 X 1 - 1
   hc    n²i n²f

RH is Ryberg’s constant which turns out to be equal to (-E1/ hc ), so we have:

Rutherford's Discoverary of the Nucleus

Quantum Model