Bohr's Model of Hydrogen Atom

Bohr's Model of Hydrogen Atom:-

 Bohr's atomic model:

  In order to explain the stability of an atom, Neils bohr give a new arrangement of electrons in the atom in 1913. According to Neils bohr,the electrons revolve around the nucleus in the only 'certain orbits' (energy level), each Orbit having a different radius.
   When an electron is revolving in a particular Orbit or particular energy level around the nucleus, the electron does not radiate energy (loss energy even through it has accelerated motion around the nucleus.

Niels Bohs proposed an  atomic model, describing an atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the positively charged nucleus as planet around in the sun in our solar system,  with attraction provided by electrostatic force, popularly known as Bohr's atomic model.It was basically an improved vision of Rutherford's  atomic model overcoming its limitations.On most of the points, he is an agreement with him, like concepts of nucleus and electron orbiting it.

Limitations of Bohr's Atomic model  theory:-

  1. It violates the Heisenberg Uncertainty Principle. the Bohr atomic model theory considers electron to have both a known radius and Orbit i.e. known position and Momentum at the same time, when is impossible according to Heisenberg.

  2.It failed to explain the zeeman effect when the spectral line is split into several components in the presence of a magnetic field.

  3.The Bohr atomic model theory  made correct predictions for smaller sized atom like Hydrogen, but poor spectral predictions are obtained when larger atoms are considered.

  4.It  failed to explain the stark effect when the spectral line gets split up into fine lines in the presence of electronic field.

The silent feature of Bohr's atomic model are:-

  a. Electrons revolve around the nucleus in stable orbits without emission of Radiant energy flow stop each Orbit has a definite energy and its called energy cell or energy level.

  b. An electron emits or absorbs energy.When it jumps from one Orbit or energy level to another. when it jumps from higher energy level to lower energy level it emits energy while it absorbs energy when it jumps from lower energy level to higher energy level.

  c. An  Orbit or energy level is designated as K,L,M,N shells.when the electron is in the lowest energy level, it is said to be in the ground state.

  d. The  energy absorbed or eimitted is equal to the difference between the energies of the two energy levels(E1,E2) and determined by Planck's equation.

   ΔE = E2 – E1 = hv = hc / λ
          Where,
            ΔE= energy absorbed or emitted
              h= Planck’s constant
              c= velocity of radiation
              v = frequency of radiation.

e. Angular momentum of an electron revolving in energy shell is given by:-
    
          mvr = nh/2π
    Where,
          n =  Orbit number or principal
                quantum number (n =  1,2,3….)
          h= Planck’s constant
         m= mass of electron
         v = velocity of electron
         r= radius of orbit in which electron        
               is revolving

Some important formulae :

  ▪ This model was based on quantum theory of radiation and classica laws of physics.
▪ Bohr model is applicable only for single  ectron species like H, He+ , Li2+ etc.
▪ Bohr model is based on particle nature of electron.

       Coulombic Force :-


        Centrifugal Force :-
   

         Angular Momentum :-