Bohr's Atomic Theory

It is based on the application of quantum theory of radiation.

Postulates:

• The electrons revolve around the nucleus with definite velocity in certain fixed closed paths called orbits.There are numbered as 1, 2, 3, 4…… (Or) K, L, M, N from the Nucleus.
• The angular momentum of electron is an integral multiple of the factor    
       
        n – Principle quantum number      m - Mass of electron
        v - Velocity of electron      h - Planck’s constant

•  Each stationary state is associated with definite amount of energy.
• As long as an electron is revolving in an orbit neither loses nor gains energy. Hence these orbits are called stationary states.
• The energy of an electron changes only when it moves from one orbit to another.
• Outer orbits have higher energy and Inner orbits have lower energy.
• The energy is absorbed when electron moves from inner orbit to outer orbit.
• The energy is releases when electron jumps from outer orbit to inner orbit.
• ΔE = E₂ – E₁ = hv

According to Bohr’s theory for hydrogen atom:

• Radius of n^th orbit Hydrogen atom.
  
• r_n = 0.529 * 10^-8 n² cm
  If n = 1, r = 0.529 ^oA
  
• For Hydrogen like ions (He⁺, Li²⁺, Be³⁺)
  
• The radii may be given as
                                     
  Z – Atomic number of species
                                     
  Where,                         
                                      
   e = charge of electron
  
•  Energy of electron in hydrogen atom.
  
  
• Energy expression for hydrogen like ions (He⁺, Li²⁺, Be³⁺) is
  
                                                                                          E_n = E_H * Z²
• Velocity of electron in the first orbit of hydrogen atom is 2.18 * 10⁸ cm s^-1
• Velocity of electron in the one electron species (He⁺, Li²⁺, Be³⁺) is given as
                               
• Time period of revolution of electron in n^th orbit
                              
• Orbital frequency: Number of revolutions per second of an electron in a shell. It is given as:
  
                                           
• When an electron returns from n₂ to n₁ state, the number of lines in the spectrum will be
                                        
  

Advantages of Bohr's model:-

·        It explains the stability of the atom.

·        It explains the atomic spectrum of hydrogen.

·        It also explains hydrogen like species spectrum
Ex: He⁺, Li²⁺ and Be³⁺.

·        Experimentally determined frequencies of spectral line are in close agreement with those calculated by Bohr’s theory.

Limitations:-

·        It fails to explain spectra of multi electron atoms.

·        It could not explain fine structure or atomic spectrum.

·        Bohr’s theory is not in agreement with Heisenberg’s uncertainty principle.

·        It could not explain the ability of atoms to form molecules by chemical bonding.

·        It is unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman Effect) or an electric field (Stark effect).

·        Ignores dual behavior of matter.