Bohr Atomic Model - Structure of Atom

Bohr Model of Atom was based on theories of wave motion. It considered that electron, while spinning, maintains its energy and does not cascade into the nuclei. Hence, unlike Rutherford's model, it correctly explained the stability of atom. 

Some salient features and conclusions made from this model were:

• This model was based on quantum theory of radiation and classical laws of physics. 
• Bohr model is applicable only for single electron species like H, He⁺, Li²⁺ etc. 
• Bohr model is based on particle nature of electron. 
• Coulombic force=kq₁q₂/r²
• Centrifugal force = mv²/r
•  Angular momentum = mvr

Postulates of Bohr's Model

Postulate 1

• Atom has a nucleus where all protons and neutrons are present.
• The size of nucleus is very small and it is present at the centre of the atom.

Postulate 2

• Negatively charged electron revolve around the nucleus in the same way as the planets revolve around the sun. 
• The path of electron is circular. 
• The attraction force (Coulombic or electrostatic force) between nucleus and electron is equal to the centrifugal force on electron.
  i.e. Attraction force towards nucleus = centrifugal force away from nucleus.

Postulate 3

• Electrons can revolve only in those orbits in which angular momentum (mvr) of electron is integral multiple of h/2π i.e.
  
  mvr = nh/2π;
  where m=mass,
  v=velocity,
  r=radius of orbit,
  n=number of orbit,
  h=Plank's constant
• Angular momentum can have values such as h/2π , h/π, 3h/2π... but cannot have fractional values such as (1.5)h/2π , (1.2) h/2π etc. 

Postulate 4

• The orbit in which electron can revolve are known as stationary orbit because in these orbit energy of electron is always constant

Postulate 5

• Each stationary orbit is associated with definite amount of energy therefore these orbits are also called as energy levels and are numbered as 1, 2, 3, 4, 5, .... or K, L, M, N, O, ..... from the nucleus outwards.

Postulate 6

• The emission or absorption of energy in the form of photon can only occur when electron jumps from one stationary state to another & it is
  
  ΔE=E_higher-E_lower=E_n2-E_n1
  ΔE=hv 
• Energy is absorbed when electron jumps from inner to outer orbit and is emitted when electron moves from outer to inner orbit. 
• n₂ > n₁ whether emission or absorption of energy will occur.

Applications of Bohr's Model

1. Radius of Various Orbits (Shell)

This formula is only applicable for hydrogen and hydrogen like species i.e. species containing single electron. 

2. Velocity of an electron in an Orbit (Shell)

3. Energy of an Electron

Let the total energy of an electron be E. 

1. This formula is applicable for hydrogen atom & hydrogen like species i.e. single electron species. 
2. Since n can have only integral values, it follows that total energy of the e– is quantised. 
3. The –ve sign indicates that the electron is bonded towards nucleus.

4. Explanation of Line Spectrum of Hydrogen

How Hydrogen Spectrum is recorded:

• When an electric excitation is applied on hydrogen atomic gas at low pressure, a bluish light is emitted.
• When a ray of this light is passed through a prism, a spectrum of several isolated sharp lines is obtained.
• The wavelength of various lines show that spectrum lines lie in Visible, Ultraviolet and Infra red region. 
• These lines are grouped into different series.

Line spectrum of Hydrogen atom:

Various Lines corresponds to different levels of excitations of electrons. Excitation and line formed corresponding are shown below:

5. Rydberg's Formula

Rydberg gave a very simple theoretical equation for the calculation of the energy and wavelength of various lines of hydrogen like spectrum which are formed when electron in a hydrogen atom move from n₁

 orbit to n₂. 

Limitations of Bohr Model

1. Bohr's theory does not explain the spectrum of multi electron atom/ion. 
2. Why the Angular momentum of the revolving electron is equal to nh 2π , has not been explained by Bohr's theory. 
3. Bohr inter related quantum theory of radiation and classical laws of physics without any theoretical explanation. 
4.  Bohr's theory does not explain the fine structure of the spectral lines. Fine structure of the spectral line is obtained when spectrum is viewed by spectroscope of more resolution power. 
5. Bohr's theory does not explain the splitting of spectral lines in the presence of magnetic field (Zemman's effect) or electric field (Stark's effect). 

Next topic: Dual Nature of Electron. Heisenberg's Uncertainty principle, De Broglie hypothesis. 

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