Explain the success of Bohr's theory for hydrogen atom.

Explanation

The main success of Bohr's model :
(1) Bohr's model could explain the stability of an atom : According to Bohr's model , an electron revolving in a particular orbit cannot lose energy. An electron will absorb energy when it jumps from lower energy level to higher energy level or lose energy when it jumps from higher energy level to lower energy level . When there is no vacant lower energy level the electron keeps revolving in the same orbit without losing energy and thus explains the stability .
(2) Bohr theory helped to calculate the energy of an electron in an orbit : Basing on Bohr's model a mathematical relation can be developed to calculate the energy of an electron in `n^("th")` orbit .
`E_(n)=(-K^(2)2pi^(2)"me"^(4))/(n^(2)h^(2))`
where m = Mass of electron
e = Charge on electron
h = Planck's constant
k = coulombs constant `9.0xx10^(9)"Jm"//C^(2)`
Substituting the values of m , e, h , `pi` and k in the above expression we get
`E_(n)=-(2.178xx10^(-18))/(n^(2))J//"atom"`
`=-(13.595)/(n^(2))eV//"atom"=-(1312)/(n^(2))"kJ"//"mole"`
Using Bohr's model the radius of an orbit in hydrogen atom can be calculated
`r_(n)=(n^(2)h^(2))/(4pi^(2)"k me"^(2))=n^(2)xx0.529xx10^(-10)m`
`" " =n^(2) xx0.529Å`
(3) Bohr's model could explain the atomic spectrum of hydrogen : The different spectral lines in hydrogen spectrum is due to the emission of energy in the form of light when the electron jumps to lower energy level . When hydrogen gas is supplied from some external source , the electrons in different atoms absorb energy and excited to higher energy levels . When the electron returns back to lower energy levels it gives out energy in the form of quantum equal to the difference of energies between the two energy levels.
`E_(2)-E_(1)=hupsilon " or "upsilon=(E_(2)-E_(1))/(h)`
where `E_(1)` is the energy of lower energy level , `E_(2)` is the energy of high energy level and h is Planck's constant.
According to Bohr 's model , in a hydrogen atom (or in any other atom) `E_(2) andE_(1)` can have only certain definite values . From this , it follows that `upslion` can have only certain fixed values . Thus Bohr's model explains why there are certan discrete lines in the spectrum of hydrogen.