What are the various postulates of Bohr's model of atom? How could Bohr's model explain the existance of so many lines in the specturm of hydrogen?

Answer

Assumptions of Bohr's model:
There are certain orbits around the nucleus such that if electron will be revolving in these orbit, without emmitting any electromagnetic radiation. These are called stationary orbit.
The necessary centripetal force is produced by attraction forces of nucleus.
`(mv^(2))/(r)=(Ke^(2)Z)/(r^(2))`
Angular momentum of the electron in these stationary orbit is always an integral multiple of `h/(2pi)`
`mvr=(nh)/(2pi)`
Electron can make jump from one stationary orbit to another stationary orbit by absorbing or emitting a photon of energy equal to difference in the energies of the stationary orbit.
`(hc)/lambda=DeltaE " " DeltaE`= difference in the energy of orbit
Line Spectrum of Hydrogen : Line spectrum of hydrogen is observed due to excitation or de-excitation of electron from one stationary orbit to another stationary orbit
Let electron makes transition from `n_(2)` to `n_(1) (n_(2) gt n_(1))` in a H-like sample
`(##RES_PHY_CHM_V01_XI_C02_E01_035_A01##)`
Energy of emitted photon `=(DeltaE)_(n2 rarr n1)=(-13.6Z^(2))/(n_(2)^(2))-((-13.6Z^(2))/(n_(1)^(2)))=13.6Z^(2) (1/n_(1)^(2)-1/n_(2)^(2))`
Wavelength of emitted photon
`lambda=(hc)/((DeltaE)_(n_(2) rarr n_(1)))`
`lambda=(hc)/(13.6Z^(2)(1/n_(1)^(2)-1/n_(2)^(2)))`
`1/lambda=((13.6)z^(2))/(hc)(1/n_(1)^(2)-1/n_(2)^(2))`
Wave number, `1/lambda=bar(v)=RZ^(2)(1/n_(1)^(2)-1/n_(2)^(2))`
`R="Rydberg constant"=1.09678xx10^(7) m^(-1); R cong 1.1xx10^(7) m^(-1); R=(13.6 eV)/(hc); R ch=13.6 eV`
`(##RES_PHY_CHM_V01_XI_C02_E01_035_A02##)`