Limitations of Rutherford Atomic Model
( i ) About the Stability of Atom According to Maxwell ’ s electromagnetic wave theory electron should emit energy in the form of electromagnetic wave during its orbital motion . Therefore . radius of orbit of electron will decrease gradually and ultimately it will fall in the nucleus .
( ii ) About the Line Spectrum Rutherford atomic model cannot explain atomic line spectrum .
Bohr ’ s Atomic Model
Electron can revolve in certain non-radiating orbits called stationary or bits for which the angular momentum of electron is an integer multiple of ( h / 2π )
mvr = nh / 2π where n = I , 2 . 3 ,… called principle quantum number .
The radiation of energy occurs only when any electron jumps from one permitted orbit to another permitted orbit .
Energy of emitted photon hv = E 2 – E 1 where E 1 and E 2 are energies of electron in orbits .
Radius of orbit of electron is given by r = n 2 h 2 / 4π 2 mK Ze 2 ⇒ r ∝ n 2 / Z
where , n = principle quantum number , h = Planck ’ s constant , m = mass of an electron , K = 1 / 4 π ε , Z = atomic number and e = electronic charge .
Velocity of electron in any orbit is given by v = 2πKZe 2 / nh ⇒ v ∝ Z / n
Frequency of electron in any orbit is given by
v = KZe 2 / nhr = 4π 2 Z 2 e 4 mK 2 / n 3 h 3
⇒ v prop ; Z 3 / n 3