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