Bohr’s Atomic Model & Electron Orbits - Notes | Study Physics Class 12 - NEET

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 = E₂ – E₁

where E₁ and E₂are energies of electron in orbits.

Radius of orbit of electron is given by

r = n²h² / 4π² mK Ze² ⇒ r ∝ n² / 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 = 2πKZe² / nh ⇒ v ∝ Z / n

Frequency of electron in any orbit is given by

v = KZe² / nhr = 4π²Z²e⁴mK² / n³ h³

⇒ v prop; Z³ / n³

Kinetic energy of electron in any orbit is given by

E_k = 2π²me⁴Z²K² / n² h² = 13.6 Z² / n² eV

Potential energy of electron in any orbit is given by

E_p = – 4π²me⁴Z²K² / n² h² = 27.2 Z² / n² eV

⇒ E_p = ∝ Z² / n²

Total energy of electron in any orbit is given by

E = – 2π²me⁴Z²K² / n² h² = – 13.6 Z² / n² eV

⇒ E_p = ∝ Z² / n²

Wavelength of radiation emitted in the radiation from orbit n₂ to n₁ is given by

In quantum mechanics, the energies of a system are discrete or quantized. The energy of a particle of mass m is confined to a box of length L can have discrete values of energy given by the relation

E_n = n² h² / 8mL² ; n < 1, 2, 3,…