Question

Why can't the Bohr Theory be used to calculate the predicted wavelengths of emitted photons in the line spectra of polyelectronic elements?

Answer 1

Bohr Theory cannot explain the line spectra of polyelectronic elements

(1) Bohr model is based upon imposing a quantization condition on an otherwise purely classical model. However, even though it gets some of the properties correct.As a consequence, it fails to get the spectroscopic splittings and energetics of a H atom in a magnetic field. It also fails in getting the spin-orbit (LS Coupling) interactions correct.

(2) Because of electron - electron interactions

(3) Pauli exclusion and electron spin not valid for these

So in the case of poly-electronic elements, the presence of other electrons in the shell interferes with the moving of electrons into an excited state, as they repulse other electrons as well as exert other forces. This makes the Rydberg equation no longer valid.

From Rydburg's Equation , 1/ λ = R[(1/n_i²) – (1/n_f²)]
   Where R = Rydburg's constant = 10.96 x10⁶ m^-1
               λ = wavelength = ?
               n_i = initial n value
               n_f = final n value