Bohr Model Limitations And Quantum Mechanical Model

Bohr's model was a landmark achievement that introduced quantized energy levels and accurately predicted the hydrogen spectrum. However, its failures arise from three interconnected limitations that become critical in multi-electron atoms. First, Bohr treats electrons as classical particles moving in well-defined circular (or elliptical in Sommerfeld's extension) orbits, which contradicts Heisenberg's uncertainty principle — the very concept of a definite path for an electron is quantum mechanically untenable. Second, for atoms with two or more electrons (starting from He, Z=2), electron-electron repulsion introduces complex many-body interactions that cannot be handled by Bohr's pairwise nuclear attraction model. The energy of each electron depends on the positions of all other electrons, creating an inseparable mathematical problem. Third, Bohr's model produces only a single quantum number n, unable to account for the directional character (l, m_l) and spin (m_s) of electron states, which are needed to explain the fine structure of spectral lines, the Zeeman effect, and the detailed chemistry of multi-electron atoms. Option (A) is partially correct in mentioning spin but incorrect to say Bohr uses 'wrong quantum numbers'; Bohr correctly introduced n but incompletely. Option (C) is factually wrong; Bohr's quantization of angular momentum L = nh/2π with integer n was a correct and foundational assumption. Option (D) is incorrect; adjusting R_H does not resolve the electron-electron repulsion problem in He. The quantum mechanical model, using wavefunctions and the Schrödinger equation, overcomes all these limitations. Plausibility check: even He (Z=2, 2 electrons) cannot be solved exactly by Bohr's model due to the three-body problem (nucleus + 2 electrons), while quantum mechanics uses perturbation theory or variational methods to handle it approximately.