Reasons for Failure of the Bohr Model

Bohr's model failed for a reason deeper than any single missing detail: it treats the electron as an ordinary classical particle travelling along a precisely-defined circular path, with both its position and its momentum known exactly at every instant. Two developments in the 1920s showed this picture cannot be right. First, in 1924, Louis de Broglie proposed that matter — not just radiation — has a dual character: a moving particle such as an electron should show wave-like behaviour as well as particle-like behaviour, meaning it has both a momentum p (a particle property) and an associated wavelength $\lambda$ (a wave property), related by $\lambda = \frac{h}{mv} = \frac{h}{p}$. This prediction was confirmed experimentally by diffraction experiments on electron beams, a distinctly wave-like phenomenon. Second, in 1927, Werner Heisenberg stated the uncertainty principle: it is impossible to determine, simultaneously and exactly, both the position and the momentum (or velocity) of a particle such as an electron. The more precisely one of the two quantities is known, the less precisely the other can be known; for an electron of definite energy, this means only its PROBABILITY of being found at a given point can be determined, not its exact location. Mathematically, $\Delta x \times \Delta p_x \geq \frac{h}{4\pi}$ (equivalently $\Delta x \times \Delta(mv_x) \geq \frac{h}{4\pi}$, or $\Delta x \times \Delta v_x \geq \frac{h}{4\pi}$), where $\Delta x$ is the uncertainty in position and $\Delta p_x$ (or $\Delta v_x$) the uncertainty in momentum (or velocity). Bohr's model implicitly assumes the electron's position and momentum are BOTH known exactly at the same time — precisely what the uncertainty principle rules out. …