Question

Why does Bohr's model of the atom violate the Heisenberg Uncertainty Principle?

Answer 1

Well, Bohr's model of the atom assumes fixed orbits AND trajectories for the electron. Simultaneously known orbits and trajectories violate the Heisenberg Uncertainty Principle.

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Bohr's model of the nitrogen atom is:

The problem is, electrons do NOT travel in fixed orbits, and they do NOT travel with fixed trajectories. That is, they should NOT have simultaneously well-known positions `x` and momenta `p_x`.

Therefore, it should NOT be that the uncertainties in position and momentum are `Deltax = Deltap_x = 0`.

Heisenberg's Uncertainty Principle is:

`DeltaxDeltap_x >= ℏ//2`

The constant `ℏ = h//2pi` is the reduced Planck's constant, where `h = 6.626 xx 10^(-34) "J"cdot"s"`.

If `DeltaxDeltap_x = 0`, it cannot be greater than or equal to `ℏ//2`.

Therefore, the uncertainty `Deltax` in position, and the uncertainty `Deltap_x` in momentum, cannot both be zero...