Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom ?

First recall the basic postulates of Bohr for the hydrogen atom:

(i) The electron can revolve only in those circular orbits in which its angular momentum is an integral multiple of $$\hbar$$ and the energy of the atom is constant in each allowed orbit (stationary state).
(ii) While the electron stays in any one stationary state it does not radiate energy.
(iii) Energy is emitted or absorbed only when the electron jumps between two stationary states, the photon frequency being fixed by the energy difference of the two states.
(iv) Inside each stationary state the electron actually follows a definite circular path of radius $$r_n$$ around the nucleus.

Now compare these statements with the principles of the modern quantum-mechanical (wave-mechanical) model:

(a) Quantum mechanics also allows only discrete energies for bound electrons, hence statements about distinct energies and stationary states remain valid.
(b) The time-dependent Schrödinger equation shows that if an electron is in an energy eigen-state (stationary state) its probability density is time-independent, so no radiation is emitted — fully agreeing with Bohr’s “no radiation in a stationary state”.
(c) When an electron undergoes a transition between two energy eigen-states, quantum mechanics predicts emission or absorption of a photon whose energy equals the energy difference — matching Bohr’s third postulate.
(d) However, quantum mechanics does not assign a precise trajectory (circular or otherwise) to the electron. Instead, it gives only a probability distribution described by the wave function $$\psi(\mathbf{r})$$. Hence the idea of the electron moving in a well-defined circular orbit is incompatible with the uncertainty principle and the wave nature of the electron.

Examine each option in light of this comparison:

Option A: “An atom in a stationary state does not emit electromagnetic radiation …” — this is fully consistent with quantum mechanics.
Option B: “An atom can take only certain distinct energies $$E_1, E_2, E_3, …$$” — also consistent with quantum mechanics.
Option C: “When an electron makes a transition … it emits a photon …” — again agrees with quantum mechanics.
Option D: “The electron in a H atom’s stationary state moves in a circle around the nucleus” — this assumes a definite trajectory, which is ruled out by the quantum-mechanical picture.

Therefore, the postulate that contradicts the quantum mechanical model is Option D.

Final Answer: Option D