Question

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

• A. An atom in a stationary state does not emit electromagnetic radiation as long as it stays in the same state
• B. An atom can take only certain distinct energies \( E_1 \), \( E_2 \), \( E_3 \), etc. These allowed states of constant energy are called the stationary states of atom
• C. When an electron makes a transition from a higher energy stationary state to a lower energy stationary state, then it emits a photon of light
• D. The electron in a H atom's stationary state moves in a circle around the nucleus

Hint:

Bohr's model assumes electrons move in circular orbits, while quantum mechanics describes electrons in terms of probability distributions (orbitals).

Answer 1

The Correct Option is D

The question asks to identify which postulate of Bohr's atomic model is inconsistent with the modern quantum mechanical model of the atom.

Concept Used:

We need to compare the fundamental postulates of Bohr's model for the hydrogen atom with the principles of the quantum mechanical model. Bohr's Model Postulates:

1. Electrons revolve around the nucleus in fixed, circular orbits called stationary states.
2. The angular momentum of an electron in these orbits is quantized: \( L = mvr = n\frac{h}{2\pi} \).
3. An electron in a stationary state does not radiate energy.
4. Energy is emitted or absorbed as a photon only when an electron transitions between two stationary states, with photon energy \( E = h\nu = E_{initial} - E_{final} \).

Quantum Mechanical Model Principles:

1. The behavior of an electron is described by a wave function (\( \psi \)), which gives the probability of finding the electron in a region of space.
2. The concept of a well-defined orbit is replaced by an orbital, a three-dimensional region of high probability. This is a consequence of the Heisenberg Uncertainty Principle, which states that it's impossible to know both the exact position and momentum of an electron simultaneously.
3. The energy of an electron is quantized, leading to discrete energy levels, which correspond to stationary states.
4. Transitions between these energy levels involve the emission or absorption of photons.

Step-by-Step Solution:

Step 1: Analyze option (1).

"An atom in a stationary state does not emit electromagnetic radiation as long as it stays in the same state." This is a key postulate of Bohr's model. In the quantum mechanical model, the solutions to the time-independent Schrödinger equation are stationary states with well-defined energies. An atom in such a state will not spontaneously change or radiate energy. This concept is in agreement with the quantum model.

Step 2: Analyze option (2).

"An atom can take only certain distinct energies E₁, E₂, E₃, etc. These allowed states of constant energy are called the stationary states of atom." This is the principle of energy quantization. Bohr introduced this idea, and it is a fundamental result of solving the Schrödinger equation in the quantum mechanical model. So, this postulate is in agreement.

Step 3: Analyze option (3).

"When an electron makes a transition from a higher energy stationary state to a lower energy stationary state, then it emits a photon of light." This explains atomic emission spectra and is known as the Bohr frequency condition. The quantum mechanical model also explains spectral lines through transitions between quantized energy levels. This postulate is also in agreement.

Step 4: Analyze option (4).

"The electron in a H atom's stationary state moves in a circle around the nucleus." This postulate defines a precise trajectory (a circular orbit) for the electron. This is a classical mechanics concept of a particle. The quantum mechanical model, however, fundamentally rejects the idea of well-defined paths for electrons due to the Heisenberg Uncertainty Principle. It describes the electron's location using a probability distribution called an orbital. For the ground state of a hydrogen atom (n=1), the orbital (1s) is spherically symmetrical, meaning the electron can be found anywhere around the nucleus within a certain radius, not just in a planar circle. Therefore, this postulate is in direct contradiction with the quantum mechanical model.

The postulate of Bohr's model that is not in agreement with the quantum mechanical model of an atom is (4) The electron in a H atom's stationary state moves in a circle around the nucleus.