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 objective is to determine which postulate of Bohr's atomic model contradicts the modern quantum mechanical model of the atom.

Concept Used:

A comparison between Bohr's fundamental postulates for the hydrogen atom and the principles of the quantum mechanical model is required. Key Postulates of Bohr's Model:

1. Electrons orbit the nucleus in specific, circular paths known as stationary states.
2. The angular momentum of an orbiting electron is quantized: \( L = mvr = n\frac{h}{2\pi} \).
3. Electrons in stationary states do not emit energy.
4. Energy is exchanged as a photon only when an electron transitions between stationary states, with the photon's energy defined as \( E = hu = E_{initial} - E_{final} \).

Core Principles of the Quantum Mechanical Model:

1. Electron behavior is described by a wave function (\( \psi \)), which indicates the probability of finding the electron in a given spatial region.
2. The concept of a precisely defined orbit is replaced by an orbital, which is a three-dimensional probability distribution. This arises from the Heisenberg Uncertainty Principle, precluding simultaneous knowledge of an electron's exact position and momentum.
3. Electron energy is quantized, resulting in discrete energy levels that correspond to stationary states.
4. Transitions between these energy levels are associated with photon emission or absorption.

Step-by-Step Solution:

Step 1: Evaluate postulate (1).

"An atom in a stationary state does not emit electromagnetic radiation as long as it remains in that state." This is a central postulate of Bohr's model. In the quantum mechanical model, stationary states, determined by the time-independent Schrödinger equation, possess well-defined energies. Atoms in these states do not undergo spontaneous change or energy radiation. This principle aligns with the quantum model.

Step 2: Evaluate postulate (2).

"An atom can only possess specific discrete energies E₁, E₂, E₃, etc. These permissible energy states are termed the atom's stationary states." This refers to energy quantization, an idea introduced by Bohr and a fundamental outcome of solving the Schrödinger equation in the quantum mechanical model. This postulate is consistent.

Step 3: Evaluate postulate (3).

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

Step 4: Evaluate postulate (4).

"The electron in a H atom's stationary state moves in a circle around the nucleus." This postulate posits a specific trajectory (a circular orbit) for the electron, reflecting a classical mechanics perspective of a particle. The quantum mechanical model, however, fundamentally rejects the notion of precisely defined electron paths due to the Heisenberg Uncertainty Principle. Instead, it describes electron location via a probability distribution called an orbital. For the hydrogen atom's ground state (n=1), the 1s orbital is spherically symmetric, indicating the electron can be found at various distances from the nucleus, not confined to a planar circle. Consequently, this postulate directly contradicts the quantum mechanical model.

The postulate from Bohr's model that is inconsistent 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.