Bohr's Model of the Atom

Introduction

Bohr's model kept the small positive nucleus but changed the rules used for electrons. Only selected states were allowed, and radiation was associated with transitions between them. This was a major departure from a classical planetary atom and explained important features of hydrogen's spectrum, although it did not become a complete theory of all atoms.

Core explanation

In Bohr's historical picture, the electron occupied certain allowed orbits with definite energies. While in one of these stationary states, it did not continuously radiate energy as a classical orbiting charge would. This was a new postulate, not a result derived from ordinary classical circular motion.

Energy could be absorbed or emitted when the atom changed between allowed states. The photon energy equalled the difference: hν = Efinal − Einitial . Upward transitions required energy input; downward transitions could emit it. Discrete energies therefore produced a discrete line spectrum.

For hydrogen, the simplest energy expression is approximately Eₙ = −13.6/n² eV with the ionisation limit chosen as zero. The lowest level n = 1 is the ground state. Higher n values have energies closer to zero and correspond to less tightly bound states. The negative sign indicates binding relative to a separated electron and proton; it is not a negative amount of usable light.

Bohr's approach reproduced the main hydrogen spectral pattern and extended usefully to one-electron ions with an adjusted nuclear-charge factor. It did not accurately describe ordinary many-electron atoms using the same simple formula. Their electron-electron interactions require a richer theory.

The familiar shell drawing remains helpful for counting electrons in introductory chemistry, but modern quantum mechanics uses orbitals rather than definite circular paths. A ring model is therefore a teaching representation, not a photograph of how electrons travel.

Bohr's Nobel lecture on atomic structure records the historical development of these quantum ideas. When studying the model, separate the enduring idea of quantised states from the historical orbital-path assumptions later replaced.

Step-by-step reasoning

1. Identify the atom's initial and final allowed energy levels. 2. Decide whether the transition raises or lowers its energy. 3. Calculate the magnitude of the energy difference. 4. Interpret that difference as absorbed or emitted photon energy, keeping the atomic change and photon energy signs distinct.

Visual explanation

Draw horizontal energy lines with n = 1 lowest and higher levels progressively closer together. Use an upward arrow for absorption and a downward arrow for emission. The vertical spacing represents energy, not the physical thickness or separation of solid shells.

Real-world analogy

A staircase permits standing on distinct steps rather than arbitrary heights between them. Moving upward requires added energy. This illustrates discrete states but has limits: atomic transitions are quantum processes, and electrons do not walk through every intermediate stair position.

Real-world example

Hydrogen discharge spectra contain lines that can be grouped by transitions ending at a common lower energy level. Their systematic frequencies were a key success for Bohr's energy model. The observed line positions test energy differences rather than directly confirming tiny planetary paths.

Why?

Why introduce allowed states instead of keeping every possible classical orbit? Continuous classical energies do not naturally supply the observed discrete spectral pattern or stable non-radiating states. The new restrictions addressed both problems, even though their deeper justification required later quantum mechanics.

Common misconception

“Bohr proved that electrons are little planets on visible rings.” The model assigned special orbits as a historical assumption. Modern orbitals describe quantum states and probability distributions, so the success of its hydrogen energy formula does not establish literal ring-shaped trajectories.

Worked example

Use Eₙ = −13.6/n² eV for hydrogen. E₁ = −13.6 eV and E₂ = −3.4 eV. Exciting the atom from n = 1 to n = 2 requires 10.2 eV. Returning from n = 2 to n = 1 releases a photon of that energy. The atomic energy change is negative during emission, but the emitted photon energy is positive.

Quick check

1. Does an electron continuously lose radiation energy while occupying a Bohr stationary state? Answer: No. The model postulates no continuous radiation from an allowed stationary state.

Exam focus

Explain allowed energies and transitions before using a formula. State that the simple energy expression applies to hydrogen in this form. Do not use it unchanged for sodium or other many-electron atoms simply because they also have shells.

Advanced insight

For a hydrogen-like one-electron ion, the idealised energies scale approximately with Z². The electron-electron interaction absent from such systems is one reason the one-electron formula is tractable. Precision treatments also include effects omitted from the introductory model.

Summary

Bohr introduced allowed stationary states and photon-producing transitions, explaining the main hydrogen energy pattern. Higher levels are less tightly bound, and photon energy equals a level difference. The quantised-state idea survives, while exact circular paths and unrestricted many-electron application do not.

Practice questions

1. Which hydrogen level is lower in energy, n = 1 or n = 2? Answer: n = 1, the more strongly bound ground state. 2. Must a transition to a higher energy level absorb energy or emit it? Answer: It must gain energy, for example by absorbing a suitable photon. 3. Why should a Bohr ring drawing not be called a modern electron orbital? Answer: A historical orbit specifies a path, whereas an orbital is a quantum state with a probability distribution.