Bohr Model of the Atom

The Bohr model says that an electron in hydrogen can exist only in certain allowed energy levels, not at any energy it wants. That idea helps explain why hydrogen absorbs and emits only specific wavelengths of light.

This model matters because it makes quantized energy easy to see. It is not the modern picture of the atom, but it is still a useful first step for understanding line spectra and energy-level jumps.

What The Bohr Model Means

Bohr proposed a simple picture for the hydrogen atom.

An electron can occupy only certain allowed energy levels around the nucleus. While it stays in one of those levels, it does not continuously lose energy.

Light is emitted or absorbed only when the electron jumps between levels. The photon energy matches the energy gap:

$$\Delta E = E_{\text{final}} - E_{\text{initial}}$$

If the electron moves to a lower-energy level, the atom emits a photon. If it absorbs exactly the right amount of energy, it can move to a higher level.

Why The Bohr Model Explains Hydrogen Spectra

Hydrogen does not produce every possible wavelength. It produces distinct spectral lines. The Bohr model explains that pattern by saying the electron can jump only between specific energy levels, so only specific energy changes are possible.

That is the main value of the model. If only certain energy gaps exist, only certain photon energies can be emitted or absorbed.

Worked Example: Hydrogen From $n = 3$ To $n = 2$

For hydrogen, the Bohr energy levels are commonly written as:

$$E_n = -\frac{13.6\ \text{eV}}{n^2}$$

This formula is for hydrogen in the basic Bohr model. It should not be treated as a general formula for all atoms.

For $n = 3$:

$$E_3 = -\frac{13.6}{9} \approx -1.51\ \text{eV}$$

For $n = 2$:

$$E_2 = -\frac{13.6}{4} = -3.40\ \text{eV}$$

Now find the electron's energy change:

$$\Delta E = E_2 - E_3 = -3.40 - (-1.51) \approx -1.89\ \text{eV}$$

The negative sign shows the electron ended at a lower-energy state. The atom emits a photon with energy $1.89\ \text{eV}$.

That is the Bohr model in action: one allowed jump gives one specific photon energy, not a continuous range.

Where The Bohr Model Stops Working Well

The Bohr model works best for hydrogen and hydrogen-like one-electron species. In multi-electron atoms, electron-electron interactions are too important for the simple orbit picture to stay accurate.

It also treats electrons as if they move in fixed circular paths. Modern quantum mechanics uses orbitals, which describe probability distributions rather than exact little planetary tracks.

Common Mistakes About The Bohr Atomic Model

Thinking it works equally well for every atom

It does not. In most chemistry courses, the Bohr model is mainly a stepping stone toward quantum theory.

Treating Bohr orbits as modern orbitals

Bohr orbits and quantum-mechanical orbitals are not the same idea. Orbitals describe probability distributions, not fixed circular paths.

Forgetting the hydrogen condition

Many statements about the Bohr model are safest when the atom is hydrogen. If that condition is not met, the model usually becomes much less reliable.

When You Still Use The Bohr Model

You still use the Bohr model when you want to:

1. introduce quantized energy levels
2. explain the hydrogen emission spectrum
3. connect atomic structure to photon absorption and emission
4. build intuition before learning orbitals and quantum numbers

Try A Similar Problem

Try your own version with the jump from $n = 2$ to $n = 1$ in hydrogen. Calculate both energy levels, find the gap, and decide whether the atom emits or absorbs light.

If you want the more accurate picture that replaces the Bohr model, electron configuration is the natural next step because it moves from fixed orbits to the modern language of shells, subshells, and orbitals.