The Bohr Model: What It Got Right and Where It Fails

Draw an atom and most people produce the same picture: a small nucleus with electrons circling it in neat rings, like planets around the Sun. That picture comes largely from the Bohr model, proposed by the Danish physicist Niels Bohr in 1913. It was a bold, partly correct, partly wrong idea that transformed physics and chemistry. This article explains what Bohr proposed, why it was such a breakthrough, and why it was eventually replaced.

The problem Bohr set out to solve

In 1911, Ernest Rutherford showed that atoms have a tiny, dense, positive nucleus, with electrons somewhere around it. See inside the atomic nucleus and the history of atomic models.

But Rutherford’s atom had a serious problem. According to the physics of the time (classical electromagnetism), an electron moving in a circle is constantly accelerating, and accelerating charges emit radiation. So an orbiting electron should continuously lose energy, spiral inwards and crash into the nucleus in a tiny fraction of a second. Atoms shouldn’t be stable at all, yet they obviously are.

There was a second puzzle. When hydrogen gas is excited by electricity, it glows, and if that light is passed through a prism, it doesn’t produce a continuous rainbow. It produces a few sharp coloured lines at very specific wavelengths. Classical physics couldn’t explain why. See the hydrogen emission spectrum.

Bohr’s postulates

Bohr combined Rutherford’s nucleus with the new quantum ideas of Max Planck and Albert Einstein. He made three bold assumptions:

1. Electrons move in certain allowed circular orbits around the nucleus, and while in these orbits, they don’t radiate energy. These orbits are called stationary states or energy levels.
2. Each orbit has a fixed energy. Orbits are numbered n = 1, 2, 3… (the principal quantum number). The n = 1 orbit is closest to the nucleus and lowest in energy.
3. Electrons can jump between orbits. When an electron moves from a higher energy level to a lower one, it emits a photon whose energy exactly equals the energy difference between the levels. To move up, it must absorb a photon of exactly the right energy.

ΔE = E(higher) − E(lower) = hf

where h is Planck’s constant and f is the frequency of the light. See photons and energy levels.

Bohr also proposed a rule for which orbits are allowed: the electron’s angular momentum must be a whole-number multiple of h/2π. From this, he could calculate the energy and radius of each orbit.

How it explained hydrogen

Bohr’s model gave a simple formula for the energy of each level in a hydrogen atom:

Eₙ = −2.18 × 10⁻¹⁸ J ÷ n² (equivalently, −13.6 eV ÷ n²)

• n = 1: −13.6 eV (the ground state)
• n = 2: −3.4 eV
• n = 3: −1.51 eV
• n = ∞: 0 (the electron has escaped: the atom is ionised)

The energies are negative because the electron is bound to the nucleus; energy must be supplied to free it.

When an electron falls from n = 3 to n = 2, the energy released is 3.4 − 1.51 = 1.89 eV, which corresponds to red light with a wavelength of about 656 nm. That’s exactly one of the lines seen in hydrogen’s spectrum. Bohr’s model reproduced all the visible hydrogen lines (the Balmer series), and it predicted others in the ultraviolet and infrared that were then confirmed. It also predicted the correct ionisation energy of hydrogen, 13.6 eV (1,312 kJ/mol). For the calculations, see Bohr model calculations.

This was a spectacular success. Bohr received the Nobel Prize in Physics in 1922.

What the Bohr model got right

• Quantised energy levels. Electrons in atoms can only have certain energies. This is still true in modern quantum theory.
• Photon emission and absorption during transitions between levels, explaining line spectra, flame test colours and neon signs.
• The principal quantum number n, which survives in the modern model as the shell number.
• The idea of shells that fill with electrons, which chemists extended into the 2, 8, 8 model. See electron shells explained.
• Ionisation energy of hydrogen, calculated correctly.

Where the Bohr model fails

Despite its success with hydrogen, the model has serious limitations:

1. It only works for one-electron systems. It correctly predicts spectra for hydrogen and one-electron ions such as He⁺ and Li²⁺, but fails badly for helium and every other atom with two or more electrons, because it ignores electron–electron repulsion.
2. It can’t explain the fine details of spectra. High-resolution spectroscopy shows that many lines are actually closely spaced groups of lines (fine structure), and lines split in magnetic fields (the Zeeman effect) in ways the model can’t fully explain.
3. It can’t explain relative intensities of spectral lines.
4. It says nothing useful about chemical bonding or the shapes of molecules.
5. It violates the uncertainty principle. Bohr’s electrons have precise orbits with exact radii and speeds. In 1927, Werner Heisenberg showed that it’s impossible to know both an electron’s exact position and exact momentum at the same time. Precise orbits simply can’t exist.
6. It has no explanation for why only certain orbits are allowed; the rule was assumed, not derived.

What replaced it

In the mid-1920s, quantum mechanics (developed by Heisenberg, Schrödinger, Dirac and others) replaced the Bohr model:

• Electrons are described by wavefunctions, not orbits.
• Instead of circular paths, electrons occupy orbitals: three-dimensional regions where they’re likely to be found. See the shapes of s, p, d and f orbitals.
• Energy levels arise naturally from the wave nature of the electron, like the allowed notes on a guitar string.
• Additional quantum numbers (l, mₗ, mₛ) describe subshells, orbitals and spin. See quantum numbers explained.

For hydrogen, the Schrödinger equation gives exactly the same energy levels as Bohr’s formula, which is why his model worked so well there.

Why the Bohr model is still taught

• It introduces quantised energy levels in a simple, visual way.
• It explains line spectra and why atoms emit specific colours.
• It gives correct numbers for hydrogen with straightforward calculations.
• It’s a perfect example of how science progresses: a model that explains some data brilliantly, reveals its own limits, and leads to a better theory.

Just remember that it’s a stepping stone. Electrons don’t really orbit like planets.

A fair summary: Bohr asked the right question and found the right kind of answer, even though the details were wrong.

Key takeaways

• Bohr (1913) proposed that electrons occupy fixed energy levels and emit or absorb photons when they jump between them.
• His model explained the line spectrum of hydrogen and its ionisation energy with remarkable accuracy.
• Energy levels in hydrogen are Eₙ = −13.6 eV ÷ n².
• It fails for atoms with more than one electron, can’t explain bonding, and conflicts with the uncertainty principle.
• Quantum mechanics replaced orbits with orbitals, but kept Bohr’s central idea of quantised energy.