The Bohr model or Rutherford-Bohr model of the atom is a cake or planetary model that describes the structure of atoms mainly in terms of quantum theory. It’s called a planetary or cake model because electrons orbit the atomic nucleus like planets orbit the Sun, while the circular electron orbits form shells, like the layers of a cake. Danish physicist Niels Bohr proposed the model in 1913.

The Bohr model was the first atomic model incorporating some quantum mechanics. Earlier models were the cubic model (1902), plum-pudding model (1904), Saturnian model (1904), and Rutherford model (1911). Ultimately, models based entirely on quantum mechanics replaced the Bohr model. Yet, it’s an important model because it describes the quantum behavior of electrons in simple terms and explains the Rydberg formula for the spectral emission lines of hydrogen.

### Key Points of the Bohr Model

- The atomic nucleus consists of protons and neutrons and has a net positive charge.
- Electrons have a negative charge and orbit the nucleus.
- Electron orbits are circular, but not all electrons orbit in the same plane (like planets around a star), resulting in spheres or shells where an electron might be found. While gravity determines orbits of planets around stars, electrostatic forces (Coulomb force) causes electrons to orbit the nucleus.
- The lowest energy for an electron (most stable state) is in the smallest orbit, which is closest to the nucleus.
- When an electron moves from one orbit to another, energy is absorbed (moving from lower to higher orbit) or emitted (moving from higher to lower orbit).

### The Bohr Model of Hydrogen

The simplest example of the Bohr Model is for the hydrogen atom (Z = 1) or for a hydrogen-like ion (Z > 1), in which a negatively charged electron orbits a small positively charged nucleus. According to the model, electrons only occupy certain orbits. The radius of possible orbits increases as a function of n^{2}, where n is the principle quantum number. If an electron moves from one orbit to another, energy is absorbed or emitted. The 3 → 2 transition produces the first line of the Balmer series. For hydrogen (Z = 1), this line consists of photons with a wavelength of 656 nm (red).

### Bohr Model for Heavier Atoms

The hydrogen atom only contains one proton, while heavier atoms contain more protons. Atoms require additional electrons to cancel out the positive charge of multiple protons. According to the Bohr model, each orbit only holds a certain number of electrons. When the level filled, additional electrons occupy the next higher level. So, the Bohr model for heavier electrons introduces electron shells. This explains some properties of heavy atoms, such as why atoms get smaller as you move from left to right across a period (row) of the periodic table, even though they contain more protons and electrons. The model also explains why noble gases are inert, why atoms on the left side of the periodic table attract electrons, and why elements on the right side (except noble gases) lose electrons.

One problem applying the Bohr model to heavier atoms is that the model assumes electron shells don’t interact. So, the model doesn’t explain why electrons don’t stack in a regular manner.

### Problems With the Bohr Model

While the Bohr model surpassed earlier models and described absorption and emission spectra, it had some issues:

- The model couldn’t predict spectra of large atoms.
- It doesn’t explain the Zeeman effect.
- It doesn’t predict relative intensities of spectral lines.
- The model violates the Heisenberg Uncertainty Principle because it defines both the radius and orbit of electrons.
- It incorrectly calculates ground state angular momentum. According to the Bohr model, ground state angular momentum is
*L*=*ħ*. Experimental data shows L=0. - The Bohr model doesn’t explain fine and hyperfine structure of spectral lines.

### Improvements to the Bohr Model

The Sommerfeld or Bohr-Sommerfeld model significantly improved on the original Bohr model by describing elliptical electron orbits rather than circular orbits. This allowed the Sommerfeld model to explain atomic effects, such as the Stark effect in spectral line splitting. However, the Sommerfeld model couldn’t accommodate the magnetic quantum number.

In 1925, Wolfgang’s Pauli’s atomic model replaced the Bohr model and those based upon it. Pauli’s model was based purely on quantum mechanics, so it explained more phenomena than the Bohr model. In 1926, Erwin Schrodinger’s equation introduced wave mechanics, leading to the modifications of Pauli’s model that are used today.

### References

- Bohr, Niels (1913). “On the Constitution of Atoms and Molecules, Part I”.
*Philosophical Magazine*. 26 (151): 1–24. doi:10.1080/14786441308634955 - Bohr, Niels (1914). “The spectra of helium and hydrogen”.
*Nature*. 92 (2295): 231–232. doi:10.1038/092231d0 - Lakhtakia, Akhlesh; Salpeter, Edwin E. (1996). “Models and Modelers of Hydrogen”.
*American Journal of Physics*. 65 (9): 933. Bibcode:1997AmJPh..65..933L. doi:10.1119/1.18691 - Pauling, Linus (1970). “Chapter 5-1”.
*General Chemistry*(3rd ed.). San Francisco: W.H. Freeman & Co. ISBN 0-486-65622-5.