Bohr Model

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Following Ernest Rutherford’s 1911 alpha-scattering experiment, which established the planetary model of the atom, classical physics faced a critical flaw regarding atomic stability.

The Classical Dilemma: Radiation Collapse

According to Maxwell’s Electromagnetic Theory, any accelerating charged particle must continuously radiate energy in the form of electromagnetic waves.

Because an electron orbiting a positively charged nucleus undergoes continuous centripetal acceleration (ac = v2 / r), classical theory predicts that the electron must continuously lose kinetic energy. As its energy decreases, the orbital radius shrinks, causing the electron to spiral inward toward the nucleus and collapse the atom in a fraction of a second (∼ 10−11 s).

ac = v2⁄r = e2⁄4π ε0 me r2

Clearly, stable atoms exist—meaning classical electrodynamics fails at the atomic scale.

Bohr's Quantum Breakthrough

In 1913, Danish physicist Niels Bohr resolved this paradox by incorporating Max Planck’s concept of energy quantization into the atomic model.

Before examining Bohr’s key postulates and mathematical formulation, we must look at another critical piece of experimental evidence that shaped his work: discrete atomic spectral lines.


In the late 1800s, spectroscopy and spectral analysis advanced significantly following Joseph von Fraunhofer’s discovery of dark absorption lines in the solar spectrum.

However, a major question remained:

Was there a mathematical pattern to these discrete spectral lines?

The key breakthroughs came from Swedish physicist Johannes Rydberg and Swiss mathematician Johann Balmer, who derived empirical formulas to predict the exact wavelengths of light emitted by hydrogen atoms.

Watch the video to learn how their mathematical equations paved the way for Niels Bohr's quantum model of the atom.

Sample Problem
We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.



An emission spectrum of hydrogen reveals four lines in the visible range, called the Balmer Series. What frequency of light is emitted if the electron transition associated with this frequency moves from 5 to 2?

Theory

We have now covered the groundwork behind Bohr's model: the behavior of atomic spectra, the empirical mathematical models of Balmer and Rydberg, the instability of the classical Rutherford model, and Planck’s quantum hypothesis that energy is quantized.

With these foundational concepts in place, Niels Bohr set out to construct a new atomic model founded on quantized energy states (though, as you will see, it still retained several classical elements).

Interactive
​From Walter Fendt - self explanatory. It does mention de Broglie , which is in the next lesson
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