Electrons in Atoms


The Properties of Light

The Wavelike Description of Light

Light–like all other types of waves–moves at a constant velocity through a single medium.

The speed of light in a vacuum, symbolized by the letter c, is 3.00 x 10^8 m/s.

All waves have a wavelength, the distance between wave crests, symbolized by Greek letter lambda, or λ; and all waves have frequencies, the number of crests that pass a given point in one second, symbolized by the Greek letter nu, or ν.

The unit of wavelength is m, the unit of frequency is /s, Hertz, or Hz.

The speed of a wave equals its wavelength times it frequency. Therefore the speed of light, c=λν

Practice Question:
Determine the frequency of light whose wavelength is 4.257 x 10^-9 m


October 11, 2012

The Particle Description of Light

Two experiments in the early 1900s, involving interactions between light and electrons, could not be explained by the wave theory of light.

One of those experiments was the emission spectrum of hydrogen. When hydrogen atoms are excited, they do not give off a continuous spectrum of light like a rainbow, but rather a set of discrete frequencies. Wave theory predicts a continuous spectrum.

To explain this, German physicist Max Planck proposed that atoms can only absorb and emit light in energy in discrete quantities. He called the smallest bundle of energy that can be absorbed or emitted by an atom a quantum.

A second experiment, the photoelectric effect, showed that electrons are ejected from the surface of metal by high-frequency light but not low-frequency light. Wave theory predicted that if you shone enough low frequency light on the metal, enough energy would build up to eject electrons. This did not occur.

Albert Einstein, building on Planck’s idea that energy is quantized, proposed this explanation: Light is actually a stream of particles, called photons.

A photon’s energy depends on its frequency, according to the following equation: E=hν, where h is Planck’s constant, and ν is the frequency.

Only light with a high enough frequency has the energy to overcome the binding energy of the electrons in the metal.

October 15, 2012

Here is an excellent lecture on calculating the relationship between wavelength, frequency and speed of electromagnetic radiation. The lecturer also shows you how to calculate the relationship between energy and frequency of EM radiation using Planck’s constant.
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You can also Click here, or paste the following link into your browser to watch the lecture:


Here is a cool experiment involving microwaves and the photoelectric effect. (Don’t try this at home.)

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You can also click here, or paste the following link into your browser to watch the experiment:


Practice Questions:

Which theory of light—the wave or particle theory—best explains the following phenomena?

  • the interference of light
  • the photoelectric effect
  • the emission of electromagnetic radiation by an excited atom

Determine the energy in Joules of a photon whose frequency is 3.55 x 10^17 Hz.

Use E=hv
h = 6.63 x 10^-34 J * s

In 1913, Niels Bohr explained the hydrogen-atom line spectrum by proposing that a single electron of the H atom circles the nucleus only in a limited number of allowed paths, or orbits. These orbits have fixed energies, since energy is quantized.

Thus a line spectrum is produced when an electron drops from a definite higher-energy orbit to a definite lower energy orbit, emitting a photon of a discrete frequency.

Practice Questions:

  1. Distinguish between the ground state and an excited state of an atom.
  2. According Bohr’s model of the hydrogen atom, how is hydrogen’s emission spectrum produced?
  3. Name a flaw in Bohr’s reasoning about the nature of electron orbitals.

October 16, 2012

Louis deBrogle proposed that electrons, like light, also had a dual wave-particle nature as well. The wave-nature of electrons explained why the electron is confined to specific orbitals around the nucleus–waves have resonant frequencies.

Louis deBroglie’s wave-particle duality and Heisenberg’s Uncertainty Principle, which stated that it is impossible to determine simultaneously the position and velocity of an electron, laid the groundwork for a general equation defining the location of electrons in atoms.


Erwin Schrodinger’s Wave Equation defines the most probable location of electrons in terms of 4 Quantum Numbers.

Watch this video lecture describing electron orbitals:


Download our orbitals PowerPoint here:

This is so cool. And it’s yet another application of electron energy levels.