The knowledge which scientists have gained about the location of electrons is based on the fact that electrons are normally found in an area around the nucleus of the atom that is called an electron cloud. This is simply an area of probability, or the place where an electron is most likely to be found during the greater percentage of time. In an atom that is not stimulated by extra energy source, the electron in question is said to be in its ground state.  The electron may be stimulated to move away from the nucleus to higher energy states by adding energy to the atom in the form of heat or a measurable amount of electricity, etc.  When this is done, the electron momentarily reaches an excited state.  In the process of falling back to the original ground state, the electron releases energy in the form of visible light.  The picture above was taken as one of our students was  performing a simple flame test for the presence of certain metal ions in a salt soultion.  The wave length of this light is also more precisely measurable and is therefore an indicator of the average distance of the electron from the nucleus of the atom.  This information gives us the best and closest indicator of the electron's location.  The amount of energy emitted by an electron falling from the excited state to the ground state was measured by Neils Bohr, who also made use of Planck's equation to calculate the frequency of the emitted light.  Planck's equation is E = hv, where E is energy, h is a constant, called Planck's constant and has a value of 6.6262 X 10^-34 Joule seconds, and v which stands for the frequency.  Another formula allows for additional derived formulas which relate wavelength and the speed of light to be related to energy and Planck's constant.  Following is the formula, the meaning of the expressions, and some possible inter-relationships between it and Planck's equation:

In order to see the significance of these equations and what we mean by wave length, frequency, etc, it would be helpful for the student to study the parts of a wave diagram such as the one below which is labeled to show the parts of a transverse wave such as a wave which may form in water.  Even though all waves are not transverse, the typical parts of waves are still essentially the same...

By definition:
crest = the topmost point on a transverse wave.
trough = the lowest point in a transverse wave.
equatorial plane = the resting position of the media when no waves are traveling.
                                        (i.e. peaceful calm water, without even a ripple)
amplitude = the distance that a wave moves from its normal resting position when disturbed (the height of the water wave in this case).
wave length = the distance (usually in meters) between two successive crests or
between two successive troughs or between any two like corresponding parts.
frequency = the number of wave pulses (i.e crests) that pass a given point in one second.
                    (measured in cycles per second - cps or Hertz - Hz)
speed = How fast is the wave moving?  (Usually expressed in meters per second - m/s)
 

The Visible Spectrum Since we are dealing with light in learning about electrons, it is helpful for the student to approach the study with an understanding of the nature and characteristics of light before actually proceeding into the study of electron locations.  Since it was accepted all the way back in 1923 that light travels as tiny particles called photons (Arthur Compton), then we should understand light in this way, BUT light also displays characteristics which can be described in terms of frequencies and wavelength, so naturally we must also include this idea in our perception of the nature of light.  Consequently, it is now assumed that light may only be described as having both wave AND particle characteristics and thus has a  dual nature.  This is called wave-particle duality.  This allows us to use light to study the 'placement' of electrons around the atom.  As stated before, the wavelength of light emitted by an excited electron falling back to the ground state is an indicator of its usual location.  This light is visible and falls somewhere within the visible spectrum.  We perceive these wavelengths as different colors which range from violet (shortest) to red at the other end (longest).  Visible light is a small part of the entire electromagnetic spectrum which includes gamma and X-rays at the shortest end to TV and radio waves at the long end. (Click on picture to go to the page source and more information) Elements can be identified from their spectral lines.  The following is a spectral analysis of the gas, hydrogen:

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Some other important terminology and contributors to this study:
1. photoelectric effect - an effect created by light shining on the surface of a metal,
   whereby electrons are ejected from the surface.  Whether it is possible or not for
   electrons to be ejected depends on whether or not the wavelength of light has enough
   energy.  For example, red light cannot create this effect with sodium metal, but violet
   light can cause the ejection of electrons.
2. photons - First named by Einstein, thse are thought by some to be the particles of
    light which travel through space.  Einstein described the photon as a tiny "quanta" or
    amount of light.  He also said that the photon carries an amount of energy which can be
    found by Planck's equation, E = hv .
3. quantum - Proposed by Max Planck... a "piece" of energy emitted or absorbed by an
    object.
4. quantum number - Named by Bohr, he used the number to describe what he then called
    the "orbit" of the electron around the atom.  the abreviation is n, and the concept is
    still used today to help us understand the major energy levels in atoms.  It is also
    important to understand that when an electron is stimulated and then falls back to the
    ground state it emits an amount of energy equal to the difference between the higher
    and lower energy level.
5. Louis De Broglie - Predicted that all moving objects exhibit wave-like behavior.
6. Werner Heisenberg - Proposed the uncertaintity principle, which states that since
    photons are used to locate electrons, then the electron is so small that its position
    will change immediately upon being struck by the photon.  Consequently, the principle
    states that it is impossible to know both the position and the momentum of a moving
    object both at the same time.
7. quantum mechanical model - The latest and most widely accepted model of the atom
    today.  The model is based on all of the ideas about waves, light, etc. that have been
    presented on this page.  Another name is the wave mechanical model, and it should be
    noted that this study is sometimes referred to as quantum optics or quantum theory.

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Now, before moving on, try your hand at some potential SOL questions on this topic:

1. Emission of light from an atom occurs when?
    a. an electron jumps from a lower to a higher energy level
    b. an electron drops from a higher to a lower energy level
    c. an electron falls into the nucleus
    d. two electrons collide and are converted into pure energy

2. 

3. Who is given credit for the uncertaintity principle?
    a. Einstein   b. De Broglie    c. Bohr    d. none of these

4. Which of the following is Planck's equation?
    a. E = hv    b. E = mc²    c. wavelength = speed of light/frequency   d. none of these

5. Which of the following light waves has the greatest energy?
    a. red        b. blue      c. violet      d. yellow

6. What does the first quantum number (n) stand for?
    a. the electron's orbital
    b. the electron's sublevel
    c. the electron's spin
    d. the electron's main energy level

7. What is an electron cloud ?
    a. an area where an electron is not likely to be found
    b. an area where an electron is found only a small percentage of the time
    c. an area where an electron has the greatest probability of being found
    d. an area around an atom where an electron can move to when excited

8. Which of the following can be used to calculate the wavelength of a band of light?
    a. hc/E        b. E/hc        c. hc X E        d. none of these

9. The speed of light in meters/sec. is
    a. 186,000    b. 3.00 X 10⁸     c. 6.01 X 10²³    d. none of these

10. Another name for atomic emission spectrum is
    a. frequency        b. amplitude        c. quanta    d. line spectrum

11. The frequency of a wave is inversely proportional to its
    a. wavelength       b. amplitude    c. energy    d. speed

12. Microwaves have shorter wavelengths than
    a. X-rays    b. radio waves    c. ultraviolet light    d. gamma rays

13. Who proposed that light is emitted or absorbed by an object in fixed amounts called
      quanta?
    a. Einsten    b. de Broglie    c. Thompson    d. None of these

14. Upon what does the photoelectric effect depend?
    a. the wavelength of light    b. the energy of photons    c. the intensity of light
    d. the presence of red light

15. What has properties of both particles and waves?
    a. protons    b. light    c. all energy    d. nothing

16. What identifying feature of elements is produced when elements emit light?
    a. a continuous spectrum    b. a line spectrum    c. photoelectricity    d. none of these

17. Why do elements supposedly have unique line spectra?
    a. electrons are in fixed orbits                 c. elements are most stable when excited
    b. energy is reflected by electrons          d. energy of electrons is quantized

18. When you measure the position of an electron, you invariably change the electron's
     momentum.  This idea was stated in
    a. Einstein's equation                                    c. the Aufbau Principle
    b. Heisenburg's Uncertainty Principle        d. Hund's Rule
>Check answers<

Some Interesting and Informative Links:
Light
Ultraviolet Light
Infrared Light I
The Electromagnetic Spectrum I
The Electromegnetic Spectrum II

>Now, it's time to move on to the second page of
   electron configuration studies... Click Here