The Electromagnetic Spectrum Quantum Theory The Electromagnetic Spectrum

Definition: The electromagnetic spectrum is a collection of all of the types of electromagnetic radiation. These are forms of energy that move from point to point as waves – not requiring the presence of matter to transfer that energy.

Diagram of a Wave

Parts of Waves

Definition - Amplitude

Wavelength

Frequency Frequency is defined as the number of complete wavelengths that pass a defined point per unit time. The usual time unit is seconds, so the correct units for time are actually 1/sec ( or sec-1 ). This odd unit may be called “hertz”, which is the scientific equivalent for 1/sec.

Consider the following graphs: Take special note of how the wavelength and the frequency are inversely related to each other.

The “Wave Equation” Physics gives us that the speed of electromagnetic waves is equal to the frequency times the wavelength. In equation form, it is c = f  λ Where “c” is the speed of light which is 3.0 x 108 meters/sec “f” is the frequency in hertz (1/sec) λ is the wavelength in meters

The Wave Equation Pyramid c f λ

Electrons and Changing Energy Levels

Think back to Planck’s ladder: Remember that Planck has defined the specific energies that electrons may have. These energies are like the rungs of a ladder – whole number multiples of a specific and basic energy value.

Electron Energy Changes It is possible for an electron at a lower level to gain energy and “jump” to a higher energy level. To do this, the electron must absorb a “photon” – a burst of energy from some source – quite often electromagnetic radiation. It is also possible for an electron at a higher level to “fall” to lower energy level. When this occurs, the electron must “emit” a photon – this is always in the form of electromagnetic radiation.

Energy Changes Must emit a photon to “fall” back down ! Must absorb a photon to “jump” up there !

Important Conclusion! Since energy is required to cause an electron to “jump” to a higher level… and energy is given off when an electron “falls” to a lower level… and both processes involve electromagnetic radiation… We have to conclude that electromagnetic waves have measureable energies.

The Wave Energy Equations: Since electron energies are all multiples of Planck’s basic energy, the equation has to have a constant to reflect that value. We use the symbol “h” to represent “Planck’s Constant” and assign it the value 6.63 x 10-34 Joulesec . We also discover that the energy of these waves is directly related to the frequency of the radiation. Therefore, we can write that E = h  f. Notice how the units will work out to give Joules, which is the metric unit of energy.

The other form of the Wave Energy Equation: Remember from an earlier slide that frequency is part of the regular wave equation. If we substitute the expression c / λ for frequency (look at the pyramid to see how this works out if you need), we end up with the other form of the wave energy equation. E = h  c λ

What does this do for us? It allows us to calculate the energy of an absorbed photon. It allows us to calculate the energy of an emitted photon. It allows us to determine what type of electromagnetic radiation will be given off during a specific electron “fall”. We can actually predict what color of light will be emitted during an electron “fall”.