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# Electromagnetic Spectrum and Atomic Spectra for AP Chemistry

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By — McGraw-Hill Professional
Updated on Feb 9, 2011

Practice problems for these concepts can be found at:

Light is a part of the electromagnetic spectrum—radiant energy composed of gamma rays, X-rays, ultraviolet light, visible light, etc. Figure 10.1 shows the electromagnetic spectrum.

The energy of the electromagnetic spectrum moves through space as waves that have three associated variables—frequency, wavelength, and amplitude. The frequency, ν, is the number of waves that pass a point per second. Wavelength, λ, is the distance between two identical points on a wave. Amplitude is the height of the wave and is related to the intensity (or brightness, for visible light) of the wave. Figure 10.2 shows the wavelength and amplitude of a wave.

The energy associated with a certain frequency of light is related by the equation:

E = hν where h is Planck's constant = 6.63 × 10–34 Js

In developing the quantum mechanical model of the atom, it was found that the electrons can have only certain distinct quantities of energy associated with them, and that in order for the atom to change its energy it has to absorb or emit a certain amount of energy. The energy that is emitted or absorbed is really the difference in the two energy states and can be calculated by:

ΔE = hν

All electromagnetic radiation travels at about the same speed in a vacuum, 3.0 × 108 m/s. This constant is called the speed of light (c). The product of the frequency and the wavelength is the speed of light:

c = vλ

Let's apply some of the relationships. What wavelength of radiation has photons of energy 7.83 × 10–19 J?

### Wave Properties of Matter

The concept that matter possesses both particle and wave properties was first postulated by de Broglie in 1925. He introduced the equation λ = h/mv, which indicates a mass (m) moving with a certain velocity (v) would have a specific wavelength (l) associated with it. (Note that this v is the velocity not ν the frequency.) If the mass is very large (a locomotive), the associated wavelength is insignificant. However, if the mass is very small (an electron), the wavelength is measurable. The denominator may be replaced with the momentum of the particle (p = mv).

### Atomic Spectra

Late in the 19th century scientists discovered that when the vapor of an element was heated it gave off a line spectrum, a series of fine lines of colors instead of a continuous spectrum like a rainbow. This was used in the developing quantum mechanical model as evidence that the energy of the electrons in an atom was quantized, that is, there could only be certain distinct energies (lines) associated with the atom. Niels Bohr developed the first modern atomic model for hydrogen using the concepts of quantized energies. The Bohr model postulated a ground state for the electrons in the atom, an energy state of lowest energy, and an excited state, an energy state of higher energy. In order for an electron to go from its ground state to an excited state, it must absorb a certain amount of energy. If the electron dropped back from that excited state to its ground state, that same amount of energy would be emitted. Bohr's model also allowed scientists to develop a method of calculating the energy associated with a particular energy level for the electron in the hydrogen atom:

where n is the energy state. This equation can then be modified to calculate the energy difference between any two energy levels:

Practice problems for these concepts can be found at:

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