0.3 Quantum energy levels in atoms  (Page 2/9)

Radiation can also be characterized by the frequency of the electromagnetic wave, which is the number of peaksin the wave which pass a point in space per second. Frequency is symbolized by $\nu$ . The speed which light travels in a vacuum in the same for all forms of electromagnetic radiation, $c=2.997E8\frac{m}{s}$ . As such, we can relate the frequency of light to the wavelength of light by the equation

The longer the wavelength $\lambda$ , the lower the frequency $\nu$ . This makes sense when we remember that light travels at a fixed speed. When the wavelength is longer,fewer peaks will pass a point in space in a second. From this equation, there is a specific relationship between frequency andwavelength, and either or both can be used to characterize the properties of radiation.

With this background in hand, we can use our understanding of light to pursue more data about the energies ofelectrons in atoms. Ionization energies tell us how much energy is required to remove an electron from an atom, but do not tell whathappens if an electron changes its energy in an atom. To analyze this, we need a means to measure the energies gained or lost by anatom. One way to do so is to analyze the "spectrum" of an atom, which is the set of frequencies of light emitted by the atom. Since hydrogen is the simplest atom, we analyze the hydrogenspectrum first. We find that, if we pass a current of electricity through a sample of hydrogen gas, light is emitted. Carefulanalysis shows that, although some of this light is emitted by $H_2$ molecules, some of the light is also emitted by H atoms. Since light is a form of energy, then these H atoms must release energysupplied to them by the electrons in the current.

Most importantly, if we pass the light emitted by the hydrogen gas sample through a prism, we can separate thecolors as in a rainbow, each with a characteristic frequency. The resultant image of separated colors is called the spectrum of hydrogen. We find in this experiment that there are only four frequencies (four colors) of light in theemission that are visible. The most intense of the lines in the spectrum is bright red, but there are blue and violet lines. Itturns out that there are also many other frequencies of light emitted which are invisible to the human eye.

Careful observation and analysis reveals that every frequency in the hydrogen atom spectrum can be predicted by avery simple formula, called the Rydberg equation:

where $R$ is the Rydberg constant ( $3.29E15s^{-1}$ ). $n$ and $m$ are integers (1,2,3,...). Each choice of $n$ and $m$ predicts a single observed frequency in the hydrogen atomspectrum.

The atoms of all elements emit radiation when energized in an electric current, and as do all molecules of allcompounds. However, we find that the specific frequencies of light emitted are characteristic of each atom or molecule. In otherwords, the spectrum of each element is unique to each element or compound. As a result, the spectrum of each substance can be usedto identify that substance. (Note that the Rydberg equation tells us only the spectrum of hydrogen.)