0.3 Quantum energy levels in atoms  (Page 3/9)

Our interest is in the fact that the radiation emitted by an atom tells us about the amounts of energy which canbe released by an atom. For a hydrogen atom, for example, these changes in energy must correspond to the amounts of energy whichthe electrons inside the atom can gain or lose.

At this point, we need to relate the frequency of radiation emitted by an atom to the amount of energy lost by theelectron in the atom. We thus examine some observations about the energy of radiation.

Observation 2: the photoelectric effect

When a light source is directed at a metal surface, it is found under many circumstances that electrons areejected from the surface. This phenomenon is called the "photoelectric effect." These electrons can becollected to produce a usable electric current. (This effect has a variety of common practical applications, for example, in"electric eye" devices.) It is reasonable to expect that a certain amount of energy is required to liberate an electronfrom a metal surface, since the electron is attracted to the positively charged nuclei in the metal. Thus, in order for theelectron to escape, the light must supply sufficient energy to the electron to overcome this attraction.

The following experimental observations are found when studying the photoelectric effect. First, in order forthe effect to be observed, the light must be of at least a minimum frequency which we call the threshold frequency , ${\nu }_0$ . This frequency is a characteristic for a given metal. That is, it is the same value foreach sample of that metal, but it varies from one metal to the next. For low frequency light, photoelectrons are not observed inany number, no matter how intense the light source is. For light with frequency above ${\nu }_0$ , the number of photoelectrons emitted by the metal (measured by the photoelectriccurrent, $\Phi$ ) increases directly with the intensity of the light. These results are shown in .

Second, we can measure the energies of the electrons emitted by the metal. For a given metal, allphotoelectrons have the same kinetic energy for a fixed frequency of light above ${\nu }_0$ . This fixed kinetic energy is independent of the intensity of the light source. As the frequency of the lightis increased, the kinetic energy of the emitted electrons increases proportionally. These results are shown in .

Are these results surprising? To the physicists at the end of the nineteenth century, the answer wasyes, very surprising indeed. They expected that the energy of the light source should be determined by its intensity. Hence, theenergy required to eject a photoelectron should be supplied by light of high intensity, no matter how low the frequency of theradiation. Thus, there should be no threshold frequency, below which no electrons are emitted. Moreover, the kinetic energy of theelectrons should increase with intensity, not with light frequency. These predictions arenot observed, so the results are counter to physical intuition.