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The Energy of an Electron

The energy of an electron is of the same order of magnitude (is in the same range) as the energy of light. The lines in the spectrum of an element represent changes in the energy of electrons within the atoms of that element. By studying these spectra, scientists have drawn various conclusions about the behavior of electrons in atoms.

1. The energy of an electron depends on its location with respect to the nucleus of an atom. The higher the energy of an electron in an atom, the farther is its most probable location from the nucleus. Notice that we say probable location. Because of the electron's small size and high energy, we are limited in how precisely we can mark its position at any instant. We can only describe regions around the atom's nucleus within which the electron may be found.

2. In describing these regions of space, we also recognize that the energy of an electron is quantized. What does this statement mean? A property is quantized if it is available only in multiples of a set amount. If you are pouring a soft drink from a can, you can pour out as much or as little as you like. However, if you are buying a soft drink from a machine, you can buy only a certain amount. You cannot buy a half or a third of a can of soda; you can buy only a whole can or several cans. Soft drinks dispensed by a machine are available only in multiples of a set volume, or quantum. Thus, the dispensing of soft drinks by machine has been quantized.

Energy can also be quantized. If you are climbing a ladder, you can stop only on the rungs; you cannot stop between them. The energy needed to climb the ladder is used in finite amounts to lift your body from one rung to the next. To move upward, you must use enough energy to move your feet to the next higher rung. If the available energy is only enough to move partway up to the next rung, you cannot move at all because you cannot stop between rungs. Thus, in climbing the ladder, your expenditure of energy is quantized. If you are going up a hill instead of a ladder, your energy expenditure is not quantized. You can go straight up the hill or you can zigzag back and forth, going up gradually. You can take big steps or little steps; no limitations are placed on where you can stop or on how much energy you must use.

Let us apply the analogy of the ladder and its rungs to an atom and its electrons. In climbing the ladder, you can place your feet only on the rungs. Similarly, an atom has only certain places, set distances from the nucleus called energy levels, where electrons may be found. Unlike a ladder, which has a limited length, the energy levels of an atom extend infinitely out from the nucleus and the energy levels are not evenly spaced. As the distance from the nucleus increases, the levels get closer together and contain more-energetic electrons (Figure 5.4). The energy of an electron in one of the levels at a considerable distance from the nucleus is greater than that of an electron in a closer level.


FIGURE 5.4 Energy levels. The energy levels in an atom are similar to the rungs of a ladder, but they get closer together as they get farther from the nucleus.


For an electron to move from one energy level to the next higher level, it must gain the right amount of energy. If less than that amount is available, the electron stays where it is. Electrons always move from one level to another; they cannot stop in between. Thus there are certain regions of space within an atom where an electron can be and other regions where an electron cannot be.

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