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In the nineteenth century, many physicists tried to use atomic spectra to determine the structure of the atom Hydrogen was studied extensively because it is the lightest element and has the simplest spectrum The visible spectrum of hydrogen consists of four lines: red, green, blue, and violet, as shown in Figure 28-7 Any theory that explained the structure of the atom would have to account for these wavelengths and support the nuclear model However, the nuclear model as proposed by Rutherford was not without its problems Rutherford had suggested that electrons orbit the nucleus much like the planets orbit the Sun There was, however, a serious flaw in this planetary model Problems with the planetary model An electron in an orbit constantly is accelerated toward the nucleus As you learned in 26, accelerating electrons radiate energy by emitting electromagnetic waves At the rate that an orbiting electron would lose energy, it should spiral into the nucleus within 10 9 s This, however, must not be happening because atoms are known to be stable Thus, the planetary model was not consistent with the laws of electromagnetism In addition, the planetary model predicted that the accelerating electrons would radiate energy at all wavelengths However, as you just learned, the light emitted by atoms is radiated only at specific wavelengths Danish physicist Niels Bohr went to England in 1911 and joined Rutherford s group to work on determining the structure of the atom He tried to unite the nuclear model with Planck s quantized energy levels and Einstein s theory of light This was a courageous idea because as of 1911, neither of these revolutionary ideas was widely understood or accepted

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Bohr began with the planetary arrangement of electrons, as diagrammed in Figure 28-8, but then made the bold hypothesis that the laws of electromagnetism do not apply inside the atom He postulated that an electron in a stable orbit does not radiate energy, even though it is accelerating Bohr referred to this stable condition as a stationary state He went on to assume that only stationary states with specific amounts of energy are allowed In other words, Bohr considered the energy levels in an atom to be quantized As shown in Figure 28-9, the quantization of energy in atoms can be likened to a flight of stairs with decreasing-height steps To go up the stairs you must move from one step to the next it is impossible to stop at a midpoint between steps Instead of steps, atoms have quantized amounts of energy, each of which is called an energy level Just as you cannot occupy a position between steps, an atom s energy cannot have a value between allowed energy levels An atom with the smallest allowable amount of energy is said to be in the ground state When an atom absorbs energy, it moves, or makes a transition to, a higher energy level Any energy level above the ground state is called an excited state Energy of an Atom What determines the amount of energy an atom has An atom s energy equals the sum of the kinetic energy of the electrons and the potential energy from the attractive force between the electrons and the nucleus The energy of an atom with electrons in a nearby orbit is less than that of an atom with electrons in a faraway orbit because work must be done to move the electrons away from the nucleus Thus, atoms in excited, higher-energy states have electrons in larger, or more distant, orbits Because energy is quantized and energy is related to the size of the orbit, the size of the orbit also is quantized The model of an atom just described, that of a central nucleus with orbiting electrons having specific quantized energy levels, is known as the Bohr model of the atom If Bohr was correct in hypothesizing that stable atoms do not radiate energy, then what is responsible for an atom s characteristic emission spectrum To answer this question, Bohr suggested that electromagnetic energy is emitted when the atom changes from one stationary state to another Incorporating Einstein s photoelectric theory, Bohr knew that the energy of every photon is given by the equation, Ephoton hf He then postulated that when an atom absorbs a photon, the atom s energy increases by an amount equal to that of the photon This excited atom then makes a transition to a lower energy level by emitting a photon.

Figure 28-8 Bohr s planetary model of the atom was based on the postulation that electrons move in fixed orbits around the nucleus

Figure 28-9 These decreasingheight steps are analogous to the allowed energy levels in an atom Note how the difference in energy between adjacent energy levels decreases as the energy level increases

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When the atom makes the transition from its initial energy level, Ei, to its final energy level, Ef, the change in energy, Eatom, is given by the following equation Eatom Ef Ei

As shown in Figure 28-10, the change in energy of the atom equals the energy of the emitted photon Ephoton or Eatom Ef Ei

Figure 28-10 The energy of the emitted photon is equal to the difference in energy between the initial and final energy levels of the atom

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