# ENERGY LEVELS

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ENERGY LEVELS

spectra whose wavelengths can be represented by a simple formula such as Balmer’s. But it is always possible to analyze the more complicated spectra of other elements in terms of transitions among various energy levels and to deduce the numerical values of these levels from the measured spectrum wavelengths. Every atom has a lowest energy level that includes the minimum internal energy state that the atom can have. This is called the ground-state level, or ground level, and all higher levels are called excited levels. A photon corresponding to a particular spectrum line is emitted when an atom makes a transition from a state in an excited level to a state in a lower excited level or the ground leveL Some energy levels for sodium are shown in Fig. 40-9 with energies relative to the ground leveL You may have noticed the yellow-orange light emitted by sodium vapor street lights. Sodium atoms emit this characteristic yellow-orange light with wavelengths 589.0 and 589.6 nm when they make transitions from the two closely spaced levels labeled lowest excited levels to the ground leveL A sodium atom in the ground level can also absorb a photon with wavelength 589.0 or 589.6 nm. To demonstrate this process, we pass a beam of light from a sodium-vapor lamp through a bulb containing sodium vapor. The atoms in the vapor absorb the 589.0- nm or 589.6-nm photons from the beam, reaching the lowest excited levels; after a short time they return to the ground level, emitting photons in all directions and causing the sodium vapor to glow with the characteristic yellow light. The average time spent in an excited level is called the lifetime of the level; for the lowest excited levels of the sodium atom, the lifetime is about 1.6 x 10-1 S.

More generally, a photon emitted when an atom makes a transition from an excited level to a lower level can also be absorbed by a similar atom that is initially in the lower level (Fig. 4O-6b, page 1236). If we pass white (continuous-spectrum) light through a gas and look at the transmitted light with a spectrometer, we find a series of dark lines corresponding to the wavelengths that have been absorbed, as shown in Fig. 40-10. This is called an absorption spectrum. A related phenomenon is fluorescence. An atom absorbs a photon (often in the ultraviolet region) to reach an excited level and then drops back to the ground level in steps, emitting two or more photons with smaller energy and longer wavelength. For example, the electric discharge in a fluorescent tube causes the mercury vapor in the tube to emit ultraviolet radiation. This radiation is absorbed by the atoms of the coating on the inside of the tube. The coating atoms then re-emit light in the longer-wavelength visible portion of the spectrum. Fluorescent lamps are more efficient than incandescent lamps in converting electrical energy to visible light because they do not waste as much energy producing (invisible) infrared photons.

The Bohr hypothesis established the relation of wavelengths to energy levels, but it provided no general principles for predicting the energy levels of a particular atom. Bohr provided a partial analysis for the hydrogen atom; we will discuss this in Section 40-6.

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