Quantum Physics

28.11 Atomic Transitions 921electron in the K shell (because one is missing) and 8 in the L shell, making 9 electrons shielding the nuclearcharge. This means Z eff 74 9 and E M Z eff 2 E 3 , where E 3 is the energy of the n 3 level in hydrogen. Thedifference E M E K is the energy of the photon.SolutionUse Equation 28.20 to estimate the energy of an electronin the K shell of tungsten, atomic number Z 74:Estimate the energy of an electron in the M shell in thesame way:Calculate the difference in energy between the M and Kshells:Find the wavelength of the emitted light:E K (74 1) 2 (13.6 eV) 72 500 eVE M Z 2 eff E 3 (Z 9) 2 E 0(13.6 eV)32 (74 9)296 380 eVE M E K 6 380 eV ( 72 500 eV) 66 100 eVE hf hc: hcE (6.63 1034 Js)(3.00 10 8 m/s)(6.61 10 4 eV)(1.60 10 19 J/eV) 1.88 10 11 m 0.018 8 nmExercise 28.5Repeat the problem for a 2p electron transiting from the L shell to the K shell. (For technical reasons, the L shellelectron must have 1, so a single 1s electron and two 2s electrons shield the nucleus.)Answer (a) 5.54 10 4 eV (b) 0.022 4 nm28.11 ATOMIC TRANSITIONSWe have seen that an atom will emit radiation only at certain frequencies that correspondto the energy separation between the various allowed states. Consider anatom with many allowed energy states, labeled E 1 , E 2 , E 3 , . . . , as in Figure 28.16.When light is incident on the atom, only those photons whose energy hf matchesthe energy separation E between two levels can be absorbed by the atom. Aschematic diagram representing this stimulated absorption process is shown in ActiveFigure 28.17. At ordinary temperatures, most of the atoms in a sample are inthe ground state. If a vessel containing many atoms of a gas is illuminated with alight beam containing all possible photon frequencies (that is, a continuous spectrum),only those photons of energies E 2 E 1 , E 3 E 1 , E 4 E 1 , and so on, canbe absorbed. As a result of this absorption, some atoms are raised to various allowedhigher energy levels, called excited states.Once an atom is in an excited state, there is a constant probability that it will jumpback to a lower level by emitting a photon, as shown in Active Figure 28.18 (page 922).E 4E 3E 2E 1Figure 28.16 Energy level diagramof an atom with various allowedstates. The lowest energy state, E 1 ,is the ground state. All others areexcited states.hfAtom inground state∆EE 2Atom inexcited stateE 2ACTIVE FIGURE 28.17Diagram representing the process ofstimulated absorption of a photon by an atom.The blue dot represents an electron. Theelectron is transferred from the ground stateto the excited state when the atom absorbs aphoton of energy hf E 2 E 1 .BeforeE 1 E 1AfterLog into PhysicsNow at www.cp7e.com andgo to Active Figure 28.17 to observestimulated absorption.