42 1 Solve momentum is L 1 1 1 cid 61 cid 61 2 a A 4p state corresponds to n 4 and l 1 From Equation 42 3 the orbital angular b In the case of a 5f state n 5 and l 3 So L 3 3 1 cid 61 cid 61 12 42 2 Solve a Excluding spin a state is described by three quantum numbers n l and m 3p states correspond to n 3 and l 1 The quantum number m takes values from l to l The quantum numbers of the various 3p states are displayed in the table below b A 3d state is described by n 3 and l 2 Including the quantum number m the quantum numbers of the various 3d states are displayed in the table below 3 1 1 n l m 3 2 2 3 1 1 3 2 1 3 1 0 3 2 0 3 2 1 3 2 2 n l m 42 3 Solve a The orbital angular momentum is L l l 1 cid 61 Thus l l 1 2 L cid 61 3 65 10 1 05 10 34 34 J s J s 2 12 l 3 This is an f electron b The l quantum number is required to be less than n Thus the minimum possible value of n for an electron in the f state is nmin 4 The corresponding minimum possible energy is E min E 4 0 85 eV 13 60 eV 2 4 42 4 Solve From Equation 42 2 the hydrogen atom s energy is nE 13 60 eV 2 n 0 544 eV n 5 The largest l value for an n 5 state is 4 Thus the magnitude of the maximum possible angular momentum L L l l 1 cid 61 4 4 1 cid 61 cid 61 20 is 42 5 Solve A 6f state for a hydrogen atom corresponds to n 6 and l 3 Using Equation 42 2 The magnitude of the angular momentum is E 6 13 6 eV 2 6 0 378 eV L l l 1 cid 61 3 3 1 cid 61 cid 61 12 42 6 Model No two electrons can have exactly the same set of quantum numbers n l m ms Solve For n 1 there are a total of two states with the quantum numbers given by 1 1 0 0 there are a total of eight states 2 For n 2 2 0 0 2 1 1 1 2 1 2 2 1 0 2 1 1 1 2 1 2 For n 3 there are a total of 18 states 3 0 0 1 2 3 1 1 3 1 0 3 1 1 1 2 1 2 3 2 2 3 2 1 3 2 0 3 2 1 3 2 2 1 2 1 2 1 2 1 2 1 2 1 2 42 7 Solve a A lithium atom has three electrons two are in the 1s shell and one is in the 2s shell The electron in the 2s shell has the following quantum numbers n 2 l 0 m 0 and ms ms could be either 2 or 2 Thus lithium atoms should behave like hydrogen atoms because lithium atoms could exist in the following two states Thus there are two lines 2 0 0 2 0 0 and 1 1 1 1 2 2 b For a beryllium atom we have two electrons in the 1s shell and two electrons in the 2s shell The electrons in both the 1s and 2s states are filled Because the two electron magnetic moments point in opposite directions beryllium has no net magnetic moment and is not deflected in a Stern Gerlach experiment Thus there is only one line 42 8 Solve Mg Sr and Ba are all in the second column of the periodic table The electron configuration of Mg Z 12 is 1s22s22p63s2 The electron configuration of Sr Z 38 is 1s22s22p63s23p64s23d104p65s2 The electron configuration of Ba Z 56 is 1s22s22p63s23p64s23d104p65s24d105p66s2 It is necessary to recall that the 4s subshell fills before the 3d subshell the 5s before the 4d and the 6s Assess before the 4f or 5d 42 9 Solve P As and Sb are all in the same column of the periodic table as nitrogen The electron configuration of P Z 15 is 1s22s22p63s23p3 The electron configuration of As Z 33 is 1s22s22p63s23p64s23d104p3 The electron configuration of Sb Z 51 is It is necessary to recall that the 4s subshell fills before the 3d subshell 1s22s22p63s23p64s23d104p65s24d105p3 Assess a Nine electrons Z 9 make the element fluorine F These are the nine lowest energy 42 10 Solve states so this is the ground state of F b Thirty one electrons Z 31 make the element gallium Ga States fill in the order 4s 3d 4p So 3d104s24p with filled 3d and 4s shells has the 31 electrons in the lowest possible energy states This is the ground state of Ga a Ten electrons Z 10 make the element neon Ne These are not the ten lowest energy 42 11 Solve states because 1s22s22p6 would be lower in energy than 1s22s22p53d This is an excited state of Ne b Twenty six electrons Z 26 make the element iron Fe These are not the 26 lowest energy states because the 3d shell is not filled This is an excited state of Fe 42 12 Solve Accurate to three significant figures the factor is hc 6 63 10 J s 3 00 10 m s 19 89 10 34 8 26 J m 1243 eV nm 1240 eV nm 1 eV 1 60 10 19 J 42 13 Visualize Please refer to Figure 42 15 Solve The diagram shows the energy levels for electrons in a multielectron atom A lithium atom in the ground state has two electrons in the 1s shell and 1 electron in the 2s shell In other words the ground state electron configuration of lithium is 1s22s1 The electron configuration for the first excited state is 1s22p1 and for the second excited state is 1s23s1 42 14 Model Assume the hydrogen atom starts in the ground state Visualize The electron gains 12 5 eV 3n with the electron left with some energy but no higher See Figure 42 4 atom to Solve The atom could emit a photon in the two possible quantum jump transitions 3 corresponding energies photons emitted the are of 1 51 eV 3 40 eV 1 89 eV 2 and 3 1 The and of energy in the acceleration This is enough to excite the hydrogen 1 51 eV 13 60 eV 12 09 eV The corre sponding wavelengths are given by hc E photon transition E eV photon 3 3 2 1 1 89 12 09 nm 656 102 Assess The wavelength for the 3 transition is in the ultraviolet region 2 transition is in the visible Balmer series while the one for the 3 1 42 15 Solve Figure 42 25 the wavelength is a A 4p 4s transition is allowed because l 1 Using …
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