The arrangement of electrons in successive energy levels in the atom provides an explanation of the periodicity of the elements, as found in the periodic table. The charges on the nuclei of the atoms increase in a regular manner as the atomic number increases. Therefore, the number of electrons surrounding the nucleus increases also. The number and arrangement of the electrons in the outermost shell of an atom vary in a periodic manner (compare Table 4-6). For example, all the elements in Group IA—H, Li, Na, K, Rb, Cs, Fr—corresponding to the elements that begin a new row or period, have electronic configurations with a single electron in the outermost shell, specifically anssubshell.
H 1s1
Li 1s22s1 Na 1s22s22p63s1 K 1s22s22p63s23p64s1
Rb 1s22s22p63s23p64s23d104p65s1
Cs 1s22s22p63s23p64s23d104p65s24d105p66s1
Fr 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s1
The noble gases, located at the end of each period, have electronic configurations of the typens2np6, where nrepresents the number of the outermost shell. Also,nis the number of the period in the periodic table in which the element is found.
Since atoms of all elements in a given group of the periodic table have analogous arrangements of electrons in their outermost shells and different arrangements from elements of other groups, it is reasonable to conclude that the outermost electronic configuration of the atom is responsible for the chemical characteristics of the element. Elements with similar arrangements of electrons in their outer shells will have similar properties. For example, the formulas of their oxides will be of the same type. The electrons in the outermost shells of the atoms are referred to asvalence electrons. The outermost shell is called thevalence shell.
As the atomic numbers of the elements increase, the arrangements of electrons in successive energy levels vary in a periodic manner. As shown in Fig. 4-5, the energy of the 4ssubshell is lower than that of the 3dsubshell.
Therefore, at atomic number 19, corresponding to the element potassium, the 19th electron is found in the 4s subshell rather than the 3d subshell. The fourth shell is started before the third shell is completely filled. At atomic number 20, calcium, a second electron completes the 4ssubshell. Beginning with atomic number 21 and continuing through the next nine elements, successive electrons enter the 3d subshell. When the 3dsubshell is complete, the following electrons occupy the 4psubshell through atomic number 36, krypton. In other words, for elements 21 through 30, the last electrons added are found in the 3dsubshell rather than in the valence shell. The elements Sc through Zn are calledtransition elements, ordblock elements. A second series of transition elements begins with yttrium, atomic number 39, and includes 10 elements. This series corresponds to the placement of 10 electrons in the 4dsubshell.
The elements may be divided into types (Fig. 4-8), according to the position of the last electron added to those present in the preceding element. In the first type, the last electron added enters the valence shell. These elements are called themain group elements. In the second type, the last electron enters ad subshell in the next-to-last shell. These elements are thetransition elements. The third type of elements has the last electron
enter the f subshell in then−2 shell—the second shell below the valence shell. These elements are theinner transition elements.
1s
Main groups Transition groups
Inner transition groups
Main groups 1s 2s
3s 4s 5s 6s
2p 3p 4p 5p 7s 6p
3d
4f 5f 4d 5d 6d
Fig. 4-8. Periodic table as an aid to assigning electronic configurations
An effective way to determine the detailed electronic configuration of any element is to use the periodic table to determine which subshell to fill next. Eachssubshell holds a maximum of 2 electrons; each psubshell holds a maximum of 6 electrons; eachd subshell holds a maximum of 10 electrons; and each f subshell holds a maximum of 14 electrons (Table 4-5). These numbers match the numbers of elements in a given period in the various blocks. To get the electronic configuration, start at hydrogen (atomic number=1) and continue in order of atomic number, using the periodic table of Fig. 4-8.
EXAMPLE 4.12. Using the periodic table, determine the detailed electronic configuration of magnesium.
Ans. Starting at hydrogen, we put two electrons into the 1ssubshell, then two more electrons into the 2ssubshell. We continue (at atomic number 5) with the 2psubshell, and enter six electrons there, corresponding to the six elements (elements 5 to 10, inclusive) in that pblock of the periodic table. We have two more electrons to put into the 3s subshell, which is next. Thus, we always start at hydrogen, and we end at the element required. The number of electrons that we add to each subshell is equal to the number of elements in the block of the periodic table. In this case, we added electrons from hydrogen to magnesium, following the atomic numbers in order, and we got a configuration 1s22s22p63s2.
EXAMPLE 4.13. Write the detailed electronic configurations for K, S, and Y.
Ans. K 1s22s22p63s23p64s1
S 1s22s22p63s23p4
Y 1s22s22p63s23p64s23d104p65s24d1 In each case, the superscripts total to the atomic number of the element.
EXAMPLE 4.14. Determine the detailed electronic configuration of Gd, atomic number 64.
Ans. Gd 1s22s22p63s23p64s23d104p65s24d105p66s25d14f7
We note that the 5dsubshell started before the 4f subshell, but only one electron entered that shell before the 4f subshell started. Indeed, the periodic table predicts this correct configuration for Gd better than then+lrule or other common memory aids.
Instead of writing out the entire electronic configuration of an atom, especially an atom with many electrons, we sometimes abbreviate the configuration by using the configuration of the previous noble gas and represent the rest of the electrons explicitly. For example, the full configuration of cobalt can be given as
Co 1s22s22p63s23p64s23d7
Alternatively, we can use the configuration of the previous noble gas, Ar, and add the extra electrons:
Co [Ar] 4s23d7
To determine the electronic configuration in this manner, start with the noble gas of the previous period and use the subshell notation from only the period of the required element. Thus, for Co, the notation for Ar (the previous noble gas) is included in the square brackets, and the 4s23d7is obtained across the fourth period. It is suggested that you do not use this notation until you have mastered the full notation. Also, on examinations, use the full notation unless the question or the instructor indicates that the shortened notation is acceptable.
Solved Problems
BOHR THEORY
4.1. Draw a picture of the electron jump corresponding to the third line in the visible emission spectrum of hydrogen according to the Bohr theory.
Ans. In hydrogen, only jumps to or from the second orbit are in the visible region of the spectrum. The electron falls from the fifth orbit to the second. The picture is shown as the third arrow of Fig. 4-3.
4.2. When electrons fall to lower energy levels, light is given off. What energy effect is expected when an electron jumps to a higher-energy orbit?
Ans. Absorption of energy is expected. The energy may be light energy (of the same energies as are given off in emission), or it may be heat or other types of energy.
4.3. What changes of orbit can the electron of hydrogen make in going from its fifth orbit to its ground state?
Ans. It can go from (a) 5 → 4 → 3 → 2 → 1 (b) 5 → 4 → 3 → 1 (c) 5 → 4 → 2 → 1 (d) 5→4→1 (e) 5→3→2→1 (f) 5→3→1 (g) 5→2→1 (h) 5→1.
QUANTUM NUMBERS
4.4. What values are permitted formlin an electron in which thelvalue is 0?
Ans. 0. (The value ofmlmay range from−0 to+0; that is, it must be 0.)
4.5. Why must there betwoelectrons in an outer shell before the expansion of the next inner shell beyond eight electrons?
Ans. Thensorbital must be filled before electrons enter the(n−1)dorbitals in the shell below.
4.6. (a) In a football stadium, can two tickets have the same set of section, row, seat, and date? How many of these must be different to have a legal situation? (b) In an atom, can two electrons have the same set of n,l,ml, andms? How many of these must be different to have a “legal” situation?
Ans. (a) At least one of the four must be different (b) At least one of the four must be different 4.7. What are the possible values ofmlfor an electron withl=4?
Ans. −4,−3,−2,−1,0,+1,+2,+3,and+4.
4.8. What are the permitted values ofmsfor an electron withn=6,l =4, andml = −2?
Ans. ms = −12 or+12, no matter what values the other quantum numbers have.
4.9. What is the maximum number of electrons that can occupy the first shell? The second shell?
Ans. The first shell can hold a maximum of two electrons. The second shell can hold a maximum of eight electrons.
4.10. What is the maximum number of electrons that can occupy the third shell?
Ans. n=3; hence, the maximum number of electrons the shell can hold is 2n2=2(3)2=2×9=18
4.11. What is the maximum number of electrons that can occupy the third shell before the start of the fourth shell?
Ans. The maximum number of electrons in any outermost shell (except the first shell) is eight. The fourth shell starts before thedsubshell of the third shell starts.
QUANTUM NUMBERS AND ENERGIES OF ELECTRONS
4.12. Arrange the electrons in the following list in order of increasing energy, lowest first:
n l ml ms n l ml ms
(a) 4 2 −1 12 (c) 4 1 1 −12
(b) 5 0 0 −12 (d) 4 1 −1 12
Ans. Electrons (c) and (d) have the lowest value ofn+l (4+1=5)and the lowestn, and so they are tied for lowest in energy of the four electrons. Electron (b) also has an equal sum ofn+l (5+0=5), but itsn value is higher than those of electrons (c) and (d). Electron (b) is therefore next in energy (despite the fact that it has the highestnvalue). Electron (a) has the highest sum ofn+l (4+2= 6)and is highest in energy.
4.13. If thenandlquantum numbers are the ones affecting the energy of the electron, why are themlandms
quantum numbers important?
Ans. Their permitted values tell us how many electrons there can be with that given energy. That is, they tell us how many electrons are allowed in a given subshell.
4.14. How many electrons are permitted in the fifth shell? Explain why no atom in its ground state has that many electrons in that shell.
Ans. Forn = 5, there could be as many 2(5)2 = 50 electrons. However, there are only a few more than 100 electrons in even the biggest atom. By the time you put 2 electrons in the first shell, 8 in the second, 18 in the third, and 32 in the fourth, you have already accounted for 60 electrons. Moreover, the fifth shell cannot completely fill until several overlying shells start to fill. There are just not that many electrons in any actual atom.
SHELLS, SUBSHELLS, AND ORBITALS
4.15. What is the difference between (a) the 2s subshell and a 2s orbital and (b) the 2p subshell and a 2p orbital?
Ans. (a) Since thessubshell contains only one orbital, the 2sorbital is the 2s subshell. (b) The 2psubshell contains three 2porbitals—known as 2px,2py, and 2pz.
4.16. (a) How many orbitals are there in the fourth shell of an atom? (b) How many electrons can be held in the fourth shell of an atom? (c) How many electrons can be held in the fourth shell of an atom before the fifth shell starts to fill?
Ans. (a) 16 (onesorbital, three porbitals, fivedorbitals, and seven f orbitals). (b) 2(4)2 =32. (c) 8. (The 5ssubshell starts to fill before the 4dsubshell. Thus, only the 4sand the 4psubshells are filled before the fifth shell starts.)
4.17. How many electrons are permitted in each of the following subshells?
n l n l
(a) 3 1 (c) 3 2
(b) 3 0 (d) 4 0
Ans. (a) 6. This is apsubshell (with three orbitals). (b) 2. This is anssubshell. (c) 10. This is adsubshell, with five orbitals corresponding toml values of−2,−1,0,1,2. Each orbital can hold a maximum of 2 electrons, and so the subshell can hold 5×2=10 electrons. (d) 2. This is anssubshell. [Compare to part (b).] The principal quantum number does not matter.
4.18. How many electrons are permitted in each of the following subshells? (a) 2s(b) 6p, and (c) 4d.
Ans. (a) 2 (b) 6 (c) 10.
Note that the principal quantum number does not affect the number of orbitals and thus the maximum number of electrons. The angular momentum quantum number is the only criterion of that.
4.19. In Chap. 3 why were electron dot diagrams drawn with four areas of electrons? Why are at least two of the electrons paired if at least two are shown?
Ans. The four areas represent the onesplus threeporbitals of the outermost shell. If there are at least two electrons in the outermost shell, the first two are paired because they are in thessubshell. The other electrons do not pair up until all have at least one electron in each area (orbital).
SHAPES OF ORBITALS
4.20. Draw an outline of the shape of the 1sorbital.
Ans. See Fig. 4-4.
4.21. How do the three 2porbitals differ from one another?
Ans. They are oriented differently in space. The 2pxorbital lies along thexaxis; the 2pyorbital lies along they axis; the 2pz orbital lies along thezaxis. See Fig. 4-4.
4.22. Toward which direction, if any, is each of the following orbitals aligned: (a) 1s, (b) 2py, and (c) 3dz2? Ans. (a) None; it is spherically symmetric (b) Along theyaxis (c) Along thezaxis
4.23. Which 2porbital of a given atom would be expected to have the greatest interaction with another atom lying along thexaxis of the first atom?
Ans. The 2pxorbital. That one is oriented along the direction toward the second atom.
BUILDUP PRINCIPLE
4.24. Write detailed electronic configurations for the following atoms: (a) Li, (b) Ne, (c) C, and (d) S.
Ans. (a) 1s22s1 (b) 1s22s22p6
(c) 1s22s22p2 (d) 1s22s22p63s23p4
ELECTRONIC STRUCTURE AND THE PERIODIC TABLE
4.25. Write detailed electronic configurations for (a) N, (b) P, (c) As, and (d) Sb. What makes their chemical properties similar?
Ans. (a) 1s22s22p3 (b) 1s22s22p63s23p3
(c) 1s22s22p63s23p64s23d104p3
(d) 1s22s22p63s23p64s23d104p65s24d105p3
Their outermost electronic configurations are similar:ns2np3.
4.26. What neutral atom is represented by each of the following configurations: (a) 1s22s22p63s23p4, (b) 1s22s22p3, and (c) 1s22s22p63s23p64s2?
Ans. (a) S (b) N (c) Ca
4.27. Write the detailed electronic configuration for La (atomic number=57) in shortened form.
Ans. La [Xe] 6s25d1
4.28. Write the electronic configuration of atoms of each of the following elements, using the periodic table as a memory aid: (a) Si, (b) V, (c) Br, (d) Rb.
Ans. (a) 1s22s22p63s23p2 (b) 1s22s22p63s23p64s23d3
(c) 1s22s22p63s23p64s23d104p5 (d) 1s22s22p63s23p64s23d104p65s1
4.29. Write the electronic configuration of atoms of each of the following elements, using the periodic table as a memory aid: (a) As, (b) Ni, (c) Pd, and (d) Ge.
Ans. (a) 1s22s22p63s23p64s23d104p3 (b) 1s22s22p63s23p64s23d8
(c) 1s22s22p63s23p64s23d104p65s24d8 (d) 1s22s22p63s23p64s23d104p2
Supplementary Problems
4.30. State the octet rule in terms described in this chapter.
Ans. A state of great stability is a state in which the outermostsand psubshells are filled and no other subshell of the outermost shell has any electrons.
4.31. List all the ways given in this chapter to determine the order of increasing energy of subshells.
Ans. Then+lrule, the energy-level diagram (Fig. 4-5) and the periodic table. (There are also some mnemonics given by other texts.)
4.32. How many different drawings, like those in Fig. 4-4, are there for the 4f orbitals?
Ans. There are seven, corresponding to the seven forbitals in a subshell (Table 4-5). General chemistry students are never asked to draw them, however.
4.33. What are the advantages of using the periodic table over the other ways of determining the order of increasing energy in subshells given in Problem 4.31?
Ans. The periodic table is generally available on examinations, it is easy to use after a little practice, it allows one to start at any noble gas, it reminds one of the 5delectron added before the 4f electrons (at La), and it tells by the number of elements in each block how many electrons are in the subshell.
4.34. Write the electronic configurations of K and Cu. What differences are there that could explain why K is so active and Cu so relatively inactive?
Ans. K 1s22s22p63s23p64s1
Cu 1s22s22p63s23p64s13d10
The differences are the additional 10 protons in the nucleus and the additional ten 3delectrons that go along with them. Adding the protons and adding the electrons in an inner subshell make the outermost electron more tightly bound to the nucleus.
4.35. Starting at the first electron added to an atom, (a) what is the number of the first electron in the second shell of the atom? (b) What is the atomic number of the first element of the second period? (c) What is the number of the first electron in the third shell of the atom? (d) What is the atomic number of the first element of the third period?
(e) What is the number of the first electron in the fourth shell of that atom? (f) What is the atomic number of the first element of the fourth period?
Ans. (a) and (b) 3 (c) and (d) 11 (e) and (f) 19
There obviously is some relationship between the electronic configuration and the periodic table.
4.36. Check Table 4-3 to ensure that no two electrons have the same set of four quantum numbers.
4.37. Write the electronic configuration of atoms of each of the following elements, using the periodic table as a memory aid: (a) P, (b) Cl, (c) Mn, and (d) Zn.
Ans. (a) 1s22s22p63s23p3 (b) 1s22s22p63s23p5
(c) 1s22s22p63s23p64s23d5 (d) 1s22s22p63s23p64s23d10
4.38. Write the outer electronic configuration of atoms of each of the following elements, using the periodic table as a memory aid: (The atomic numbers are indicated for your convenience.) (a)57La, (b)92U, (c)88Ra, and (d)82Pb.
Ans. (a) La [Xe] 6s25d1 (b) U [Rn] 7s26d15f3
(c) Ra [Rn] 7s2
(d) Pb [Xe] 6s25d104f146p2
4.39. Write the expected outer electronic configuration of atoms of each of the following elements, using the periodic table as a memory aid: (The atomic numbers are indicated for your convenience.) (a)64Gd, (b)90Th, (c)55Cs, and (d)71Lu.
Ans. (a) Gd [Xe] 6s25d14f7 (b) Th [Rn] 7s26d15f1
(c) Cs [Xe] 6s1 (d) Lu [Xe] 6s25d14f14
Chemical Bonding