# " = Y(#,\$) % R(r) = 1 4& % " = Y(#,\$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V,

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1 Recitation Problems: Week 4 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s 2 2 1! ! 5 1 2! 4-1 0! ! 7 2-2! ! 2. or a the following orbital " = Y(#,\$) % R(r) = 1 4& % 2 ' Z * ), ( )exp(-. 3) where " = Zr, 81 3 ( a 0 + a 0 and a 0 = Å. a. Calculated where the radial nodes are for Z=3 and a 0 =0.529 Å. b. Can you tell what orbital it is (e.g. 1s). 3. or the following orbital: 5 " = Y(#,\$) % R(r) = 16& 3( cos(#) 4 ( Z + ( )2 '1) % * ) a 0, a. ow many angular nodes are there? b. ow many radial nodes are there? c. Name the orbital?. 2 ( )exp('. 3) 4. Penetration: Put the following orbitals into the order in which they penetrate best: 2s, 2p 3s, 3p, 3d, 4s 5. Draw! vs r and r 2! 2 (on anti nodes) vs. r for the above orbitals and show why you have put them in the above order. 6. Which has lower energy in a neutral atom and give an example of an atom: a. 3p or 4s b. 4p or 5s c. 3d or 4s d. 5d or 4f or 5p 7. tate: a. the Pauli exclusion principle b. the Aufbau principle. c. und s rule. Why is it true? 8. how the electron configuration (ground state) for the following atoms a. 5 B, 14 i, 29 Cu, 8, b. 6 C 10, Ne Mg + 15 P 2+ c. 23 V, 23 V V 3+ d. 24 Cr 24 Cr + 24 Cr 2+ e. 30 Zn, 30 Zn +, 30 Zn 2+ f. 27 Co, 27 Co +, 27 Co What other element than Cr in the first transition metal series is an exception to the general rule on orbital filling. 10. The following elements are exceptions to the general rule on orbital filling explain each a. Nb 41, Pd 46 b. Mo 42, Ag 47 c. Ru 44, Rh Ionization Potential: Put in order: a. Ni, Ni + b. Ne, Ar c. Ne, Na + d., Ar 12. Electronic Configuration: a. Tc 43 and Pd 46 ow many 5s electrons do they have? b. Are C 6, 9, Ne 10 paramagnetic c. Write 4 excited states of Nitrogen d. Which atoms with Z < 18 are paramagnetic 13. ize: Consider the orbitals: 2s, 2p, 3s, 3p, 3d, 4s, 4p Place the orbitals in order of: a. Which extend the furthest from the nucleus b. which see the largest effective nuclear charge c. which screen other electrons best. 14. or each of the following pairs of atoms or ions which is larger a. Na, K b. Cs, Cs + ) c. K, Ca d. m, m 3+ e. Mg, Ca f. I -, Xe g. 2-, 2- h. -, ize: Put in order of increasing size a. N 3-, 2-, -, Ne, Na + b. Mg 2+, Al 3+ c. N,, d. -, Cl -, Br - e. Li +, Be 16. EA: Put in order of increasing electron affinity a. Cu, Zn b., Cl

2 c. K, Ca d., Li e. As, Ge 17. Lewis Dot: Write the Lewis dot structures for: a. 2, 2, N 2, C, 2 b. B 3, B 3 N 3 c. C 2, CN -, Cl d. 6, 2 4, 3 P 4 e. C 4, 2 C 2, 4 C 2, 2, N Write Resonace and Lewis Dot structures for: N 2 -, N 3 -, 2, xi Acids: The four rules of xiacids are: a. As electronegativity of central atom increases the acidity increases b. As the positive formal charge (no expanded octet) on the central atom increases the acidity increases c. As the number of resonance structures of the dissociated acid increase the acidity increases. d. As the number of atoms that do not have an attached increases acidity increases. 20. Explain why these rules are true. Answers 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s 2 2 1! NG (l) ! K 5 1 2! NG (ml) 4-1 0! NG (l) NG (ms) ! k 7 2-2! K ! NG (l) 2. or a the following orbital " = Y(#,\$) % R(r) = 1 4& % 2 ' Z * ), ( )exp(-. 3) where " = Zr, 81 3 ( a 0 + a 0 and a 0 = Å. a. Calculated where the radial nodes are for Z=3 and a 0 =0.529 Å. ind the zeros in the radial dependence of the wavefunction by setting ( 27 "18# + 2# 2 )exp("# 3) = 0 ince the exponent is zero only at " # \$ the other piece ( 27 "18# + 2# 2 ) = 0 give two roots. Thus there are two radial nodes. You solve using the quadratic formula and get ( 27 "18# + 2# 2 ) = 0 # 0 = "("18) ± 182 " 4(2)(27 =1.9,7.1 2(2) r = 0.34 and 1.25 Å. b. Can you tell what orbital it is (e.g. 1s). (It has no angular nodes and 2 radial nodes thus it is a 3s) 3. or the following orbital: 5 " = Y(#,\$) % R(r) = ( 16& 3( cos(#) 4 ( Z + )2 '1) % * - (. 2 )exp('. 3) 81 30) a 0, a. ow many angular nodes are there? (" goes from 0 to p if you look at the " dependence you can solve 2( cos" ) 2 #1 = 0 for the angular nodes. You get " = 54.7 and degrees. Thus there are two angular nodes and it is a d orbital) b. ow many radial nodes are there? (Can solve radial part for the zeros and get # = 0 so only a node at zero which is really only part of the angular node that we found above. Thus no radial nodes. c. Name the orbital? (rom above we have 0 radial nodes and 2 angular nodes thus total of 2 nodes you have a 3d orbital

3 4. Penetration: Put the following orbitals into the order in which they penetrate best: 2s, 2p 3s, 3p, 3d, 4s (2s, 2p, 2p, 4s, 3d) 5. Draw r 2 Y 2 (on anti nodes) vs. r for the above orbitals and show why you have put them in the above order. (ee handout). 6. Which has lower energy: a. 3p or 4s (3p) Mg b. 4p or 5s (4p) r c. 3d or 4s (4s) Ti d. 5d or 4f or 5p (5p) n 7. tate: a. the Pauli exclusion principle (No two electrons can have the same 4 quantum numbers) b. the Aufbau principle (When adding electrons to a nucleus they go into the lowest energy orbital that can accept another electron). c. und s rule. Why is it true? (When electrons are added to orbitals of equal energy the configuration with the highest total spin will have the lowest energy. If there are multiple orbitals that have the same energy but occupy regions of space it is better to place electrons into separate spatial orbitals to reduce their repulsion energy and with parallel spins to reduce their magnetic interaction energy, thus it is better to have one electron it two orbitals than two electrons in one orbital and for two electrons in orbitals it is better if their E 1 configuration 1 > E 2 configuration 2 > E 3 configuration 3 spins are aligned. or a p 2 configuration see figure to right). 8. how the electron configuration (ground state) for the following atoms a. 5 B, 14 i, 29 Cu, 8, (1s 2 2s 2 2p 1 ), (1s 2 2s 2 2p 6 3s 2 3p 2 ), (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 ), (1s 2 2s 2 2p 4 ) b. 6 C, 10 Ne Mg + 15 P 2+ (1s 2 2s 2 2p 2 ), (1s 2 2s 2 2p 62 ), (1s 2 2s 2 2p 6 3s 2 ), (1s 2 2s 2 2p 6 3s 2 3p 1 ) c. 23 V, 23 V V 3+ (1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 3 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 2 ) d. 24 Cr 24 Cr + 24 Cr 2+ (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 4 ) e. 30 Zn, 30 Zn +, 30 Zn 2+, (1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 ), (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 ) f. 27 Co 27 Co + 27 Co 2+ (1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 7 ), (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 7 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 7 ) 9. What other element than Cr in the first transition metal series is an exception to the general rule on orbital filling. (Cu) 10. The following elements are exceptions to the general rule on orbital filling explain each a. Nb 41, Pd 46 (steals two 5s electrons to get half filled 4d shell, steals two 5s electrons to get completely filled 4d shell) b. Mo 42, Ag 47 (the both steal a 5s electron to get half filled or completely filled 4d shell) c. Ru 44, Rh 45 (steal a 5s electron to add another electron to 4d shell) ee page 551 or GN. 11. Ionization Potential: Put in order: a. Ni, Ni + (Ni < Ni + ) b. Ne, Ar (Ar < Ne) c. Ne, Na + (Ne < Na + ) d., Ar (Ar < ) 12. Electronic Configuration: a. Tc 43 and Pd 46 ow many 5s electrons do they have? (2, 0) b. Are C 6, 9, Ne 10 paramagnetic (yes, yes, no) c. Write 4 excited states of Nitrogen (1s 2 2s 2 2p 3 where two spins are paired and either the electron are in all p orbitls or the same p orbits (2 states), and 1s 2 2s 2 2p 2 3s 1 ) d. Which atoms with Z < 18 are paramagnetic (, Li, B, C, N,,, Na, Al, i, P,, Cl) 13. ize: Consider the orbitals: 2s, 2p, 3s, 3p, 3d, 4s, 4p Place the orbitals in order of: a. Which extend the furthest from the nucleus (4s, >4p > 3s > 3p > 3d > 2s > 2p) b. which see the largest effective nuclear charge (2s > 2p > 3s > 3p > 4s > 3d > 4p) c. which screen other electrons best. (2s > 2p > 3s > 3p > 3d > 4s > 4p ) 14. or each of the following pairs of atoms or ions which is larger a. Na, K (K) b. Cs, Cs + (Cs) c. K, Ca (K) d. m, m 3+ (m) e. Mg, Ca (Ca) f. I -, Xe (I - ) g. 2-, 2- ( 2- ) h. -, 2- ( 2- ) 15. ize: Put in order of increasing size a. N 3-, 2-, -, Ne, Na + ( -, Na +, Ne, -, 2--, N 3- ) b. Mg 2+, Al 3+ (Al 3+ Mg 2+ ) c. N,, (,, N) d. -, Cl -, Br - ( -, Cl -, Br - ) e. Li +, Be (Li +, Be) 16. EA: Put in order of increasing electron affinity a. Cu, Zn Zn > Cu b., Cl Cl > c. K, Ca Ca > K d., Li > Li e. As, Ge As > Ge 17. Lewis Dot: Write the Lewis dot structures for: a. 2, 2, N 2, C, 2 (:, ::, :C::::, b. B 3, B 3 N 3

4 B B N c. C 2, CN -, Cl C C N C N Cl Answers Week 4 Recitation ection 1 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s d. 6, 2 4, 3 P e. C 4, 2 C 2, 4 C 2, 2, N 3 C C C C C f. 18. Write Resonace and Lewis Dot structures for: N 2-, N 3-, 2, 3 N _ - N xi Acids: The four rules of xiacids are: a. As electronegativity of central atom increases the acidity increases b. As the positive formal charge (no expanded octet) on the central atom increases the acidity increases c. As the number of resonance structures of the dissociated acid increase the acidity increases. d. As the number of atoms that do not have an attached increases acidity increases. 20. Explain why these rules are true. N 2 2 1! NG (l) ! K 5 1 2! NG (ml) 4-1 0! NG (l) NG (ms) ! k 7 2-2! K ! NG (l) 2. or a the following orbital " = Y(#,\$) % R(r) = 1 4& % 2 ' Z * ), ( )exp(-. 3) where " = Zr, 81 3 ( a 0 + a 0 and a 0 = Å. a. Calculated where the radial nodes are for Z=3 and a 0 =0.529 Å.Take the derivative dr dr set equal to 0 and solve for #. You get: # = 11.47, and 3.53 or r = 2.02 and 0.62 Å. b. Can you tell what orbital it is (e.g. 1s). (It has no angular nodes and 2 radial nodes thus it is a 3s) 3. or the following orbital: 5 " = Y(#,\$) % R(r) = ( 16& 3( cos(#) 4 ( Z + )2 '1) % * - (. 2 )exp('. 3) 81 30) a 0, c. ow many angular nodes are there? (" goes from 0 to p if you look at the " dependence you can solve 2( cos" ) 2 #1 = 0 for the angular nodes. You get " = 54.7 and degrees. Thus there are two angular nodes and it is a d orbital) d. ow many radial nodes are there? (Can solve radial part for the zeros and get # = 0 so only a node at zero which is really only part of the angular node that we found above. Thus no radial nodes. e. Name the orbital? (rom above we have 0 radial nodes and 2 angular nodes thus total of 2 nodes you have a 3d orbital 4. Penetration: Put the following orbitals into the order in which they penetrate best: 2s, 2p 3s, 3p, 3d, 4s (2s, 2p, 2p, 4s, 3d) Draw r 2 Y 2 (on anti nodes) vs. r for the above orbitals and show why you have put them in the above order. (ee handout). 5. Which has lower energy:

5 f. 3p or 4s (3p) g. 4p or 5s (4p) h. 3d or 4s (4s) i. 5d or 4f or 5p (5p) 6. tate: j. the Pauli exclusion principle (No two electrons can have the same 4 quantum numbers) k. the Aufbau principle (When adding electrons to a nucleus they go into the lowest energy orbital that can accept another electron). l. und s rule. Why is it true? (When electrons are added to orbitals of equal energy the configuration with the highest total spin will have the lowest energy. If there are multiple orbitals that have the same energy but occupy regions of space it is better to place electrons into separate spatial orbitals to reduce their repulsion energy and with parallel spins to reduce their magnetic interaction energy, thus it is better to have one electron it two orbitals than two electrons in one orbital and for two electrons in E 1 > E 2 > E 3 orbitals it is better if their configuration 1 configuration 2 configuration 3 spins are aligned. or a p 2 configuration see figure to right). 7. how the electron configuration (ground state) for the following atoms m. 5 B, 14 i, 29 Cu, 8, (1s 2 2s 2 2p 1 ), (1s 2 2s 2 2p 6 3s 2 3p 2 ), (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 ), (1s 2 2s 2 2p 4 ) n. 6 C, 10 Ne Mg + 15 P 2+ (1s 2 2s 2 2p 2 ), (1s 2 2s 2 2p 62 ), (1s 2 2s 2 2p 6 3s 2 ), (1s 2 2s 2 2p 6 3s 2 3p 1 ) o. 23 V, 23 V V 3+ (1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 3 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 2 ) p. 24 Cr 24 Cr + 24 Cr 2+ (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 4 ) q. 30 Zn, 30 Zn +, 30 Zn 2+, (1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 ), (1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 ), (1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 ) 8. What other element than Cr in the first transition metal series is an exception to the general rule on orbital filling. (Cu) 9. The following elements are exceptions to the general rule on orbital filling explain each r. Nb 41, Pd 46 (steals two 5s electrons to get half filled 4d shell, steals two 5s electrons to get completely filled 4d shell) s. Mo 42, Ag 47 (the both steal a 5s electron to get half filled or completely filled 4d shell) t. Ru 44, Rh 45 (steal a 5s electron to add another electron to 4d shell) ee page 551 or GN. 10. Ionization Potential: Put in order: u. Ni, Ni + (Ni < Ni + ) v. Ne, Ar (Ar < Ne) w. Ne, Na + (Ne < Na + ) x., Ar (Ar < ) 11. Electronic Configuration: y. Tc 43 and Pd 46 ow many 5s electrons do they have? (2, 0) z. Are C 6, 9, Ne 10 paramagnetic (yes, yes, no) aa. Write 4 excited states of Nitrogen (1s 2 2s 2 2p 3 where two spins are paired and either the electron are in all p orbitls or the same p orbits (2 states), and 1s 2 2s 2 2p 2 3s 1 ) bb. Which atoms with Z < 18 are paramagnetic (, Li, B, C, N,,, Na, Al, i, P,, Cl) 12. ize: Consider the orbitals: 2s, 2p, 3s, 3p, 3d, 4s, 4p Place the orbitals in order of: cc. Which extend the furthest from the nucleus (4s, >4p > 3s > 3p > 3d > 2s > 2p) dd. which approach closest to nucleus (2s < 2p < 3s < 3p < 4s < 3d < 4p) ee. which see the largest effective nuclear charge (2s > 2p > 3s > 3p > 4s > 3d > 4p) ff. which screen other electrons best. (2s > 2p > 3s > 3p > 3d > 4s > 4p ) 13. or each of the following pairs of atoms or ions which is larger gg. Na, K (K) hh. Cs, Cs + (Cs) ii. K, Ca (K) jj. m, m 3+ (m) kk. Mg, Ca (Ca) ll. I -, Xe (I - ) mm. 2-, 2- ( 2- ) nn. -, 2- ( 2- ) 14. ize: Put in order of increasing size oo. N 3-, 2-, -, Ne, Na + ( -, Na +, Ne,, 2--, N 3- ) pp. Mg 2+, Al 3+ (Al 3+ Mg 2+ ) qq. N,, (,, N) rr. -, Cl -, Br - ( -, Cl -, Br - ) ss. Li +, Be (Li +, Be) 15. EA: Put in order of increasing electron affinity tt. Cu, Zn uu., Cl vv. K, Ca ww., Li xx. As, Ge 16. Lewis Dot: Write the Lewis dot structures for: yy. 2, 2, N 2, C, 2 (:, ::, :C::::, zz. B 3, B 3 N 3 B aaa. B N C 2, CN -, Cl C C N C N Cl bbb. 6, 2 4, 3 P 4

6 ccc. C 4, 2 C 2, 4 C 2, 2, N 3 C C C C C ddd. 17. Write Resonace and Lewis Dot structures for: N 2-, N 3-, 2, 3 N _ - N N 18. xi Acids: The four rules of xiacids are: eee. As electronegativity of central atom increases the acidity increases fff. As the positive formal charge (no expanded octet) on the central atom increases the acidity increases ggg. As the number of resonance structures of the dissociated acid increase the acidity increases. hhh. As the number of atoms that do not have an attached increases acidity increases. 19. Explain why these rules are true.

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