Chapter 5
Periodicity and Atomic Structure

5.1 Gamma ray = 8.43 x 10¹⁸ s^-1 = 8.43 x 10¹⁸ Hz

Radar wave = 2.91 x 10⁹ s^-1 = 2.91 x 10⁹ Hz

5.2  102.5 MHz = 102.5 x10⁶ Hz = 102.5 x10⁶ s^-1

= 9.55 x 10¹⁷ Hz = 9.55 x 10¹⁷ s^-1

5.3 The wave with the shorter wavelength (b) has the higher frequency. The wave with the larger amplitude (b) represents the more intense beam of light. The wave with the shorter wavelength (b) represents blue light. The wave with the longer wavelength (a) represents red light.

5.4 Balmer series: m = 2; R = 1.097 x 10^-2 nm^-1

; ; 2.519 x 10^-3 nm^-1; = 397.0 nm

5.5 Paschen series: m = 3; R = 1.097 x 10^-2 nm^-1

; ; = 5.333 x 10^-4 nm^-1; = 1875 nm

5.6 Paschen series: m = 3; R = 1.097 x 10^-2 nm^-1

; ; = 1.219 x 10^-3 nm^-1; = 820.4 nm

5.7  91.2 nm = 91.2 x 10^-9 m

= 3.29 x 10¹⁵ s^-1
E = h = (6.626 x 10^-34 Js)(3.29 x 10¹⁵ s^-1) = 2.18 x 10^-18 J/photon
E = (2.18 x 10^-18 J/photon)(6.022 x 10²³ photons/mol) = 1.31 x 10⁶ J/mol = 1310 kJ/mol

5.8 IR, = 1.55 x 10^-6 m
E = 7.72 x 10⁴ J/mol = 77.2 kJ/mol
UV, = 250 nm = 250 x 10^-9 m
E = 4.79 x 10⁵ J/mol = 479 kJ/mol
X ray, = 5.49 nm = 5.49 x 10^-9 m
E = 2.18 x 10⁷ J/mol = 2.18 x 10⁴ kJ/mol
5.9 = 2.34 x 10^-38 m
5.10 (x)(mv) ; uncertainty in velocity = (45 m/s)(0.02) = 0.9 m/s

5.11

There are 25 possible orbitals in the fifth shell.

5.12 (a) 2p (b) 4f (c) 3d

5.13 (a) 3s orbital: n = 3, l = 0, m_l = 0
(b) 2p orbital: n = 2, l = 1, m_l = -1, 0, +1
(c) 4d orbital: n = 4, l = 2, m_l = -2, -1, 0, +1, +2

5.14 The g orbitals have four nodal planes.

5.15 The figure represents a d orbital, n = 4 and l = 2.

5.16 m = 1, n = ; R = 1.097 x 10^-2 nm^-1
; ; = 1.097 x 10^-2 nm^-1; = 91.2 nm

E =

E = 1.31 x 10⁶ J/mol = 1.31 x 10³ kJ/mol

5.17 (a) Ti, 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d² or [Ar] 4s² 3d²

(b) Zn, 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ or [Ar] 4s² 3d¹⁰

(c) Sn, 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p² or [Kr] 5s² 4d¹⁰ 5p²

(d) Pb, [Xe] 6s² 4f¹⁴ 5d¹⁰ 6p²

5.18 For Na⁺, 1s² 2s² 2p⁶

5.19 The ground-state electron configuration contains 28 electrons. The atom is Ni.

5.20 Cr, Cu, Nb, Mo, Ru, Rh, Pd, Ag, La, Ce, Gd, Pt, Au, Ac, Th, Pa, U, Np, Cm

5.21 (a) Ba; atoms get larger as you go down a group.
(b) W; atoms get smaller as you go across a period.
(c) Sn; atoms get larger as you go down a group.
(d) Ce; atoms get smaller as you go across a period.

5.22 The aurora borealis begins on the surface of the sun with a massive solar flare. These flares eject a solar "gas" of energetic protons and electrons that reach earth after about 2 days and are then attracted toward the north and south magnetic poles. The energetic electrons are deflected by the earth's magnetic field into a series of sheetlike beams. The electrons then collide with O₂ and N₂ molecules in the upper atmosphere, exciting them, ionizing them, and breaking them apart into O and N atoms. The energetically excited atoms, ions, and molecules generated by collisions with electrons emit energy of characteristic wavelengths when they decay to their ground states. The O₂⁺ ions emit a red light around 630 nm; N₂⁺ ions emit violet and blue light at 391.4 nm and 470.0 nm; and O atoms emit a greenish-yellow light at 557.7 nm and a deep red light at 630.0 nm.

5.24

5.29 (a) 3p_y n = 3, l = 1 (b) n = 4, l = 2

5.34 (a) = 99.5 MHz = 99.5 x 10⁶ s^-1
E = h = (6.626 x 10^-34 Js)(99.5 x 10⁶ s^-1)(6.022 x 10²³ /mol)
E = 3.97 × 10^-2 J/mol = 3.97 × 10^-5 kJ/mol
= 115.0 kHz = 115.0 x 10³ s^-1
E = h = (6.626 x 10^-34 Js)(115.0 x 10³ s^-1)(6.022 x 10²³ /mol)
E = 4.589 x 10^-5 J/mol = 4.589 x 10^-8 kJ/mol
The FM radio wave (99.5 MHz) has the higher energy.

(b) = 3.44 x 10^-9 m

E = 3.48 x 10⁷ J/mol = 3.48 x 10⁴ kJ/mol
= 6.71 × 10^-2 m

E = 1.78 J/mol = 1.78 x 10^-3 kJ/mol
The X ray ( = 3.44 x 10^-9 m) has the higher energy.

5.47 Brackett series: m = 4, n = 5; R = 1.097 x 10^-2 nm^-1

; = 2.468 x 10^-4 nm^-1; = 4051 nm

Brackett series: m = 4, n = 6; R = 1.097 x 10^-2 nm^-1

; = 3.809 x 10^-4 nm^-1; = 2625 nm

5.57 (a) 3s (b) 2p (c) 4f (d) 4d

5.59 Co 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁷
(a) is not allowed because for l = 0, m_l = 0 only.
(b) is not allowed because n = 4 and l = 2 is for a 4d orbital.
(c) is allowed because n = 3 and l = 1 is for a 3p orbital.

5.65 The n and l quantum numbers determine the energy level of an orbital in a multielectron atom.

5.71 (a) Z = 55, Cs [Kr] 5s² 4d¹⁰ 5p⁶ 6s¹ (b) Z = 40, Zr [Kr] 5s² 4d²

(c) Z = 80, Hg [Xe] 6s² 4f¹⁴ 5d¹⁰ (d) Z = 62, Sm [Xe] 6s² 4f⁶

5.77 Z = 119 [Rn] 7s²5f¹⁴6d¹⁰7p⁶8s¹

5.81 A g orbital would begin filling at atomic number = 121 (see 5.80). There are nine g orbitals that can each hold two electrons. The first element to have a filled g orbital would be atomic number = 138.

5.83 Across a period, the effective nuclear charge increases, causing a decrease in atomic radii.

5.93 = 9,192,631,770 s^-1 = 9.19263 x 10⁹ s^-1

E = h = (6.626 x 10^-34 Js)(9.19263 x 10⁹ s^-1)(6.022 x 10²³/mol)
E = 3.668 x 10^-3 kJ/mol

Although Hf ([Xe] 6s² 4f¹⁴ 5d²) is directly below Zr ([Kr] 5s² 4d²) in the periodic table, Zr and Hf have almost identical atomic radii because the 4f electrons in Hf are not effective in shielding the valence electrons. The valence electrons in Hf are drawn in closer to the nucleus by the higher Z_eff.

5.101 75 W = 75 J/s; 550 nm = 550 x 10^-9 m; (0.05)(75 J/s) = 3.75 J/s

number of photons =

5.107 (a) Cl₂, 70.91 amu
M + Cl₂ ® MCl₂
mol Cl₂ = 0.8092 g Cl₂ x = 0.01141 mol Cl₂
mol M = 0.01141 mol Cl₂ x = 0.01141 mol M
molar mass of M = = 87.64 g/mol
atomic mass of M = 87.64 amu; M = Sr
(b) q = = 829 kJ/mol