Electromagnetic Radiation

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1 Chapter 7 Atomic structure and periodicity ( 原子結構和週期性 ) Electromagnetic radiation ( 電磁輻射 ) The nature of matter ( 物質的本質 ) Atomic spectrum ( 原子光譜 ) Quantum mechanics ( 量子力學 ) Orbital ( 軌域 ) Electron spin ( 電子自旋 ) Periodic table ( 週期表 )

2 7.1 Electromagnetic Radiation ( 電磁輻射 ) Radiant energy that exhibits wavelength-like behavior and travels through space at the speed of light in a vacuum. 電磁輻射是輻射能量以波的方式在空間中傳遞, 不論頻率為何, 在真空中的速度都是光速

3 Waves have 3 primary characteristics: ( 波有三個特性 ) 1. Wavelength ( 波長, λ): distance between two peaks in a wave. ( 兩個波峰間的距離 ) 2. Frequency ( 頻率, ν): number of waves per second that pass a given point in space. ( 每一秒通過空間中一點的波數 ) 3. Speed: speed of light ( 光速 ), c = m/s.

4 速度一樣時, 波長與頻率成反比 Figure 7.1: The nature of waves. Note that the radiation with the shortest wavelength has the highest frequency.

5 Wavelength and frequency can be interconverted. 波長和頻率可以互相轉換 c = νλ c = speed of light ( 光速,m s 1 ) ν = frequency ( 頻率,Hz,s 1 ) λ = wavelength ( 波長,m)

6 Figure 7.2: Classification of electromagnetic radiation. 電磁輻射的分類

7 Ultraviolet (UV): 紫外線 ( 短於 400 nm) Visible (VIS): 可見光 ( nm) Infrared (IR): 紅外線 ( 長於 700 nm) Microwave (MW): 微波 Radio waves: 無線電波

8 When a strontium salt is dissolved in methanol (with a little water) and ignited, it gives a brilliant red flame. The red color is produced by emission of light when electrons, excited by the energy of the burning methanol, fall back to their ground states. 鍶鹽溶解在甲醇後, 點火燃燒電子從激發態回到基態並發光作業 : Sample Exercise 7.1

9 7.2 The nature of matter Energy is quantized and can occur only in discrete units, called quanta. 在微觀系統中 ( 例如原子分子 ), 能量是量子化的, 每一個能量單位稱為一個量子 (quantum) 作業 : Sample Exercise 7.2

10 ΔE = hν = hc λ ΔE = change in energy, in J h = Planck s constant ( 普朗克常數 ), J s ν = frequency, in s 1 (Hz) λ = wavelength, in m

11 Photoelectric effect ( 光電效應 ) 用光照射金屬表面, 當光的頻率大於 ν 0 時, 才會產生光電子. 其動能與入射頻率成正比, 產量與光的強度 (intensity) 成正比. KE e = 1 2 mv 2 = hν hν 0

12 Energy and Mass 根據狹義相對論 (special theory of relativity) Energy has mass ( 能量也有質量 ) E = energy m = mass c = speed of light E = mc 2

13 E m photon = photon = hc λ h λ c The dual nature of light. 光具有波和粒子的雙重性質, 稱為波粒二象性光沒有靜止質量 (rest mass)

14 Figure 7.4: Electromagnetic radiation exhibits wave properties and particulate properties. Photon: 光子

15 de Broglie s Equation ( 德布羅意物質波 ) λ = h = p h mv λ = wavelength, in m h = Planck s constant, J s (J s = kg m 2 s 1 ) m = mass, in kg ν = velocity, in m s 1

16 Sample Exercise 7.3 m e = kg, v = m/s m(ball) = 0.10 kg, v = 35 m/s λ =? λ = h mv = = ( m) λ( ball) = m 球的波長很短, 可忽略電子的波長與原子大小差不多, 不可忽略

17 Figure 7.5 Diffraction pattern 繞射圖式建設性干涉, 增強破壞性干涉, 減弱

18 Continuous spectrum: 連續光譜 7.3 Atomic Spectrum of Hydrogen Line spectrum: 線光譜

19 Figure 7.7: A change between two discrete energy levels emits a photon of light. 電子在氫原子中的能量是量子化的 ΔE = hν

20 7.4 The Bohr Model ( 波耳模型 ) The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits. 波耳模型假設氫原子中的電子, 只能繞某些容許的圓形軌道運動

21 氫原子的電子, 在不同能階間躍遷 (transition), 所以產生線光譜 Figure 7.8: Electronic transitions ( 電子躍遷 ) in the Bohr model for the hydrogen atom.

22 18 2 E = J ( z 2 / n ) E = energy of the levels in the H-atom ( 氫原子能階的能量 ) z = nuclear charge ( 核電荷,for H, z = 1) n = an integer ( 整數 )

23 Ground State ( 基態 ): 在原子或分子中, 能量最低的狀態 For an hydrogen-like atom, it is the state with n = 1. 類氫原子的基態, 就是 n = 1 的狀態能量比基態高的都稱為激發態 (excited state)

24 Energy Changes in the Hydrogen Atom ΔE = E final state E initial state λ = hc ΔE 吸光或放光時, 原子內部的能階差, 等於光的能量

25 ΔE H, n = 1 n = 2 λ =? = λ = Sample Exercise m 1 ( ) = 1nm m = nm 9 10 m ( ( 紫外光 ) ) ( λ 作業 : Sample Exercise )

26 7.5 The quantum mechanical model of the atom Figure 7.9: The standing waves ( 駐波 ) Node ( 節點 )

27 Figure 7.10: The hydrogen electron visualized as a standing wave around the nucleus. 將電子繞原子核的運動, 視為穩定的駐波, 所以只有特定的軌道是容許的

28 Quantum mechanics( 量子力學 ) Schrodinger equation ( 薛丁格方程式 ) $H $Hψ = Eψ ψ = wave function ( 波函數 ) = operator ( 算子 ) E = total energy of the atom ( 總能 )

29 一維粒子位能為 V的薛丁格方程式 & : h 2 2m Hˆ = d 2 dx h ψ 2 2 2m + V d dx 2 2 ψ = + V E ψ ( h = 2 h π ) 解 E 和 ψ A specific wave function is often called an orbital. 軌域就是波函數

30 Heisenberg Uncertainty Principle ( 海森堡測不準原理 ) Δx Δp h 4π x = position ( 位置 ) p=mv = momentum ( 動量 ) h = Planck s constant ( 普朗克常數 )

31 The more accurately we know a particle s position, the less accurately we can know its momentum, and vice versa. ( 翻譯 ) 我們對一個粒子的位置測量得越準確, 則對其動量的測量越不準確, 反之亦然

32 氫 1s 軌域的機率分布 Figure 7.11: hydrogen 1s orbital Ψ 1s

33 Probability Distribution ( 機率分布 ) Ψ 2 正比於在空間中某一點發現電子的機率 2 [ ψ ( x1, y1, z1)] N1 = 2 [ ψ ( x, y, z )] N Radial probability distribution: ( 徑向機率分布 ) 2 發現電子在原子核外某一薄球殼內的機率 2 2 2

34 氫原子 1s 軌域的徑向機率分布通常以包含 90% 電子機率的圓球為原子大小 Figure 7.12: Hydrogen 1s orbital radial probability distribution

35 7.6 Quantum Numbers ( 量子數, QN) 1.Principal QN ( 主量子數 ) n = 1, 2, 3,... related to size and energy of the orbital. ( 決定原子的大小和能量 ) 2. Angular Momentum QN ( 角量子數 ) l = 0 to n 1 relates to shape of the orbital. ( 決定軌域的形狀 )

36 f 之後按字母順序排列光譜學對鹼金屬光譜的分類 : s: sharp ( 尖銳的 ) p: principal ( 主要的 ) d: diffuse ( 擴散的 ) f: fundamental ( 基本的 )

37 3. Magnetic QN ( 磁量子數 ) m l = l to l relates to orientation of the orbital in space relative to other orbitals. ( 決定軌域的位向 ) 4. Electron Spin QN ( 電子自旋量子數 ) m s = + 1 /2, 1 /2 relates to the spin states of the electrons. ( 決定電子的自旋狀態 )

38 每種軌域的數目 = 2l + 1

39 n = 5 Sample Exercise 7.6 Subshells ( 次殼層, l) =? Answer l = s 5p 5d 5f 5g 上台演練 : 3d, 4f orbitals, n, l, m l =?

40 7.7 Orbital shapes and energies ( 軌域的形狀和能量 ) 節面 6s 軌域有幾個節面? Answer: 5 個 Figure 7.13: Two representations of the hydrogen 1s, 2s, and 3s orbitals.

41 2p 軌域 Figure 7.14: Representation of the 2p orbitals. (a) The electron probability distributed for a 2p orbital. (b) The boundary surface representations of all three 2p orbitals.

42 3p 軌域, 有一個球節面 Figure 7.15: A cross section of the electron probability distribution for a 3p orbital.

3d 軌域 : d xy, d yz, d xz, d x 2 -y 2, d z 2 - + - + - + + + - +

43 3d 軌域 : d xy, d yz, d xz, d x 2 -y 2, d z Figure 7.16: Representation of the 3d orbitals.

44 Figure 7.17: Representation of the 4f orbitals in terms of their boundary surface ( 界面 ).

45 氫原子能階圖, 相同殼層的軌域是簡併的 (degenerate, 能量一樣 ) Figure 7.18: Orbital energy levels for the hydrogen atom.

46 7.8 Electron spin and the Pauli principle Electron spin: 電子自旋有兩種狀態, 會產生方向相反的磁矩 (magnetic moment) Figure 7.19: A picture of the spinning electron.

47 Pauli Exclusion Principle 包立不相容原理 In a given atom no two electrons can have the same set of four quantum numbers (n, l, m l, m s ). Therefore, an orbital can hold only two electrons, and they must have opposite spins. ( 翻譯 )

48 包立不相容原理 : 在一個原子中, 沒有任何兩個電子可以擁有同組的四個量子數 (n, l, m l, m s ) 所以, 每個軌域最多只能填兩個電子, 且其自旋是相反的

49 7.9 Polyelectronic atoms 多電子 (> 1 e - ) 原子 Na e - e e - - e- e e - e - e - e - e - e - 遮敝效應 (shielding effect): 電子感受到的有效核電荷, 會小於原子核電荷, 因為其它電子的斥力, 會抵銷部分原子核的吸引力

50 比較 2s 與 2p 軌域的徑向機率分布 Figure 7.20: A comparison of the radial probability distributions of the 2s and 2p orbitals.

51 Penetration effect ( 穿透效應 ): 電子穿透至較接近原子核的區域, 因吸引力增強, 導致能量降低穿透 :3s > 3p > 3d Figure 7.21: (a) The radial probability distribution for an electron in a 3s orbital. (b) The radial probability distribution for the 3s, 3p,

52 由於遮敝和穿透效應, 在多電子原子中, 同殼層的軌域能量不同, 但次殼層仍簡併 E ns < E np < E nd < E nf Figure 7.22: The orders of the energies of the orbitals in the first three levels of polyelectronic atoms.

53 7.10 The history of the periodic table ( 週期表 ) Figure 7.24: Mendeleev's early periodic table, published in Note the spaces left for missing elements with atomic masses 44, 68, 72, 100.

54 門得列夫用週期表預測的元素性質, 與實驗相符

55 週期表可用來預測新元素的性質

56 7.11 The Aufbau Principle ( 遞建原理 ) and the periodic table As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these hydrogen-like ( 類氫 ) orbitals. 電子填入原子軌域, 低能量的軌域先填

57 Hund s Rule ( 洪德定則 ) The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals. ( 翻譯 )

58 洪德定則 : 電子填入簡併軌域時, 會先填入不同的軌域, 且其自旋相同, 因為自旋相同但不成對電子最多的組態 (configuration), 能量最低

59 Electron configuration 電子組態電子填入軌域的順序 : (1s), (2s, 2p), (3s, 3p), (4s, 3d, 4p), (5s, 4d, 5p) 可填電子數 : s(2), p(6), d(10), f(14) H: 1s 1 He: 1s 2 Li: 1s 2 2s 1 ( 上台演練 : Be Ne)

60 Figure 7.25: The electron configurations in the type of orbital occupied last for the first 18 elements.

61 Valence Electrons 價電子 The electrons in the outermost principle quantum level of an atom. (n 最大的殼層 ) Atom Valence Electrons Ca 2 N 5 Br 7 Inner electrons are called core electrons ( 內層電子 ).

62 K: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 or [Ar] 4s 1 Ca: [Ar]4s 2 Sc: [Ar]4s 2 3d 1 or [Ar] 3d 1 4s 2 ( 上台演練 : 24 Cr, 26 Fe, 29 Cu)

63 不規則 : Cr: [Ar]3d 5 4s 1 ; Cu: [Ar]3d 10 4s 1 Figure 7.26: Electron configurations for potassium through krypton.

64 Broad Periodic Table Classifications 週期表粗略的分類 Representative Elements (main group): filling s and p orbitals (groups 1,2,13-18) 典型元素的電子填入 s 和 p 軌域 Transition Elements: filling d orbitals (groups 3-12) 過渡元素的電子填入 d 軌域

65 Inner transition elements ( 內過渡元素 ) Lanthanide series ( 鑭系元素 ): 在 La([Xe]6s 2 5d 1 ) 之後的 14 個元素 ( 原子序 58-71), 電子填入 4f 軌域 Actinide Series ( 錒系元素 ): 在 Ac([Rn]7s 2 6d 1 ) 之後的 14 個元素 ( 原子序 ) 電子填入 5f 軌域

66 Figure 7.27: The orbitals being filled for elements in various parts of the periodic table.

67 Figure 7.28: The periodic table with atomic symbols, atomic numbers, and partial electron configurations.

68 Figure 7.29: The positions of the elements considered in Sample Exercise 7.7 作業 : Sample Exercise 7.7

69 7.12 Periodic trends in atomic properties 原子性質的週期趨勢 Ionization energy ( 游離能 ): The quantity of energy required to remove an electron from the gaseous atom or ion. X(g) X + (g) + e - 將一個電子從氣態原子或離子移除所需要的能量

70 開始移除內層電子時, 游離能會急劇升高第一游離能第二游離能

71 I 1 < I 2 < I 3 < Al + + e - Al 2+ + e - I 1 I 2 3p 3s 移除一個電子後, 正電荷增加, 對電子的吸引力增強, 軌域能量下降, 所以游離能變大 Al Al +

72 Periodic Trends First ionization energy: increases from left to right across a period ( 同週期的原子, 游離能從左至右遞升, 因質子數增多, 原子核對電子的吸引力增強 ); decreases going down a group ( 由上至下遞減, 因電子與原子核的距離增大, 吸引力減弱 ).

73 Figure 7.30: The values of first ionization energy for the elements in the first six periods.

74 同族的原子, 游離能從上至下遞減

75 Figure 7.31: Trends in ionization energies (kj/mol) for the representative elements.

76 Sample Exercise 7.8 I 1 (P) = 1060 kj/mol, I 1 (S) 1005 kj/mol, why? Answer P: 3s 2 3p 3 S: 3s 2 3p 4 依趨勢而言, 週期表向右游離能應變大, 但因硫有一個 p 軌域填了兩個電子, 電子對的斥力使其能量升高, 因此游離能較小作業 : Sample Exercise 7.9

77 Electron Affinity 電子親和力 The energy change associated with the addition of an electron to a gaseous atom. X(g) + e X (g) 加一個電子到氣態原子的能量變化 ( 本書定義放熱為負, 與熱力學定義相同, 但其它作者可能定義放熱為正 )

78 C - (1s 2 2s 2 2p 3 ) 穩定 ; N - (1s 2 2s 2 2p 4 ) 不穩定, 因為外加電子使 p 軌域電子的斥力增加週期表向右, 放熱多 ( 核電荷增加 ) Figure 7.32: The electron affinity values for atoms among the first 20 elements that form stable, isolated X - ions.

79 週期表向下, 放熱少 ( 距離遠, 吸引力小 ) F 不規則, 因為原子較小, 2p 電子的斥力較大

80 Atomic Radii ( 原子半徑 ): decrease going from left to right across a period; increase going down a group. 同週期, 原子半徑由左至右遞減, 因為有效核電荷增加, 吸引力增強 ; 同一族, 半徑由上至下遞增, 因為主量子數變大, 軌域變大

81 Liquid bromine ( 溴, Br 2 ) in equilibrium with its vapor.

82 同核雙原子分子鍵長的一半, 定義為共價原子半徑 (covalent atomic radius) Figure 7.33: The radius of an atom (r) is defined as half the distance between the nuclei in a molecule consisting of identical atoms.

83 Sample Exercise 7.10 Radius ( 半徑 ) Be 2+ < Mg 2+ < Ca 2+ < Sr 2+ 同一族, 週期表向下, 外層電子的主量子數增加, 半徑越大

84 Figure 7.34: Atomic radii (in picometers, m) for selected atoms.

85 7.13 The properties of a group: The alkali metals ( 鹼金屬 ) The number and type of valence electrons primarily determine an atom s chemistry. ( 翻譯 ) 原子的化學性質, 主要決定於價電子的數目和類型

86 鹼鹼土金屬鹵素鈍金屬過渡元素氣 Figure 7.35: Special names for groups in the periodic table. 鑭系金屬錒系非金屬類金屬

87 鹼金屬 : 價殼層電子組態類似, 化學性質類似

88 Alkali metals ( 鹼金屬 ) 易失去一個價電子 2Na(s) + Cl 2 (g) 2NaCl(s) 可當還原劑 (reducing agent) 2Na(s) + S(s) Na 2 S(s)

89 固態時與非金屬反應的還原力 : Cs > Rb > K > Na > Li 在水溶液中的還原力 : Li > K > Na 2M(s) + 2H 2 O(l) H 2 (g) + 2M + (aq) + 2OH - (aq) + energy

90 鈉和鉀與水的放熱反應較激烈, 因其熔點較低, 反應時熔化, 反應面積較大小離子電荷密度較高, 吸引水分子的能力較強, 水合能較大

91 作業 Chapter 7 Sample Exercises: 7.1, 7.2, 7.5, 7.7, 7.9 期中考練習題 Questions and Exercises 19, 33, 37, 41, 45, 53, 55, 57, 61, 67, 71, 79, 85, 87, 97, 103

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