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Chapter 7

The Electronic Structure of Atoms. Chapter 7.

gage-myers
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Chapter 7

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  1. The Electronic Structure of Atoms Chapter 7

  2. Outline1.From classical physics to Quantum Theory2. The photoelectric effect3. Bohr’s Theory of the Hydrogen Atom4.The Dual Nature of the electron5.Quantum Mechanism 6. Quantum number7.Atomic Orbitals8.Electron Configuration 9. The Building-up Principle

  3. Properties of Waves Wavelength (l) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency (n) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = l x n

  4. Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s All electromagnetic radiation l x n = c

  5. The type of electromagnetic

  6. l n A photon has a frequency of 6.0 x 104 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? l x n = c l = c/n l = 3.00 x 108 m/s / 6.0 x 104 Hz l = 5.0 x 103 m l = 5.0 x 1012 nm

  7. Plank’s Quantum Theory 1. Planck's law, Blackbody radiation law）是用於描述在任意溫度下，從一個黑體中發射的電磁輻射的輻射率與電磁輻射的頻率的關係公式。 2. 物理學家在研究輻射密度與頻率的關係: 發現在長波長與短波長範圍與實驗觀測不同?? 3. 古典物理認為能量是連續的, 物質可以吸收或是發射任意大小的能量。 4. Plank提出假設，認為只吸收或發射特定能量包，稱為量子

  8. Mystery #1, “Heated Solids Problem”Solved by Planck in 1900 When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Radiant energy emitted by an object at a certain temperature depends on its wavelength. Energy (light) is emitted or absorbed in discrete units (quantum). E = h x n Planck’s constant (h) h = 6.63 x 10-34 J•s

  9. Mystery #2, “Photoelectric Effect”Solved by Einstein in 1905 hn • Light has both: • wave nature • particle nature KE e- Photon is a “particle” of light hn = KE + W KE = hn - W 光子能量(photon) where W is the work function and depends how strongly electrons are held in the metal

  10. The work function of metals

  11. EX: When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm. E = h x n E = h x c / l E = 6.63 x 10-34 (J•s) x 3.00 x 10 8 (m/s) / 0.154 x 10-9 (m) E = 1.29 x 10 -15 J

  12. Bohr’s Model of the HAtom

  13. Line Emission Spectrum of Hydrogen Atoms Line spectra(非連續光譜, why?)

  14. Sodium atoms in an excited state

  15. Plasma: Plasma is loosely described as an electrically neutral medium of positive and negative particles (i.e. the overall charge of a plasma is roughly zero). Nature Artificial showing oxygen, helium, and hydrogen ions that gush into space from regions near the Earth's poles. O2-plasma Ar plasma

  16. How we using “plasma” in semiconductor fabrication? • Etching • Deposition thin film

  17. ( ) En = -RH 1 n2 Bohr’s Model of the Atom (1913) • e- can only have specific (quantized) energy values • light is emitted as e- moves from one energy level to a lower energy level Ground state excited state n (principal quantum number) = 1,2,3,… RH (Rydberg constant) = 2.18 x 10-18J

  18. E = hn E = hn

  19. ni = 3 ni = 3 f i ni = 2 nf = 2 DE = RH i f ( ) ( ) ( ) Ef = -RH Ei = -RH nf = 1 nf = 1 1 1 1 1 n2 n2 n2 n2 Ephoton = DE = Ef - Ei

  20. Ephoton = DE = RH i f ( ) 1 1 n2 n2 Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. Ephoton = 2.18 x 10-18 J x (1/25 - 1/9) Ephoton = DE = -1.55 x 10-19 J Ephoton = h x c / l l = h x c / Ephoton l= 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19J l=1280 nm

  21. The Dual Nature of the Electron 電子的二元性 • Physicists were intrigued by Bohr’s Theory: • Why hydrogen electron are quantized? • Why electron restricted to orbiting the nucleus at certain • fixed distance? In 1924, de Broglie answer this: If the light waves can behave like a stream of particles(photons), then perhaps particles such as electrons can possess wave properties.

  22. h 2pr = nll = mu Why is e- energy quantized? Standing wave If the electron does behave like a wave in atom,the length of wave must fit the circumference of orbital exactly! Otherwise, it will not exist~ node De Broglie (1924) reasoned that e- is both particle and wave. h ( ) p u = velocity of e- 物質波波長 m = mass of e-

  23. 光子動量 適用於所有物質與粒子 For electron, this wavelength is ~ 72 nm

  24. Electrons can behave like X rays and display “wave properties” electron diffraction pattern of Al-foil X-ray diffraction pattern of Al-foil

  25. What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? l = h/mu h in J•s m in kg u in (m/s) l = 6.63 x 10-34 / (2.5 x 10-3 x 15.6) l = 1.7 x 10-32 m = 1.7 x 10-23 nm

  26. Quantum Mechanics

  27. Schrodinger Wave Equation • In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e- • Wave function (y) describes: • . energy of e- with a given y • . probability of finding e- in a volume of space • Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

  28. 基於德布羅伊的波動-粒子雙重性原理，為薛丁格方提出一種波動方程式:基於德布羅伊的波動-粒子雙重性原理，為薛丁格方提出一種波動方程式: 可描述粒子在空間中的波動行為。 在應用上面, 電子在晶體的運動行為可用波函數的描述。 1.無法準確量測能量E與具有此能量的時間瞬間t 2. 無法決定電子的確切位置，發展一個機率密度函數(probability density function)，來決定特定位置找到一個電子的機率。

  29. Where 90% of the e- density is found for the 1s orbital Electron density Boundary surface diagram (軌域輪廓)

  30. n=1 n=2 n=3 y is a function of four numbers called quantum numbers (n, l, ml, ms) Schrodinger Wave Equation 量子數可以用來描述原子軌域及標示不同電子 principal quantum number n 主量子數 n = 1, 2, 3, 4, …. distance of e- from the nucleus

  31. Schrodinger Wave Equation quantum numbers:(n, l, ml, ms) 角動量量子數 angular momentum quantum number l for a given value of n, l= 0, 1, 2, 3, … n-1 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e- occupies

  32. l = 1 (p orbitals) l = 0 (s orbitals)

  33. l = 2 (d orbitals)

  34. Schrodinger Wave Equation quantum numbers: (n, l, ml, ms) 磁量子數 magnetic quantum number ml for a given value of l ml = -l, …., 0, …. +l if l = 1 (p orbital), ml = -1, 0, or1 if l = 2 (d orbital), ml = -2, -1, 0, 1, or2 orientation of the orbital in space 軌域在空間中的方向

  35. 3 orientations is space ml = -1, 0, or1

  36. ml = -2, -1, 0, 1, or2 5 orientations is space

  37. Schrodinger Wave Equation (n, l, ml, ms) spin quantum number ms ms = +½or -½ 自旋量子數 ms = +½ ms = -½

  38. Schrodinger Wave Equation quantum numbers:(n, l, ml, ms) Existence (and energy) of electron in atom is described by its unique wave function y. Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time

  39. Schrodinger Wave Equation quantum numbers:(n, l, ml, ms) Shell – electrons with the same value of n Subshell – electrons with the same values of nandl Orbital – electrons with the same values of n, l, andml How many electrons can an orbital hold? If n, l, and mlare fixed, then ms = ½ or - ½ y= (n, l, ml, ½) ory= (n, l, ml, -½) An orbital can hold 2 electrons

  40. n=2 n=3 l = 1 l = 2 EX: How many 2p orbitals are there in an atom? If l = 1, then ml = -1, 0, or +1 2p 3 orbitals How many electrons can be placed in the 3d subshell? If l = 2, then ml = -2, -1, 0, +1, or +2 3d 5 orbitals which can hold a total of 10 e-

  41. Energy of orbitals in a single electron atom ( ) En = -RH 1 n2 n=1 n=2 n=3 Energy only depends on principal quantum number n

  42. Energy of orbitals in a multi-electron atom n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=3 l = 2 Energy depends on n and l 需要考慮到多電子間的能量排斥

  43. 2s 軌域的density比2p高, 軌域的穿透力高，因此被1s 電子屏蔽的效應小。

  44. Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

  45. number of electrons in the orbital or subshell principal quantum number n angular momentum quantum number l 1s1 Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 電子在原子的地址 1s1 Orbital diagram H

  46. 2p 2p 逆磁 Paramagnetic Diamagnetic 順磁 unpaired electrons all electrons paired

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