1. Chapter 7 Quantum Theory of the Atom

2. Waves 7 | 2 A wave is a continuously repeating change or oscillation in matter or in a physical field. الموجة هو التغير المتكرر باستمرار او التذبذب في المادة او في المجال الفيزيائي. Light is an electromagnetic wave, consisting of oscillations in electric and magnetic fields traveling through space. الضوء هو موجات كهرومغناطيسية تتكون من تذبذب في المجالات الالكترونية والمغناطيسية والتي تنتقل في الفراغ.

3. Waves A wave can be characterized by its wavelength and frequency. يمكن وصف الموجات باطزالها وذبذباتها وتعرف ب لامبدا وهي المسافة بين قمتي موجتين متجاورتين؟ Wavelength, symbolized by the Greek letter lambda,, is the distance between any two identical points on adjacent waves. 7 | 3

4. Waves Frequency, symbolized by the Greek letter nu,, is the number of wavelengths that pass a fixed point in one unit of time (usually a second). The unit is 1 / S or s -1, which is also called the Hertz (Hz). التردد يرمز له بالحرف اليوناني نيو وهو عدد الوجات التي تمر في نقطة ثابتة في وحدة زمن واحدة غالبا ما تكون ثانية وتسمى الهيرتز. 7 | 4

5. Waves Wavelength and frequency are related by the wave speed, which for light is c, the speed of light, 3.00 x 10 8 m/s. لها علاقة مباشرة بسرهة الموجة c = The relationship between wavelength and frequency due to the constant velocity of light is illustrated on the next slide. العلاقة بين طول الموجة والتردد تنتج من السرعة الثابتة للضوء موضح في الشريحة اللاحقة. 7 | 5

6. Waves 7 | 6 When the wavelength is reduced by a factor of two, the frequency increases by a factor of two. عندما تقل سرعة بعامل مساوي 2 يزداد التردد بمقدار 2

7. Example 1 7 | 7 What is the wavelength of blue light with a frequency of 6.4 × 10 14 /s? = 6.4 × 10 14 /s c = 3.00 × 10 8 m/s c = so = c/ = 4.7 × 10 -7 m

8. Example 2 7 | 8 What is the frequency of light having a wavelength of 681 nm? = 681 nm = 6.81 × 10 -7 m c = 3.00 × 10 8 m/s c = so = c/ = 4.41 × 10 14 /s

9. Waves The range of frequencies and wavelengths of electromagnetic radiation is called the electromagnetic spectrum. معدل الترددات واطوال الموجات للاشعاع الكهرومغناطيسي تسمى الطيف 7 | 9

10. Example 3 When frequency is doubled, wavelength is halved. The light would be in the blue-violet region. 7 | 10

11. Waves One property of waves is that they can be diffracted—that is, they spread out when they encounter an obstacle about the size of the wavelength. احدى خواص الموجات هي انها تتشتت وتنتشر عندما تصطدم بعائق بحجم طول الموجة وقد اثبت هذه النظرية توماس يونغ، وقد تعززت هذه النظرية في اوائا القرن التاسع عشر. In 1801, Thomas Young, a British physicist, showed that light could be diffracted. By the early 1900s, the wave theory of light was well established. 7 | 11

12. Photoelectric Effect The wave theory could not explain the photoelectric effect, however. نظرية الموجة لم تفسر تأثير الفوتوضوئية وهي انبعاث الكترونات من سطح معدن او اي مادة اخرى عندما يشع الضوء عليها. 7 | 12

13. Photoelectric Effect The photoelectric effect is the ejection of an electron from the surface of a metal or other material when light shines on it. 7 | 13

14. “Particles” of Light 7 | 14 Einstein proposed that light consists of quanta or particles of electromagnetic energy, called photons. The energy of each photon is proportional to its frequency: نظرية الضوء كجسيمات او ككم من الطاقة الكهرومغناطيسية افترضها اينشتاين وسمى تلك الجسيمات بالفوتونات وقد افترض بان الطاقة الناتجة عن كل فوتون تتناسب و تردده حسب المعادلة التالية : E = h h = 6.626 × 10 -34 J  s (Planck’s constant)

15. Photoelectric Effect Einstein used this understanding of light to explain the photoelectric effect in 1905. استخدم اينشتاين هذا المفهوم عن الضوء لتوضيح تأثير الكهروضوئية Each electron is struck by a single photon. Only when that photon has enough energy will the electron be ejected from the atom; that photon is said to be absorbed. كل الكترون يضرب بفوتون واحد. فقط عندما يمتلك ذلك الفوتون طاقة كافية تمكنه من الانبعاث من الذرة ويمكن القول ان ذلك الفوتون قد امتص. 7 | 15

16. Duality of Light ازدواجية الضوء 7 | 16 Light, therefore, has properties of both waves and matter. Neither understanding is sufficient alone. This is called the particle–wave duality of light. لذلك فان الضوء يجمع بين خواص كل من المادة والموجات معا. لا يمكن فهم الضوء بخاصية واحدة فقط.

17. Example 4 7 | 17 The blue–green line of the hydrogen atom spectrum has a wavelength of 486 nm. What is the energy of a photon of this light? = 4.86 nm = 4.86 × 10 -7 m c = 3.00 × 10 8 m/s h = 6.63 × 10 -34 J  s E = h and c = so E = hc/ = 4.09 × 10 -19 J

18. The Quantum Atom الكم الذري 7 | 18 In the early 1900s, the atom was understood to consist of a positive nucleus around which electrons move (Rutherford’s model). بعد ان تم اكتشاف نموذج رذرفورد عن الذرة والالكترونات والبروتونات تركت تلك النظرية معضلة نظرية وهي حسب فيزياء الزمن فان الجسيم المشحون يستمر في الدوران ويفقد في دورانه طاقة على شكل اشعاع كهرومغناطيسي. ولكن هذه النظرية ليست في حالة استقرار الذرة. This explanation left a theoretical dilemma: According to the physics of the time, an electrically charged particle circling a center would continually lose energy as electromagnetic radiation. But this is not the case—atoms are stable.

19. The Quantum Atom 7 | 19 In addition, this understanding could not explain the observation of line spectra of atoms. ايضا لم يستطع توضيح سبب ملاحظة وجود طيف خطي للذرة A continuous spectrum contains all wavelengths of light. الطيف المستمر يحتوي على كل اطوال الموجات للضوء والطيف الخطي يري فقط الوان محددة او اطوال موجات محدد للضوء. هذه العملية ينتج عنها طيف خطي معين لكل ذرة حسب نوعها A line spectrum shows only certain colors or specific wavelengths of light. When atoms are heated, they emit light. This process produces a line spectrum that is specific to that atom. The emission spectra of six elements are shown on the next slide.

20. Elemental Line Spectra 7 | 20

21. Quantum Model of Hydrogen Atom 7 | 21 In 1913, Neils Bohr, a Danish scientist, set down postulates to account for 1. The stability of the hydrogen atom 2. The line spectrum of the atom فرضيات بوهر : استقرار ذرة الهيدرجين. الطيف الخطي للذرة.

22. Quantum Model of Hydrogen Atom Energy-Level Postulate فرضية مستويات الطاقة An electron can have only certain energy values, called energy levels. Energy levels are quantized. كل الكترون له مستوى محدد من الطاقة For an electron in a hydrogen atom, the energy is given by the following equation: معادلة الهيدروجين R H = 2.179 x 10 -18 J ثابت رويدبيرغ n = principal quantum number 7 | 22

23. Quantum Model of Hydrogen Atom Transitions Between Energy Levels An electron can change energy levels by absorbing energy to move to a higher energy level or by emitting energy to move to a lower energy level. يمكن ان يغير الالكترون مستويات طاقته بامصاص الطاقة للتحرك الى مستويات طاقة اعلى او يشع طاقة عند نزوله الى مستويات اقل 7 | 23

24. Quantum Model of Hydrogen Atom For a hydrogen electron the energy change is given by 7 | 24 R H = 2.179 × 10 -18 J, Rydberg constant

25. Quantum Model of Hydrogen Atom The energy of the emitted or absorbed photon is related to  E: فرقية الطاقة تحدد الامتصاص او الاشعاع We can now combine these two equations: 7 | 25

26. Quantum Model of Hydrogen Atom Light is absorbed by an atom when the electron transition is from lower n to higher n (n f > n i ). In this case,  E will be positive. يمتص الضوء من الذرة عندما ينتقل الالكترون من المستوى الاقل الاعلى وتكون فرق الطاقة موجب. ويشع الضوء من الذرة عند الانتقال من المستوى الاعلى الى الاقل وتكون فرق الطاقة سالب. Light is emitted from an atom when the electron transition is from higher n to lower n (n f < n i ). In this case,  E will be negative. An electron is ejected when n f = ∞. 7 | 26

27. Quantum Model of Hydrogen Atom Energy-level diagram for the hydrogen atom. 7 | 27

28. Quantum Model of Hydrogen Atom Electron transitions for an electron in the hydrogen atom. 7 | 28

29. Example 5 7 | 29 What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from n = 6 to n = 3? n i = 6 n f = 3 R H = 2.179 × 10 -18 J = -1.816 x 10 -19 J 1.094 × 10 -6 m

30. Example 6 7 | 30

31. Line Spectra 7 | 31 The red line corresponds to the smaller energy difference in going from n = 3 to n = 2. The blue line corresponds to the larger energy difference in going from n = 2 to n = 1. n = 1 n = 2 n = 3 A minimum of three energy levels are required.

32. Quantum Evidence 7 | 32 Planck Vibrating atoms have only certain energies: E = h or 2h or 3h Einstein Energy is quantized in particles called photons: E = h Bohr Electrons in atoms can have only certain values of energy. For hydrogen:

33. Matter Waves 7 | 33 Light has properties of both waves and particles (matter). اذا كان هناك خواص مزدوجة للضوء وهي الامواج والمادة What about matter? ما هي علاقة المادة

34. Matter Waves 7 | 34 In 1923, Louis de Broglie, a French physicist, reasoned that particles (matter) might also have wave properties. استنتج بروغلي بان لدى الجسيمات ايضا خواص الموجة، وقد اوجد علاقة ما بين طول الموجة وكتلة الجسيمات وسرعتها كما يلي : The wavelength of a particle of mass, m (kg), and velocity, v (m/s), is given by the de Broglie relation:

35. Example 7 7 | 35 Compare the wavelengths of (a) an electron traveling at a speed that is one- hundredth the speed of light and (b) a baseball of mass 0.145 kg having a speed of 26.8 m/s (60 mph). Electron m e = 9.11 × 10 -31 kg v = 3.00 × 10 6 m/s Baseball m = 0.145 kg v = 26.8 m/s

36. Example 7 (Cont) 7 | 36 Electron m e = 9.11 × 10 -31 kg v = 3.00 × 10 6 m/s Baseball m = 0.145 kg v = 26.8 m/s 2.43 × 10 -10 m 1.71 × 10 -34 m

37. Example 8 7 | 37

38. Example 8 (Cont) 7 | 38

39. Principal Quantum Number 7 | 39 Principal Quantum Number, n الرقم الكمي يعود الى مستوى الطاقة او المدار، وهو ما تعتمد عليه طاقة الالكترون في الذرة بشكل اساسي. مدار اصغر طاقة اقل كذلك n This quantum number, which refers to energy level or shell, is the one on which the energy of an electron in an atom primarily depends. The smaller the value of n, the lower the energy and the smaller the orbital. The principal quantum number can have any positive value: 1, 2, 3,... قيمة الرقم الكمي موجبة Orbitals with the same value for n are said to be in the same shell. المدارات بنفس القيمة لهم نفس المستوى

40. Energy Levels (Shells) 7 | 40 Shells are sometimes designated by uppercase letters: تعرف المدارات بحروف كبيرة وترتيب رقمي Letter n K1K1 L2L2 M3M3 N4N4...

41. What are Quantum Numbers? Quantum number are a set of four values that define the energy state of an electron in an atom. Quantum number values are designated as n, l, m and s (s is often written as m s ) n is called the principal quantum number and ranges from 1, 2, 3, etc. (also refers to the energy level or shell l represents the orbital type and depends on n. It ranges from 0 through n – 1. It often called the azimuthal quantum number m depends on l. It ranges from – l thru 0 to + l. It defines the orbital orientation in space and is call the magnetic quantum number. S is the spin number and is either + ½ or – ½

42. Orbital Shape شكل المدار 7 | 42 Angular Momentum Quantum Number, l الرقم الكمي الزاوي النشط Sometimes called the azimuthal quantum number, this quantum number distinguishes orbitals within a given n (shell) having different shapes. له العديد من الاشكال It can have values from 0, 1, 2, 3,... to a maximum of (n – 1). قيمته من صفر وحتى اخر رقم مدار ناقص واحد For a given n, there will be n different values of l, or n types of subshells. Orbitals with the same values for n and l are said to be in the same shell and subshell. المدارات التي تحمل نفس القيمة والرقم الكمي الزاوي تكون بنفس القشرة

43. Orbital Shape Subshells are sometimes designated by lowercase letters: 7 | 43 l ≤ Letter 0s0s 1p1p 2d2d 3f3f... Not every subshell type exists in every shell. The minimum value of n for each type of subshell is shown above. n =n =1234

44. Orbital types defined by the azimuthal quantum number l = 0 s type orbital l = 1 p type orbital l = 2 d type orbital One orientation Three orientations Five orientations l = 3 f type orbital Seven orientations (not shown)

45. Orbital Orientation 7 | 45 Magnetic Quantum Number, m l الرقم الكمي المغناطيسي This quantum number distinguishes orbitals of a given n and l —that is, of a given energy and shape but having different orientations. يميز المدار والمدار الزاوي عند طاقة وشكل محدد ولكن باتجاهات مختلفة The magnetic quantum number depends on the value of l and can have any integer value from – l to 0 to + l. Each different value represents a different orbital. For a given subshell, there will be (2 l + 1) values and therefore (2 l + 1) orbitals.

46. Quantum Number Summary 7 | 46 Let’s summarize: When n = 1, l has only one value, 0. When l = 0, m l has only one value, 0. So the first shell (n = 1) has one subshell, an s- subshell, 1s. That subshell, in turn, has one orbital.

47. Quantum Number Summary When n = 2, l has two values, 0 and 1. When l = 0, m l has only one value, 0. So there is a 2s subshell with one orbital. When l = 1, m l has only three values, -1, 0, 1. So there is a 2p subshell with three orbitals. 7 | 47

48. Quantum Number Summary When n = 3, l has three values, 0, 1, and 2. When l = 0, m l has only one value, 0. So there is a 3s subshell with one orbital. When l = 1, m l has only three values, -1, 0, 1. So there is a 3p subshell with three orbitals. When l = 2, m l has only five values, -2, -1, 0, 1, 2. So there is a 3d subshell with five orbitals. 7 | 48

49. Quantum Number Summary We could continue with n =4 and 5. Each would gain an additional subshell (f and g, respectively). In an f subshell, there are seven orbitals; in a g subshell, there are nine orbitals. Table 7.1 gives the complete list of permitted values for n, l, and m l up to the fourth shell. It is on the next slide. 7 | 49

50. Summary 7 | 50

51. Shells and Subshells in Hydrogen 7 | 51 The figure shows relative energies for the hydrogen atom shells and subshells; each orbital is indicated by a dashed-line.

52. Spin Quantum Number, m s This quantum number refers to the two possible orientations of the spin axis of an electron. It may have a value of either + 1 / 2 or - 1 / 2. 7 | 52

53. Which of the following are permissible sets of quantum numbers? n = 4, l = 4, m l = 0, m s = ½ n = 3, l = 2, m l = 1, m s = -½ n = 2, l = 0, m l = 0, m s = ³/ ² n = 5, l = 3, m l = -3, m s = ½ 7 | 53 (a) Not permitted. When n = 4, the maximum value of l is 3. (b) Permitted. (c) Not permitted; m s can only be +½ or –½. (b) Permitted.

54. Orbital Shapes 7 | 54 Atomic Orbital Shapes An s orbital is spherical. A p orbital has two lobes along a straight line through the nucleus, with one lobe on either side. A d orbital has a more complicated shape.

55. Orbital Sizes 7 | 55 The cross-sectional view of a 1s orbital and a 2s orbital highlights the difference in the two orbitals’ sizes.

56. Orbital Sizes The cutaway diagrams of the 1s and 2s orbitals give a better sense of them in three dimensions. 7 | 56

57. p-Orbital Shape 7 | 57 The next slide illustrates p orbitals. Figure A shows the general shape of a p orbital. Figure B shows the orientations of each of the three p orbitals.

58. p-Orbitals 7 | 58

59. d-Orbitals 7 | 59 The complexity of the d orbitals can be seen below