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# CHAPTER 7 Atomic Structure

CHAPTER 7 Atomic Structure. Road Map Test 2 Extra credit Collection. Equations. speed of light = wavelength x frequency c = λ X  = 3.00 x 10 8 m/s E = nh  = nh(c/) n= positive integer Planck’s constant(h) = 6.626 x 10 –34 J s

## CHAPTER 7 Atomic Structure

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1. CHAPTER 7 Atomic Structure Road Map Test 2 Extra credit Collection Chem 105 Chpt 7 Lsn 21

2. Equations • speed of light = wavelength x frequency c = λ X  = 3.00 x 108 m/s • E = nh = nh(c/) n= positive integer Planck’s constant(h) = 6.626 x 10–34 J s • Eatom = Eemitted (or absorbed) radiation = nh • Rydberg equation = R • n2 > n1 • R = 1.096776 x 107 m-1 • ΔE = Efinal – Einitial = –2.18 x 10–18 J • Ephoton = Estate A – Estate B = hν Chem 105 Chpt 7 Lsn 21

3. Old Dead Dudes • Planck – blackbody radiation; hot glowing object; emit or absorb certain discrete quanta of energy • Bohr – one electron model; spectral lines explained; e- motion restricted to fixed orbits • Einstein – explained photoelectric effect - flow of current when monochromatic light of sufficient energy hits an object • Rydberg – predicted energy levels Chem 105 Chpt 7 Lsn 21

4. Practice Problem 21-1 • The frequency of electromagnetic radiation of wavelength 5.6 mm is A) 5.4 x 107 Hz B) 1.9 x 10-11 Hz C) 5.4 x 1010 Hz D) 1.1 x 108 Hz E) none of the above Chem 105 Chpt 7 Lsn 21

5. Practice Problem 21-1 Answer • The frequency of electromagnetic radiation of wavelength 5.6 mm is A) 5.4 x 107 Hz B) 1.9 x 10-11 Hz C) 5.4 x 1010 Hz D) 1.1 x 108 Hz E) none of the above Chem 105 Chpt 7 Lsn 21

6. Practice Problem 21-2 (7.12) Answer • 7.12 540 nm (10-9m/1nm)= 5.4  10–7 m E = = = = 3.7  10–19 J/photon This radiation does not have enough energy(6.7 x 10-19 J/atom) to activate the switch. This is also true for radiation with wavelengths greater than 540 nm. Chem 105 Chpt 7 Lsn 21

7. Bohr Model Energy of atoms quantized; photon emitted when e- decreases in orbit • Spectral line from emission Emission - higher to lower energy state Absorption – lower to higher energy state n = quantum number • Lower n: smaller radius of orbit (space e- circling in) • Ground state: n=1 • Excited state: n>1 Quantum staircase Chem 105 Chpt 7 Lsn 21

8. 7.20 Which of these electron transitions correspond to absorption of energy and which to emission? • n = 2 to n = 4 • n = 3 to n = 1 • n = 5 to n = 2 • n = 3 to n = 4 Absorption Emission Emission Absorbtion Chem 105 Chpt 7 Lsn 21

9. The Bohr explanation of the three series of spectral lines. n=2 visible n=3 infrared n=1 ultraviolet Numerous atoms with different excitation states (n) and subsequent  of emission Chem 105 Chpt 7 Lsn 21

10. Practice Problem 21.3 • How much energy is absorbed when an electron is excited from the first level to the fourth? Chem 105 Chpt 7 Lsn 21

11. Practice Problem 21.3 Answer • How much energy is absorbed when an electron is excited from the first level to the fourth? 2.04 x 10-18 J Chem 105 Chpt 7 Lsn 21

12. Practice Problem 21.4 • Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 3 to n = 1 energy level, based on the Bohr theory. A) 2.92 x 1015 s-1 B) 1.94 x 10-18 s-1 C) 3.21 x 1015 s-1 D) 3.05 x 10-15 s-1 E) Not enough information given to calculate answer. Chem 105 Chpt 7 Lsn 21

13. Practice Problem 21.4 Answer • Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 3 to n = 1 energy level, based on the Bohr theory. A) 2.92 x 1015 s-1B) 1.94 x 10-18 s-1 C) 3.21 x 1015 s-1 D) 3.05 x 10-15 s-1 E) Not enough information given to calculate answer. Chem 105 Chpt 7 Lsn 21

14. The Quantum-Mechanical Model of the Atom • Acceptance of the dual nature of matter and energy and of the uncertainty principle culminated in the field of quantum mechanics, which examines the wave motion of objects on the atomic scale. In 1926, Erwin Schrödinger derived an equation that is the basis for the quantum-mechanical model of the hydrogen atom. Chem 105 Chpt 7 Lsn 21

15. The Quantum-Mechanical Model of the Atom: The Atomic Orbital and the Probable Location of the Electron • Each solution to the equation is associated with a given wave function, also called an atomic orbital. It’s important to keep in mind that an “orbital” in the quantum-mechanical model bears no resemblance to an “orbit” in the Bohr model: an orbit was an electron’s path around the nucleus, whereas an orbital is a mathematical function with no direct physical meaning. Chem 105 Chpt 7 Lsn 21

16. Quantum Numbers and Atomic Orbitals • An atomic orbital is specified by three quantum numbers. n the principal quantum number; distance from nucleus (size); n = 1,2,3… l the angular momentum quantum number; shape; l =0 to n-1 ml the magnetic moment quantum number; orbital orientation; – ml =-l to +l . Chem 105 Chpt 7 Lsn 21

17. n = LEVELS Smaller n, the lower the energy level the greater the probability of the electron being closer to the nucleus • l = orbital shape • l = 0 s spherical • l = 1 p dumb bell & crash and burn, Fig 7.18 • l = 2 d cloverleaf, Fig 7.19 • l = 3 f too complicated Chem 105 Chpt 7 Lsn 21

18. The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital • Sublevel (subshell) : designate the orbital shape. Each sublevel has a letter designation: • ℓ = 0 is an s sublevel • ℓ = 1 is a psublevel. • ℓ = 2 is a d sublevel. • ℓ = 3 is an fsublevel. • Orbital. Each allowed combination of n, ℓ, and mℓ values specifies one of the atom’s orbitals. Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation. • The total number of orbitals for a given n value is n2. Smart People Don’t Fail Chem 105 Chpt 7 Lsn 21

19. The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals • Orbitals with Higher ℓ Values • Orbitals with ℓ = 3 are f orbitals and must have a principle quantum number of at least n = 4. There are seven f orbitals (2ℓ + 1 = 7), each with a complex, multi-lobed shape. Chem 105 Chpt 7 Lsn 21

20. The Quantum-Mechanical Model of the Atom: Energy Levels of the Hydrogen Atom • The energy state of the H atoms depends on the principal quantum number n only. Chem 105 Chpt 7 Lsn 21

21. Since matter is discontinuous and particulate perhaps energy is discontinuous and particulate. blackbody radiation Planck: Energy is quantized; only certain values allowed photoelectric effect Einstein: Light has particulate behavior (photons) atomic line spectra Bohr: Energy of atoms is quantized; photon emitted when electron changes orbit. CLASSICAL THEORY Matter particulate, massive Energy continuous, wavelike Summary of the major observations and theories leading from classical theory to quantum theory. Observation Theory Chem 105 Chpt 7 Lsn 21

22. PROBLEM: What values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals are allowed for n = 3? Practice Problem 21.5 Determining Quantum Numbers for an Energy Level PLAN: Follow the rules for allowable quantum numbers found in the text. l values can be integers from 0 to n-1; ml can be integers from -l through 0 to + l. SOLUTION: For n = 3, l = 0, 1, 2 For l = 0 ml = 0 For l = 1 ml = -1, 0, or +1 For l = 2 ml = -2, -1, 0, +1, or +2 There are 9 mlvalues and therefore 9 orbitals with n = 3. Chem 105 Chpt 7 Lsn 21

23. Practice Problem 21.6 Determining Sublevel Names and Orbital Quantum Numbers Give the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers: PROBLEM: (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 PLAN: Combine the n value and l designation to name the sublevel. Knowing l, we can find ml and the number of orbitals. SOLUTION: n l sublevel name possible ml values # of orbitals (a) 2 3d -2, -1, 0, 1, 2 3 5 (b) 2 0 2s 0 1 (c) 5 1 5p -1, 0, 1 3 (d) 4 3 4f -3, -2, -1, 0, 1, 2, 3 7 Chem 105 Chpt 7 Lsn 21

24. Practice Problem 21.7 What is wrong with this picture, or complete the name. n l ml name 1 1 0 1p 4 3 1 4d 3 2 -2 ? ? ? ? 2s 2 1 0 ? 3 1 -2 3p Chem 105 Chpt 7 Lsn 21

25. The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital • The energy states and orbitals of the atom are described with specific terms and associated with one or more quantum numbers. • Level (n). The atom’s energy levels, or shells, are given by the n value: the smaller the n value, the lower the energy level and the greater the probability of the electron being closer to the nucleus. Chem 105 Chpt 7 Lsn 21

26. The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital • Sublevel (ℓ). The atom’s levels contain sublevels, or subshells, which designate the orbital shape. Each sublevel has a letter designation: • ℓ = 0 is an s sublevel • ℓ = 1 is a p sublevel. • ℓ = 2 is a d sublevel. • ℓ = 3 is an f sublevel. Chem 105 Chpt 7 Lsn 21

27. The Quantum-Mechanical Model of the Atom: Quantum Numbers of an Atomic Orbital • Orbital (mℓ ). Each allowed combination of n, ℓ, and mℓ values specifies one of the atom’s orbitals. Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation. Chem 105 Chpt 7 Lsn 21

28. Practice Problem 21-8 • What value or values of mℓ are allowable for an orbital with ℓ = 2? A) 0 B) 2 C) -1 D) none of the above E) all of the above Chem 105 Chpt 7 Lsn 21

29. Practice Problem 21-8 Answer • What value or values of mℓ are allowable for an orbital with ℓ = 2? A) 0 B) 2 C) -1 D) none of the above E) all of the above Chem 105 Chpt 7 Lsn 21

30. The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals • The s Orbital • An orbital with ℓ = 0 has a spherical shape with the nucleus at its center and is called an s orbital. • The 2s orbital (Figure 7.17B) has two regions of higher electron density. Between the two regions is a spherical node, a shell-like region where the probability drops to zero. Chem 105 Chpt 7 Lsn 21

31. Practice Problem 21-9 • The nodes for a 3s atomic orbital are A) two points near the nucleus and another point at an infinite distance from the nucleus. B) three spherical solids. C) one plane and two spheres. D) two concentric circles. E) two concentric spheres. Chem 105 Chpt 7 Lsn 21

32. Practice Problem 21-9 Answer • The nodes for a 3s atomic orbital are A) two points near the nucleus and another point at an infinite distance from the nucleus. B) three spherical solids. C) one plane and two spheres. D) two concentric circles. E) two concentric spheres. Chem 105 Chpt 7 Lsn 21

33. The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals • The p Orbital • An orbital with ℓ = 1 has two regions (lobes) of high probability, one on either side of the nucleus, and is called a p orbital. In Figure 7.18, the nucleus lies at the nodal plane of this dumbbell-shaped orbital. Keep in mind that one p orbital consists of both lobes and that the electron spends equal time in both. Chem 105 Chpt 7 Lsn 21

34. The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals • The p Orbital • Since there are three mℓ values, these describe the three mutually perpendicular orientations in space. Unlike an s orbital, each p orbital does have a specific orientation in space. The ℓ = 1 value has three possible mℓ values: –1, 0, and +1, which refer to three mutually perpendicular p orbitals. They are identical in size, shape, and energy, differing only in orientation. Chem 105 Chpt 7 Lsn 21

35. The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals • The d Orbital • An orbital with ℓ = 2 is called a d orbital. There are five possible mℓ values for the ℓ = 2 value: –2, –1, 0, +1, +2. • Thus, a d orbital can have any one of five orientations, as shown in Figure 7.19. Chem 105 Chpt 7 Lsn 21

36. The Quantum-Mechanical Model of the Atom: Shapes of Atomic Orbitals • Orbitals with Higher ℓ Values • Orbitals with ℓ = 3 are f orbitals and must have a principle quantum number of at least n = 4. There are seven f orbitals (2ℓ + 1 = 7), each with a complex, multilobed shape; Figure 7.20 shows one of them. Chem 105 Chpt 7 Lsn 21

37. Practice Problem 21-10 • According to the quantum-mechanical model, how many orbitals in a given atom have n = 3? A) 4 B) 7 C) 9 D) 10 E) 18 Chem 105 Chpt 7 Lsn 21

38. Practice Problem 21-10Answer • According to the quantum-mechanical model, how many orbitals in a given atom have n = 3? A) 4 B) 7 C) 9 D) 10 E) 18 Chem 105 Chpt 7 Lsn 21

39. Next Lesson • Chapter 8 Chem 105 Chpt 7 Lsn 21

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