CHEMISTRY - TRO 4E CH.7 - THE QUANTUM-MECHANICAL MODEL OF THE ATOM

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2 CONCEPT: THE NATURE OF LIGHT Visible light represents a small portion of the continuum of radiant energy known as. The visible light spectrum ranges from to. Its wave properties of electromagnetic radiation are described by two independent variables: (ν, Greek mu) is the number of waves you have per second and is expressed in units of or. (λ, Greek lambda) is the distance from one crest of a wave to the other and is expressed in units of. Relationship between frequency & wavelength Page 2

3 PRACTICE: THE NATURE OF LIGHT A. Based on the images of different electromagnetic waves, answer each of the following questions. I. II. III. a) Which electromagnetic wave has the longest wavelength? b) Which electromagnetic wave has the greatest energy? c) Which electromagnetic wave has the lowest frequency? d) Which electromagnetic wave has the largest amplitude? Page 3

4 CONCEPT: INTERCONVERSION OF LIGHT UNITS The speed of a wave, is the product of ν and λ. In a vacuum, all forms of electromagnetic radiation travel at 3.00 x 10 8, which is a physical constant called the (c). c = ν λ EXAMPLE: Even the music we listen to deals with how energy travels to get to our car radio. If Power 96 broadcasts its music at 96.5 MHz (megahertz, or 10 6 Hertz) find the wavelength in μm and A o of the radio waves. PRACTICE: Calculate the frequency of the red light emitted by a neon sign with a wavelength of nm. Page 4

5 CONCEPT: ENERGY AND MATTER Light travels at different speeds as it passes through different media in a phenomenon known as. Light passing through the opening of a slit creates a semicircular wave in a phenomenon known as. If the light wave passes through two adjacent slits then the semicircular waves can interact with one another. inteference amplitude. inteference amplitude. Page 5

6 CONCEPT: THE PARTICLE NATURE OF LIGHT The physicists Max Planck and Albert Einstein theorized that light was made of small packets of electromagnetic energy. Each packet of energy referred to as a. The energy could be expressed with the following equation: E = hv constant is represented by the variable of h and is equal to x J s. EXAMPLE: After a night out last Halloween dressed up as Charlie Sheen I came home and microwaved some day old pizza. If the microwave I used emitted a wavelength of 3.25 cm, answer the following questions. a) What is the energy of one photon of this microwave radiation? b) What is the energy of one mole of this photon? PRACTICE: Rank the following in terms of decreasing energy: Gamma energy, visible light 1 ( E = 4.39 x J), microwave and visible light 2 (λ = 595 nm). Page 6

7 CONCEPT: THE PHOTOELECTRIC EFFECT Albert Einstein theorized that light was quantized into small packets or bundles of energy. A single particle of this quantized packet of electromagnetic energy was later named a. According to the Photoelectric effect, when photons with enough energy hit the surface of a metal electrons are emitted. Energy is directly proportional to rather than its. The Photoelectric Effect only happens with photons over a certain frequency. EXAMPLE: Illustrate what happens when a photon of sufficient energy strike the surface of a metal. Real-life Application: Page 7

8 CONCEPT: THE WAVE NATURE OF LIGHT Up to this point we have discussed light as packets or particles of energy that travel through a given space, now we will look at light as it travels as a uniform wave through a given space. According to the equation matter behaves as though it moves in a wave. To calculate the wavelength of matter we simply use the following equation: λ = λ = h mν h = m = ν = EXAMPLE: Find the wavelength (in nm) of a proton with a speed of 7.33 x (Mass of an proton = 1.67 x kg) PRACTICE: What is the speed of an electron that has a wavelength of 895 μm? (Mass of a electron = 9.11 x kg) Page 8

9 CONCEPT: HEISENBERG S UNCERTAINTY PRINCIPLE The nature of an electron is both unique and difficult to understand because it can behave as both a(n) and a(n). The of an electron is related to its wave nature, while its is related to its particle nature. Weiner Heisenberg introduced the term of to describe how an electron could be observed as either a particle or wave, but not both. By extension we also couldn t know both the or of an electron. To illustrated this dual nature of an electron Heisenberg created his Uncertainty or Indeterminacy Principle and its associated formula: Δx Δp h 4π h = Δx = Δp = EXAMPLE: An electron has an uncertainty in its position of 630 pm. What is the uncertainty in its velocity? Page 9

10 CONCEPT: THE ATOMIC MODEL An atom is composed of subatomic particles. In the center of an atom there is the. It contains the subatomic particles: and. Spinning around it we find the third subatomic particle: the. PROTONS are charged subatomic particles. ELECTRONS are charged subatomic particles. NEUTRONS are charged subatomic particles.! Model helped to explain what happened when an electron absorbed or released energy within a hydrogen atom. After the hydrogen electron absorbed sufficient energy and becomes it would jump to a higher energy level. Eventually it would return to its and release the energy it absorbed as heat or light. Page 10

11 PRACTICE: THE ATOMIC MODEL EXAMPLE: Calculate the energy of the 4 th electron found in the n = 2 state of the boron atom in kilojoules per mole. PRACTICE 1: Which of the following transitions (in a hydrogen atom) represents emission of the longest wavelength? a) n = 4 to n = 2 b) n = 3 to n= 4 c) n = 1 to n = 2 d) n = 6 to n = 5 e) n = 2 to n = 5 PRACTICE 2: Which of the following transitions represents absorption of a photon with the largest energy? a) n = 3 to n = 1 b) n = 2 to n = 4 c) n = 1 to n = 2 d) n = 6 to n = 3 e) n = 1 to n = 4 Page 11

12 CONCEPT: ATOMIC EMISSION When an electron absorbs enough energy it goes from a numbered shell to a numbered shell. The electron eventually releases or emits the energy it took in and goes from a numbered shell to a numbered shell. If the electron goes from a higher numbered shell to the 1 st shell it is referred to as a Series. 1 If the electron goes from a higher numbered shell to the 2 nd shell it is referred to as a Series. 2 If the electron goes from a higher numbered shell to the 3 rd shell it is referred to as a Series. 3 Page 12

13 PRACTICE: ATOMIC EMISSION EXAMPLE: What is the wavelength of a photon (in nanometers) emitted during a transition from n = 4 to n = 2 state in the hydrogen atom? PRACTICE: Classify each of the following transitions as either a Lyman, Balmer or Paschen series. a) n = 3 to n = 1 b) n = 6 to n = 1 c) n = 3 to n = 2 d) n = 6 to n = 3 e) n = 4 to n = 2 Page 13

14 CONCEPT: QUANTUM MECHANICAL PICTURE OF THE ATOM The main atomic sub-levels are the s, p, d and f. Each atomic sub-level has a set number of atomic or electron orbitals. Each electron orbital can hold up electrons. The s sub-level contains one electron orbital The p sub-level contains three electron orbitals The d sub-level contains five electron orbitals The f sub-level contains seven electron orbitals Page 14

15 CONCEPT: QUANTUM NUMBERS OF AN ATOMIC MODEL An atomic orbital is characterized by three quantum numbers. The quantum number deals with the atomic orbital s size and energy. It tells us the relative distance of the electron from the nucleus. It uses the variable and provides the shell number of the electron. EXAMPLE: Calculate the principal quantum number of each atomic sublevel. a. 7p b. 5s c. 3d d. 4f The electron capacity of each shell can be determined by using the formula:. Electron Shell (n) Maximum Number of Electrons The quantum number deals with the shape of the atomic orbital. Each atomic orbital has a specific shape. It uses the variable and formula. Each atomic sub-level has an L value associated with it. Sublevel s p d f g L value The quantum number deals with the orientation of the orbital in the space around the nucleus. It is a range of the previous quantum number: -l to +l. It uses the variable. Sublevel s p d f L value ML value! Page 15

16 PRACTICE: QUANTUM NUMBERS OF AN ATOMIC MODEL EXAMPLE 1: What l or ml values are allowed if n = 2? How many orbitals exist for n = 2? EXAMPLE 2: How many electrons can have the following quantum sets? a) n = 4 b) n = 3, l = 1 c) n = 4, ml = -2 d) n = 5, l = 2, ml = -2 PRACTICE 1: Provide the n, l and ml value for each of the given orbitals. a. 6p n = l = ml = b. 4d n = l = ml = c. 5f n = l = ml = PRACTICE 2: State all the l and mlvalues possible if the principle quantum number is equal to 3.! Page 16

17 CONCEPT: THE FOURTH QUANTUM NUMBER An electron in an atom is described completely by a set of four quantum numbers. The first three describe its and the fourth describes its. The quantum number (ms) helps to discuss the rotational spin of the electron and has values of either and.!! According to the : no two electrons in the same atom can have the same four quantum numbers. EXAMPLE: State the electron configuration of boron and list the four quantum numbers of the 1 st and the 5 th electron. Page 17

18 CONCEPT: ATOMIC ORBITAL SHAPE The quantum number deals with the shape of the atomic orbital. Each atomic orbital has a specific shape. It uses the variable and formula. Each atomic sub-level has an L value associated with it. Sublevel s p d f g L value EXAMPLE: Based on the following atomic orbital shape, which of the following set of quantum numbers is correct: a) n = 8, l = 1, ml = 1 2 b) n = 8, l = 2, ml = -2 c) n = 8, l = 0, ml = 1 d) n = 8, l = 0, ml = 0 PRACTICE: Based on the following atomic orbital shape, which of the following set of quantum numbers is correct: a) n = 2, l = 1, ml = +1, ms = - 1 b) n = 4, l = 1, ml = - 2, ms = c) n = 3, l = 1, ml = - 1, ms = 0 d) n = 2, l = 1, ml = + 1, ms = 1 2 Page 18

19 8. Which of the following transitions (in a hydrogen atom) represent emission of the smallest or shortest wavelength? a. n = 4 to n = 2 b. n = 3 to n= 4 c. n = 1 to n = 2 d. n = 7 to n = 5 e. n = 2 to n = 5 Page 19

20 9. Which of the following transitions represent absorption of a photon with the highest frequency? a. n = 3 to n = 1 b. n = 2 to n = 4 c. n = 1 to n =2 d. n = 6 to n = 3 e. n = 1 to n = 3 Page 20

21 10. Provide the n, l and ml value for each of the given orbitals. a) 7s n = b) 5d n = l = l = ml = ml = c) 2p n = d) 4f n = l = l = ml = ml = Page 21

22 11. Which statement about the four quantum numbers is false? a. n = principal quantum number, n = 1 to b. l = azimuthal quantum number, l = 0,1,2,..., (n+1) c. ml = magnetic quantum number, ml = (-l),...,0,..., (+l) d. ms = spin quantum number, ms = or 1 2 e. The first three quantum numbers deal with the atomic orbitals except for the ms quantum number, which deals with the electrons in the atomic orbitals. Page 22

23 12. Each of the following sets of quantum numbers gives information on a specific orbital. Find the error in each. a. n = 4, l = 0, ml = 1, ms = 1 2 b. n = 5, l = 2, ml = - 1, ms = 1 c. n = 7, l = 7, ml = - 5, ms = 1 2 d. n = 0, l = 5, ml = - 3, ms = 1 2 Page 23

24 14. How many electrons can have the following quantum sets? a) n = 4, ml = -1 b) n = 5, ml = 0, ms = 1 2 c) n = 9, l = 4, ms = 1 2 d) n = 2, ms = 1 2 Page 24

25 19. For n = 2, what are the possible sublevels? a) 0 b) 0, 1 c) 0, 1, 2 d) 0, 1,2, 3 Page 25

26 16. Based on the following atomic orbital shape, which of the following set of quantum numbers is correct: a) n = 2, l = 1, ml = 0 b) n = 3, l = 2, ml = 1 c) n = 4, l = 0, ml = +1 d) n = 1, l = 1, ml = 0 Page 26

27 17. Based on the following atomic orbital shape, which of the following set of quantum numbers is correct: a) n = 3, l = 2, ml = 0, ms = 1 2 b) n = 3, l = 1, ml = - 3, ms = 1 c) n = 4, l = 0, ml = 0, ms = 1 2 d) n = 4, l = 2, ml = - 3, ms = 1 2 Page 27

28 18. Based on the following atomic orbital shape, which of the following set of quantum numbers is correct: a) n = 3, l = 3, ml = 0, ms = 1 2 b) n = 1, l = 3, ml = -3, ms = 1 c) n = 7, l = 3, ml = - 4, ms = 1 2 d) n = 6, l = 3, ml = -3, ms = 1 2 Page 28

29 25. Give the electron configuration for the following element and its ion. For the ion, state if it is paramagnetic or diamagnetic: a. Ag Ag + Page 29

30 26. Give the electron configuration for the following element and its ion. For the ion, state if it is paramagnetic or diamagnetic: a. Cl Cl + Page 30

31 27. Which of the following represents an excited state? a) Cl: 1s 2 2s 2 2p 6 3s 2 3p 5 b) Be: 1s 2 2s 2 c) Na: 1s 2 2s 2-2p 6 3p 1 d) N: 1s 2 2s 2 2p 3 Page 31

32 28. Give the set of four quantum numbers that represent the indicated electron in the following element: a. Br (33 rd electron) n =, l =, ml =, ms = Page 32

33 29. Give the set of four quantum numbers that represent the indicated electron in the following element: a. Ca (19 th electron) n =, l =, ml =, ms = Page 33

34 30. Give the set of four quantum numbers that represent the indicated electron in the following element: a. Cu (27 th electron) n =, l =, ml =, ms = Page 34

35 31. Give the set of four quantum numbers that represent the indicated electron in the following element: a. Mo 3+ (38 th electron) n =, l =, ml =, ms = Page 35

36 32. For a multi-electron atom, arrange the electron subshells of the following listing in order of increasing energy: 6s, 4f, 2p, 5d. Page 36