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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
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
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 663.8 nm. Page 4
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
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 6.626 x 10-34 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 10-19 J), microwave and visible light 2 (λ = 595 nm). Page 6
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
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 10 9. (Mass of an proton = 1.67 x 10-27 kg) PRACTICE: What is the speed of an electron that has a wavelength of 895 μm? (Mass of a electron = 9.11 x 10-31 kg) Page 8
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
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
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
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
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
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
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 1 2 3 4 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 0 1 2 3 4 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 0 1 2 3 ML value! Page 15
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
CONCEPT: ELECTRON CONFIGURATIONS In this chapter we will focus on how an element s - the distribution of electrons within the orbitals of its atoms relates to its chemical and physical properties. History Lesson: In 1870, Dmitri Mendeleev arranged 65 elements into a. He summarized their behavior in the. When arranged by atomic mass, the elements exhibit a periodic recurrence of similar properties. The Electron Configuration According to the Principle you first have to totally fill in the lowest energy level before moving to the next. 1s 2s 2p 1s 2s$$$$$$2p 3s$$$$$$3p$$$$$$3d 4s$$$$$$4p$$$$$$4d$$$$$4f 5s$$$$$$5p$$$$$$5d$$$$$5f$$$$$5g 6s$$$$$$6p$$$$$$6d$$$$$6f$$$$$6g$$$$6h$ 7s$$$$$$7p$$$$$$7d$$$$$7f$$$$$7g$$$$7h F (9 electrons) 1s 2s 2p Hund s Rule states that electron orbitals that are are first half-filled before they are totally filled. Page 17
CONCEPT: CONDENSED ELECTRON CONFIGURATION EXAMPLE: Write the condensed configuration for each of the following elements: a. Co (27 electrons) b. Se (34 electrons) PRACTICE: Write the condensed configuration for each of the following elements: a. Ag (47 electrons) Page 18
CONCEPT: INNER CORE & VALENCE ELECTRONS EXAMPLE: How many core (inner) and valence electrons are present in each of the following elements? a. P b. Al c. Mn Page 19
CONCEPT: PARAMAGNETISM Vs. DIAMAGNETISM EXAMPLE: Write the condensed electron configuration of each ion and state if the ion is paramagnetic or diamagnetic. a. Ni 3+ b. S 2- PRACTICE: Write the condensed electron configuration of each ion and state if the ion is paramagnetic or diamagnetic. a. Cu + Page 20
CONCEPT: EFFECTIVE NUCLEAR CHARGE & SLATER S RULES When looking at any particular electron within an atom it experiences two major forces. A(n) force from the nucleus and a(n) force from the surrounding electrons. Now the electron can become shielded from the full force of the nucleus because of the other surrounding electrons. Effective Nuclear Charge (Zeff) measures the force exerted onto an electron by the nucleus, and can be calculated using Slater s Rules. e - e - e - e - e - Z = Nuclear Charge e - e - Z eff = Z S S = Shielding Constant e - e - e - e - Guidelines for Determining S for an electron: 1. The atom s electronic configuration is grouped as follows, in terms of increasing n and l quantum numbers: (1s) (2s,2p) (3s,3p) (3d) (4s,4p) (4d) (4f) (5s,5p) (5d) etc. 2. Electrons in groups to the right of a given electron do not shield electrons to the left. 3. The shielding constant S for electrons in certain groups. For ns and np valence electrons: a) Each electron in the same group will contribute to the S value. A 1s electron contributes to the S value for another 1s electron. b) Each electron in n 1 group contributes to the S value. c) Each electron in n 2 group or greater contributes to the S value. For nd and nf valence electrons: a) Each electron in the same group will contribute to the S value. b) Each electron in groups to the left will contribute to the S value. EXAMPLE: Using Slater s Rules calculate the effective nuclear charge of a 3p electron in argon. Page 21
PRACTICE: EFFECTIVE NUCLEAR CHARGE & SLATER S RULES 1 EXAMPLE 1: Using Slater s Rules calculate the effective nuclear charge of the 4s electron in potassium. EXAMPLE 2: Using Slater s Rules calculate the effective nuclear charge of a 3d electron in bromine. Page 22
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 23
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 0 1 2 3 4 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 = + 1 2 c) n = 3, l = 1, ml = - 1, ms = 0 d) n = 2, l = 1, ml = + 1, ms = 1 2 Page 24
CONCEPT: TRENDS IN ATOMIC RADIUS Atomic radius is defined as half the distance between the nuclei in a molecule of two identical elements. Generally, it going from left to right across a period and going down a group. ATOMIC RADIUS EXAMPLE: If the sum of the atomic radii of diatomic carbon is 154 pm and of diatomic chlorine is 198 pm, what is the sum of the atomic radii between a carbon and a chlorine atom. PRACTICE: Which one of the following atoms has the largest atomic radius? A) K B) Rb C) Y D) Ca E) Sr Page 25
CONCEPT: TRENDS IN IONIC RADIUS Ionic Size estimates the size of an ion in an ionic compound. (POSITIVE IONS) tend to be smaller than their parent atoms. Lithium ( 3 Electrons) 1s 2s 1s 2s (NEGATIVE IONS) tend to be larger than their parent atoms. Fluorine ( 9 Electrons) 1s 2s 2p 1s 2s 2p The pattern for ionic size correlates with the following trend when comparing ions with the same number of electrons: -3 > -2 > -1 > 0 > +1 > +2 > +3 EXAMPLE: Rank each set of ions in order of increasing ionic size. a) K +, Ca 2+, Ar b) Sr 2+, Na +, I c) V 5+, S 2-, Cl Page 26
CONCEPT: TRENDS IN IONIZATION ENERGY Metals tend to lose electrons to become positive ions called. IONIZATION ENERGY Therefore they have ionization energies. Nonmetals tend to gain electrons to become negative ions called. Therefore they have ionization energies. Ionization energy (IE) is the energy (in kj) required to remove an electron from a gaseous atom or ion. Generally, it going from left to right of a period and going down a group. Exceptions: Atom (g) ion + (g) + e E = IE1 > 0 When in the same period, Group elements have lower ionization energy than elements in Group. O 1s 2s 2p 1s 2s 2p N 1s 2s 2p 1s 2s 2p When in the same period, Group elements have lower ionization energy than elements in Group. B 1s 2s 2p 1s 2s 2p Be 1s 2s 1s 2s Page 27
PRACTICE: TRENDS IN IONIZATION ENERGY EXAMPLE: Of the following atoms, which has the smallest second ionization energy? a. Al b. Li c. Rb d. Mg e. Be PRACTICE 1: Of the following atoms, which has the smallest third ionization energy? a. Al b. Ca c. K d. Ga e. Cs PRACTICE 2: Which of the following statements is/are true? a. Sulfur has a larger IE1 than phosphorus b. Boron has a lower IE1 than Magnesium c. Magnesium has a higher IE1 than Aluminum PRACTICE 3: Shown below are the numerical values for ionization energies (IE s). Match the numerical values with each of the following elements provided in the boxes. Na Mg Al Si P S Cl Ar Numbers: 496, 578, 738, 786, 1000, 1012, 1251 & 1521. Page 28
CONCEPT: TRENDS IN ELECTRON AFFINITY Electron Affinity (EA) is the energy change (in kj) from the addition of 1 mole of e to 1 mol of gaseous atoms or ions. Generally, it going from left to right across a period and going down a group. Atom (g) + e ion (g) E = - EA1 ELECTRON AFFINITY EXAMPLE: Rank the following elements in order of increasing electron affinity. a. Cs, Hg, F, S b. Se, S, Si PRACTICE: Shown below are the numerical values for electron affinities (EA s). Match the numerical values with each of the following elements provided in the boxes. Li Be B C N O F Ne Numbers: - 328, -141, -122, -60, -27, > 0, > 0, > 0. Page 29
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 30
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 31
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 32
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 = + 1 2 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 33
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 34
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 35
19. For n = 2, what are the possible sublevels? a) 0 b) 0, 1 c) 0, 1, 2 d) 0, 1,2, 3 Page 36
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 37
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 38
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 39
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 40
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 41
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 42
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 43
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 44
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 45
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 46
32. For a multi-electron atom, arrange the electron subshells of the following listing in order of increasing energy: 6s, 4f, 2p, 5d. Page 47