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Wave Nature of Light

Wave Nature of Light. Light travels through space as a wave. There are 2 primary characteristics of waves that interest us: Wavelength ( λ): the distance between two consecutive crests or troughs. most often in nm

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Wave Nature of Light

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  1. Wave Nature of Light • Light travels through space as a wave. • There are 2 primary characteristics of waves that interest us: • Wavelength (λ): the distance between two consecutive crests or troughs. • most often in nm • Frequency (v or f): the number of wave cycles that pass a given point in a unit of time (usually per second). Once cycle per second = 1 Hz. c = ν × λ c = the speed of light, 3.00 x 108 m/s λ = in meters ν = reciprocal seconds

  2. Wave Characteristics

  3. Example 6.1 • The red light associated with the aurora borealis is emitted by excited (high energy) oxygen atoms at 630.0 nm. What is the frequency of the light. • Ans: 4.759 x 1014 Hz

  4. Particle Nature of Light • Photons – a stream of particles that give off energy in the form of light. • E photon = hν = Δ E atom (1 mole) • Δ E = hν = hc/λ • h = planck’s constant, 6.626 x 10-34 J s • c = speed of light, 3.00 x 108 m/s

  5. Electromagnetic Spectrum

  6. Example 6.2 • Referring back to example 1 calculate: • The energy in joules, of a photon emitted by an excited oxygen atom. • Ans: 3.153 x 1019 J/mole • The energy, in kJ, in a mole of such photons. • Ans: 1.899 x 102 kJ/photons

  7. Atomic Spectra • Atomic spectra give discrete lines given off at specific wavelengths. • The fact that photons making up atomic spectra have only certain discrete wavelengths implies that they can have only certain discrete energies because these photons are produced when an electron moves from one energy level to the next. These series appear in different regions of the electromagnetic spectrum.

  8. Line Emission Spectra

  9. Bohr Model of the Hydrogen Atom • There are three points to be made with the Bohr Model: • Bohr designated zero energy as the point at which the proton and electron are completely separated. • Ordinarily the hydrogen electron is in its lowest energy state, referred to as the ground state (n=1). When an electron absorbs enough energy, it moves to a higher, excited state. For hydrogen, the first excited state is n=2, then n=3. • When an excited electron drops back to its lower energy state it gives off energy as a photon of light.

  10. The Rydberg Equation • Bohr derived the following equation in applying his model to the hydrogen atom: v = RH[ 1 – 1__] h (nlo)2 (nhi)2 • RH = Rydberg’s constant = 2.18 x 10-18 J • Balmer series: when an electron jumps down to n=2 from n=3,4,5….. • Lyman series: when an electron jumps down to n=1 from n=2,3,4,….

  11. Example 6.3 • Calculate the wavelength, in nm, fo the line in the Balmer series that results from the transition when the electron is in n=4. • Ans: 486.0 nm

  12. Problem……... • Bohr’s model was flawed. We cannot assume that electrons move about in specified orbitals. • DeBroglie purposed that if light can behave as particles (photons) then electrons can act as waves (wave-particle duality). • This led to wave mechanics and the quantum mechanical model of the atom. This differs from the Bohr model, mainly, in that: • The kinetic energy of an electron is inversely related to the volume of the region to which it is confined. • It is impossible to specify the precise position of an electron in an atom at a given instant.

  13. DeBroglie Table of Wavelengths

  14. Electron Configuration • Energy Levels (1-7): looking at the periodic table you can tell how many energy levels an atom has by looking at the period the electron is in. • Sublevels (s,p,d,f): looking at the periodic table you can tell sublevels based on the 4 blocks the periodic table is broken up into. • Orbitals (3-D orientations): • s_, p _ _ _, d _ _ _ _ _, f _ _ _ _ _ _ _

  15. Examples of Electron Configuration

  16. Orbital Occupancy for first 10 elements.

  17. Some rules to follow when predicting electron configuration: Start at lowest energy level possible (hydrogen). Follow atomic numbers when filling. Use arrows to represent electrons – up arrows fill first. Predicting Electron Configuration

  18. Rules to know by name…. • Pauli Exclusion Principle: • no 2 electrons in an atom may have the same set of quantum numbers. • Hund’s Rule: • When several orbitals of equal energy are available, as in a given sublevel, electrons enter singly with parallel spins (up arrows first). • Aufbau Principle: • The principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons. As they are added, they assume their most stable conditions with respect to the nucleus and those electrons already there (lowest energy level first).

  19. Electron Arrangement in Ions • Transition metal cations to the right of the scandium group do not form ions with noble-gas configurations (like most main group elements), they would have to lose four or more electrons to do so. In transition metals the outer s-electrons are usually lost first to form positive ions. For example: Mn: Mn+2: • In ions like Fe, electrons will be lost from 4s first then the 3d. This is usually referred to as the “first in, first out” rule.

  20. Example of Fe3+ Ion

  21. Electron energy levels in order of increasing energy (pg 142).

  22. Example 6.6 – 6.9 • Find the electron configuration of iodine, sulfur, iron, copper*, and chromium*. • Find the electron configuration for Fe2+ and Br1- • Show the configuration • Write the abbreviated notation

  23. Magnetism • Paramagnetic: If there are unpaired electrons present the solid will be attracted into the field • Diamagnetic: If the atoms in the solid contain only paired electrons it is slightly repelled by the field.

  24. Quantum Numbers • The principal quantum number: • Symbolized by n, basically the energy level the electron is in. • The orbital quantum number: • Symbolized by l, basically represents the sublevel the electron is in s,p,d, or f. values for l: s = 0, p: l = 1, d: l = 2, f: l = 3 *The letters s,p,d, and f come from the adjectives used to describe spectral lines: sharp, principal, diffuse, fundamental. • The magnetic quantum number: • Symbolized by m l, this determines the direction in space of the electron cloud surrounding the nucleus. • All of the orbitals in a sublevel have the same energy s __ p __ __ __ d __ __ __ __ __ f __ __ __ __ __ __ __ • The spin quantum number: • Symbolized by ms, this represents the electron spin. • ms can equal +1/2 (up arrow) or -1/2 (down arrow)

  25. Examples • Give the quantum numbers for the outermost electron in neon, copper, and barium.

  26. Example 6.4 & 6.5 • Consider the following set of quantum numbers, which ones could not occur: • (a) 3,1,0,1/2 • (b) 1,1,0,-1/2 • (c) 2,0,0, ½ • (d) 4,3,2,1/2 • (e) 2,1,0,0

  27. Periodic Trends • The Periodic Law: The chemical and physical properties of elements are a periodic function of atomic number. • Specific trends occur because of this: • Atomic Radius • Ion Radius • Ionization Energy • Electronegativity

  28. Atomic Radius: • One half the distance of closest approach between atoms in an elemental substance. Basically from the center of the nucleus of an atom to its outermost electrons. • Decreases across a period from left to right on the periodic table • Increases down a group on the periodic table

  29. Ionic Radius: • Positive ions are smaller than the metal atoms from which they are formed • Negative ions are larger than the nonmetal atoms from which they are formed

  30. Ionization Energy: • The energy required to remove an electron from its outermost shell. • There can be a first, second, third, and so on ionization energy. For example, in Magnesium +2 there is a large jump in ionization energy from the 2nd to 3rd ionization energies. Why? • Increases across the periodic table from left to right • Decreases down the periodic table * Noble gases generally have the highest ionization energies except when compared to fluorine. There are several exceptions to the trend (reference the textbook table of IE’s).

  31. Ionization Energies for Be

  32. Electron Affinity & Electronegativity: • Electron Affinity is the actual energy change associated with the gaining of an electron. • Electronegativity is he ability to attract an electron. • Increases across the periodic table from left to right – fluorine is the most electronegative element. • Decreases down the periodic table *There are a few exceptions to this trend you must know them. * Noble gases essentially (Kr and Xe are an exception) have no electronegativities.

  33. MC #1 Use these answers for questions 1 - 3. (A) O(B) La(C) Rb(D) Mg(E) N 1. What is the most electronegative element of the above? 2. Which element exhibits the greatest number of different oxidation states? 3. Which of the elements above has the smallest ionic radius for its most commonly found ion?

  34. MC #2 Use these answers for questions 1-4: (A) Heisenberg uncertainty principle(B) Pauli exclusion principle(C) Hund's rule (principle of maximum multiplicity)(D) Shielding effect(E) Wave nature of matter 1. Can be used to predict that a gaseous carbon atom in its ground state is paramagnetic 2. Explains the experimental phenomenon of electron diffraction 3. Indicates that an atomic orbital can hold no more than two electrons 4. Predicts that it is impossible to determine simultaneously the exact position and the exact velocity of an electron

  35. MC #3 1s22s22p63s23p3 Atoms of an element, X, have the electronic configuration shown above. The compound most likely formed with magnesium, Mg, is: (A) MgX(B) Mg2X(C) MgX2(D) MgX3(E) Mg3X2

  36. MC #4 • Which of the following represents the ground state electron configuration for the Mn3+ ion? (Atomic number Mn = 25) (A) 1s2 2s2 2p6 3s2 3p6 3d4(B) 1s2 2s2 2p6 3s2 3p6 3d5 4s2(C) 1s2 2s2 2p6 3s2 3p6 3d2 4s2(D) 1s2 2s2 2p6 3s2 3p6 3d8 4s2(E) 1s2 2s2 2p6 3s2 3p6 3d3 4s1

  37. MC #5 • One of the outermost electrons in a strontium atom in the ground state can be described by which of the following sets of four quantum numbers? (A) 5, 2, 0, 1/2(B) 5, 1, 1, 1/2(C) 5, 1, 0, 1/2(D) 5, 0, 1, 1/2(E) 5, 0, 0, 1/2

  38. MC #6 • The elements in which of the following have most nearly the same atomic radius? (A) Be, B, C, N(B) Ne, Ar, Kr, Xe(C) Mg, Ca, Sr, Ba(D) C, P, Se, I(E) Cr, Mn, Fe, Co

  39. MC #7 Ca, V, Co, Zn, As Gaseous atoms of which of the elements above are paramagnetic? (A) Ca and As only(B) Zn and As only(C) Ca, V, and Co only(D) V, Co, and As only(E) V, Co, and Zn only

  40. FRQ #1 • (a) A major line in the emission spectrum of neon corresponds to a frequency of 4.341014 s-1. Calculate the wavelength, in nanometers, of light that corresponds to this line. • (b) In the upper atmosphere, ozone molecules decompose as they absorb ultraviolet (UV) radiation, as shown by the equation below. Ozone serves to block harmful ultraviolet radiation that comes from the Sun. O3 (g) O2 (g) + O (g) A molecule of O3 (g)absorbs a photon with a frequency of 1.001015 s-1. (i) How much energy, in joules, does the O3(g) molecule absorb per photon? (ii) The minimum energy needed to break an oxygen-oxygen bond in ozone is 387 kJ mol-1. Does a photon with a frequency of 1.001015 s-1 have enough energy to break this bond? Support your answer with a calculation.

  41. FRQ #2 • Discuss some differences in physical and chemical properties of metals and nonmetals. What characteristic of the electronic configurations of atoms distinguishes metals from nonmetals? On the basis of this characteristic, explain why there are many more metals than nonmetals.

  42. FRQ #3 Use the details of modern atomic theory to explain each of the following experimental observations. • (a) Within a family such as the alkali metals, the ionic radius increases as the atomic number increases. • (b) The radius of the chlorine atom is smaller than the radius of the chloride ion, Cl-. (Radii : Cl atom = 0.99Å; Cl- ion = 1.81 Å) • (c) The first ionization energy of aluminum is lower than the first ionization energy of magnesium. (First ionization energies: 12Mg = 7.6 ev; 13Al = 6.0 ev) • (d) For magnesium, the difference between the second and third ionization energies is much larger than the difference between the first and second ionization energies. (Ionization energies for Mg: 1st = 7.6 ev; 2nd = 14 ev; 3rd = 80 ev)

  43. FRQ #4 The elements are numbered randomly. Use the information in the table to answer the following questions. • (a) Which element is most metallic in character? Explain your reasoning. • (b) Identify element 3. Explain your reasoning. • (c) Write the complete electron configuration for an atom of element 3. • (d) What is the expected oxidation state for the most common ion of element 2? • (e) What is the chemical symbol for element 2? • (f) A neutral atom of which of the four elements has the smallest radius?

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