Electromagnetic spectrum

Transcription

1 All course materials, including lectures, class notes, quizzes, exams, handouts, presentations, and other materials provided to students for this course are protected intellectual property. As such, the unauthorized purchase or sale of these materials may result in disciplinary sanctions under the Campus Student Code. Electromagnetic spectrum The Wave Nature of Light c = λ ν c= speed of light in a vacuum = m/s λ = wavelength (λ, lambda), the length of one cycle units are meters ν = frequency (ν, nu), cycles per second units are s 1 (Hz= s 1 ) What is the wavelength (λ, in m) of a radio station operating at a frequency of 99.6 MHz? White light is composed of a wide swath of wavelengths We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 1 of 24

2 Puzzling discovery that elements had characteristic absorption spectra Explained by Quantum Theory Energy of a single photon (in J); h c E = hν = λ h is Planck s constant; h= J s ν = frequency (ν, nu), cycles per second in Hz (Hz= s 1 ) c= speed of light in a vacuum = m/s wavelength (λ, lambda), in meters A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20 cm. What is the energy of one photon of this microwave radiation? Concept Check Which of the following is not quantized? a. the charge on a monatomic ion b. the distance between two objects c. the population of your Chem 115 section We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 2 of 24

3 An atom changes its energy state by emitting or absorbing one (or more) quanta of energy Q This is made up crap! Do you have any evidence? A Yes, the photoelectric effect light striking a metal surface and producing an electric current (flow of electrons) If radiation is below threshold energy ( E between levels), no electrons are released explained by quantum theory If gap energy not reached, nothing happens This is true regardless of intensity (number of photons hitting per second) of radiation Only photons of sufficient energy (hν) dislodge e from metal surface Once gap energy reached photon is absorbed, and e- kicked out Postulates of The Bohr Model of the Hydrogen Atom The H atom has only certain energy levels, which Bohr called stationary states We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 3 of 24

4 The atom changes to another stationary state only by absorbing or emitting a photon energy of the photon (hν) must equals the energy difference between the two states Bohr Frequency Rule: E = energy of the photon = Rydberg equation, E = E > 0 for an absorption event E < 0 for an emission event 18 1 J 2 n final 1 2 n initial h c h ν = λ In a sample of hydrogen gas, electrons were excited to the forth energy level. How many different lines are possible in subsequent emission spectrum? n=4 n=3 excitation n=2 Energy n=1 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 4 of 24

5 A ground state hydrogen atom (n=1) absorbs a photon of UV light and its electron enters the n = 4 energy level. Calculate the energy involved in this transition (use 3 sig figs in your answer). Calculate the wavelength (in nm) of the photon (use 3 sig figs in your answer) Bohr s Triumphs: Bohr s Failures: Theory was not adequate to account for atomic spectra of species with more than one e Theory limited to only hydrogen the atom and ions such as Li + and Be 2+ After better spectrometers were built more transitions (spectral lines) discovered Bohr was unable to explain the origin of these lines Conclusion more energy states existed then predicted by Bohr s theory New theory was required one consistent with experimental data We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 5 of 24

6 The Wave-Particle Duality of Matter and Energy It s a strange small world The debroglie Wavelength h λ debroglie = m=mass in grams u= speed in m/s m u Wave motion in restricted systems Concept Check Which of the following occurs only in discrete (quantized) increments? a. the speed a car drives on the interstate b. the altitude that an airplane flies c. the rate at which a sink full of water drains d. the score in a soccer game We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 6 of 24

7 The de Broglie Wavelengths of Several Objects Classical objects (those you see everyday) Substance Mass (g) Speed (m/s) l (m) one-gram mass baseball associated wavelengths of everyday objects too small to be observable Substance Mass (g) Speed (m/s) l (m) fast electron that an electron has an associated wavelength is confirmed by x-ray diffraction analysis Find the debroglie wavelength of an electron with a speed of m/s (mass e = kg) h = J s = kg m 2 /s Heisenberg s Uncertainty Principle (It s a strange small world, revisited) Quantum mechanics allows us to predict the probabilities of where we can find an electron Heisenberg s uncertainty principle says that you cannot determine the position and momentum of an electron at the same time with absolute precision We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 7 of 24

8 Modern understanding of atomic theory / Orbital of an electron An orbital is specified by three quantum numbers; n, l and ml 1. Principal (n) 2. Azimuthal (l) 3. Magnetic (ml) 4. Spin (ms) Physical interpretation of quantum numbers The principal quantum number (n) is a positive integer The angular momentum quantum number (l) is an integer from 0 to (n -1) l notation orbital shape 0 s 1 p 2 d 3 f We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 8 of 24

9 The magnetic quantum number (ml) is an integer with values from l to + l The value of m l indicates the spatial orientation of the orbital n 4 Possible values of l subshell Possible values of ml # orbitals in subshell n l ml l ml l ml l ml s p d f We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 9 of 24

10 Question: How do we know that this is not just made up crap? Answer: It is made up crap, but it works. Image of hydrogen atom s electron orbital using quantum microscope Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure of Stark States, Phys. Rev. Lett. 110, Published 20 May 2013 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? Give the name and number of orbitals for each subshell with the following quantum numbers (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 10 of 24

11 What is wrong with each of the following quantum numbers designations and/or sublevel names? n=1, l= 1, ml = 0, name = 1p n=4, l= 3, ml = 1, name = 4d n=3, l= 1, ml = 2, name = 3p Concept Check Which combination of quantum numbers is possible for an atom with five orbitals in one subshell? a. n = 1, = 0 b. n = 2, = 4 c. n = 3, = 2 d. n = 4, = 4 Spin quantum number m s This experimental observation led to an associated designation of electron property called spin Table 8.1 Summary of Quantum Numbers of Electrons in Atoms Name Symbol Permitted Values Property principal n positive integers (1, 2, 3, ) orbital energy (size) angular momentum l integers from 0 to n1 orbital shape magnetic ml integers from - l to 0 to + l orbital orientation spin m s +½ or -½ direction of e - spin We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 11 of 24

12 Quantum Numbers and The Exclusion Principle Shell Pauli s exclusion principle states that no two electrons in the same atom can have the same four quantum numbers Sub shell or sublevel Splitting of Levels into Sublevels/ The Aufbau Diagram Electron Configurations and Orbital Diagrams We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 12 of 24

13 Aufbau Build-up Building Orbital Diagrams for multi electron atoms Hund s rule specifies that when orbitals of equal energy are available, the lowest energy electron configuration has the maximum number of unpaired electrons with parallel spins A partial orbital diagram shows only the highest energy sublevels being filled Write the Partial Orbital Diagrams and Electron Configurations for the Elements in Period 3 Z element Partial orbital diagram Full electron configuration Condensed e- config (3s and 3p subshells only) 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar A condensed electron configuration has the element symbol of the previous noble gas in square brackets Electron Configuration and Group We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 13 of 24

14 Condensed electron configurations in the first three periods. Partial Orbital Diagrams and Electron Configurations * for the Elements in Period 4. * Colored type indicates the sublevel to which the last electron is added. Orbital filling and the periodic table We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 14 of 24

15 Categories of Electrons Inner (core) electrons are those an atom has in common with the pervious noble gas and any completed transition series For transition elements, it is more complicated (Chem 422) Similar outer electron configurations correlate with similar chemical behavior Elements in the same group of the periodic table have the same outer electron configuration Elements in the same group of the periodic table exhibit similar chemical behavior Give the full and condensed electron configurations for the following elements potassium (K; Z = 19) technetium (Tc; Z = 43) lead (Pb; Z = 82) Concept Check Which of the following atoms or ions has a single unpaired electron? a. He b. Sr c. Na + d. Al Octet Rule atoms tend to ionize or combine such that they achieve eight valence electrons We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 15 of 24

16 Magnetic properties of atoms: Paramagnetic atom contain at least one unpaired electron Diamagnetic atom all electrons are spin-paired Some Transition metals are strange Element Expected e configuration 24Cr [18Ar] 4s 2 3d 4 [18Ar] 4s 1 3d 5 4s 3d 4s 3d Actual e configuration 42Mo [36Ar] 5s 2 4d 4 [18Ar] 5s 1 4d 5 5s 4d 5s 4d 74W [54Ar] 6s 2 5d 4 [18Ar] 6s 1 5d 5 6s 5d 6s 5d Why? The energy difference between the ns and (n-1)d subshell is small, so the promotion of an e into a slightly higher energy level is a good investment for the atom What is the ground state electron configuration for copper, silver, and gold? We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 16 of 24

17 Magnetic Properties of Transition Metal ions A species with one or more unpaired electrons exhibits paramagnetism it is attracted by a magnetic field A species with all its electrons paired exhibits diamagnetism it is not attracted (and is slightly repelled) by a magnetic field Magnetic behavior can provide evidence for the electron configuration of a given ion Electron configurations of monatomic Ions Octet rule atoms tend to lose, gain or share e s so that they attain 8 valence e s Using condensed electron configurations, write reactions for the formation of the common ions of the following elements: Iodine (Z = 53) Potassium (Z = 19) We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 17 of 24

18 Metals lose s e-s first when they form cations What is the ground state electron configuration for Fe, Fe +2 and Fe 3+? Concept Check What is the ground-state valence-shell electron configuration of the group of elements indicated by the shaded portion of the periodic table? a. ns 2 b. ns 2 np 2 c. ns 2 (n-1)d 2 d. ns 2 (n-2)f 2 Concept Check What is the ground-state valence-shell electron configuration of the group of elements indicated by the shaded portion of the periodic table? a. ns 2 b. ns 2 np 2 c. ns 2 (n1)d 2 d. ns 2 (n2)f 2 We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 18 of 24

19 General Trends in Atomic Properties Physical causes of all these atomic trends can be understood if we consider the attraction between the positively charged nucleus and the negatively charged electrons Force increases with magnitude of charges Force decreases rapidly with increasing distance between charges These are General Trends and exceptions to the general trends exist We will discuss trends in 1. Atomic Size or diameter 2. Ionization Energy 3. Electronegativity 4. Electron Affinity Atomic Size in Main Group Elements Atomic size increases down a group in the periodic table the number of electron shells increase and the outer electrons are further from the nucleus Atomic size decreases across a period (left to right) in the periodic table This counterintuitive- the number of e-s is increasing so why would size decrease? Ineffective screening of e-s in the same shell allow e-s feel stronger attraction to the nucleus In other words the effective nuclear charge, Zeff, increases across a period As Zeff increases, the e-s are pulled in tighter and atomic size decreases We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 19 of 24

20 Atomic radii of the main-group and transition elements Using the periodic table, rank each set of main-group elements in order of increasing atomic size Ca, Mg, Sr K, Ga, Ca Si, Ga, Ge Mg, K, Na Ionization energy (IE) IE is energy required to remove one mole of electrons from one mole of neutral atoms or ions Why? I.E. increases with attraction between nucleus and the e- being removed We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 20 of 24

21 This fits with what we know to be true from our experience Lab experience Metals tend to lose e-s to form cations What we are being told now Non-metals tend to gain e-s to form anions First ionization energies of the main-group elements Exceptions exist: Using the periodic table, rank the elements in each of the following sets in order of decreasing IE1 Kr, He, Ar In, Sb, Sn K, Ca, Rb Cl, Br, S We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 21 of 24

22 Successive ionization energies It is possible to remove more than one electron from an atom IE1 = First ionization energy : IE2 = Second ionization energy : IE3 = Third ionization energy : IE1 << IE2 << IE3 Why? A cation holds onto its remaining electrons more tightly, it becomes much more difficult to remove successive e s Review Concept Check Which groups of elements, indicated by letter on the periodic table, have three unpaired p electrons in their valence shell? We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 22 of 24

23 Electron Affinity (EA) energy change when one mole of electrons is added to one mole of gaseous atoms or ions The trends in electron affinity are not as regular as those for atomic size or IE General trends in three atomic properties Metallic Behavior (review) Metals are typically shiny solids with moderate to high melting points Metals are good conductors of heat and electricity, and can easily be shaped Metals tend to lose electrons and form cations, i.e., they are easily oxidized Since metals are easy to oxidize they are generally strong reducing agents Most metals form ionic oxides, which are basic in aqueous solution Trends in metallic behavior Concept Check The atomic radius of germanium is smaller than the atomic radius of potassium due to a. a smaller value of the n quantum number b. an increase in the effective nuclear charge c. the fact that potassium is a metal and germanium is a metalloid d. a decrease in the effective nuclear charge We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 23 of 24

24 Ionic Size vs. Atomic Size Cations are smaller than their parent atoms while anions are larger Ionic radius increases down a group as n increases Cation size decreases as charge increases An isoelectronic series is a series of ions that have the same electron configuration. Within the series, ion size decreases with increasing nuclear charge 3 > 2 > 1 > +1 > +2 > >+3 Rank each set of ions in order of decreasing size, and explain your ranking Ca 2+, Sr 2+, Mg 2+ K +, S 2, Cl Au +, Au 3+ Concept Check Which arrangement is in the correct order of decreasing radii? a. Be > Ba +2 > O 2 b. Cs < Mg +2 < F c. As 3 > Br > K + d. Na + > Cs + > I We are what we repeatedly do. Excellence, then, is not an act, but a habit. Aristotle Page 24 of 24