Electronic structure and Quantum Theory Ach The Electron

Electronic structure and Quantum Theory Ach The Electron

Electronic structure and Quantum Theory Ach The Electron Configuration way electrons are arranged around the nucleus. It is the representation of the arrangement of electrons distributed among the orbital shells and subshells. For now, remember this: 1. First shell, maximum 2 electrons 2. The rest, maximum 8 electrons. What is the charge? Atoms have no charge. Ions have charge. In general, the following are the charges: Group I --> +1 Group II --> +2 Group III --> +3 Group V --> -3 Group VI --> -2

Group VII --> -1 Inner Core and Valence Electron Configuration Inner core electrons: the filled shells Valence electrons: electrons occupying the outer energy level These are the electrons that participate in: Bonding Making cations lose Making anions gain Atoms tend to gain, lose, or share electrons until they have eight valence electrons.- The Octet Rule Electron Configuration for Ions Electrons are removed or added to the VALENCE SHELL. Valence shell is the outermost energy level that an atoms

electrons occupy. Electrons in the valence shell are referred to as the valance electrons. Cations Metals tend to form cations. Cations are elements having fewer electrons than protons. Cations are positively charged atoms. Anions Nonmetals tend to form anions. Anions are elements that have more electrons than protons. Anions are negatively charged atoms. The Full-Shell Look: Eight Valence Electrons Quantum-mechanical calculations show that an atom with eight valence electrons should be unreactive meaning the atom is very stable. The noble gases have eight valence electrons and are all very stable and unreactive.

Exception is Helium (He), which has two valence electrons, but that fills its valence shell. If a full-shell look implies stability, then elements having either one more electron (alkali metals) or one less electron (halogens) should be predicted to be very reactive. Halogens, with seven valence electrons, are the most reactive of the nonmetals. They gain ONE electron to form anions. Alkali metals, with one more electron than the preceding noble gas, are the most reactive of the metals. They lose ONE electron to form cations. 6 Energy Levels Quantum mechanics has a principal quantum number. It is represented by a little n. It represents the energy level similar to Bohrs model.

n=1 describes the first energy Red Orange Yellow Green Blue Indigo Violet n=1 n=2 n=3 n=4 n=5 n=6 n=7 level n=2 describes the second energy level

Etc. Each energy level represents a period or row on the periodic table. Its amazing how all this stuff just fits together. Table Atoms Summary of Quantum Numbers of Electrons in Name principal Symbo l n angular

momentu m l magnetic ml spin ms Allowed Values Property positive integers (1, 2, orbital energy (size) 3,) integers from 0 to n-1 orbital shape (l values of

0, 1, 2 and 3 correspond to s, p, d and f orbitals, respectively.) integers from -l to 0 to orbital orientation +l +1/2 or -1/2 direction of e- spin Each electron in an atom has its own unique set of four (4) quantum numbers. Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

10 Schrodinger Wave Equation quantum numbers: (n, l, ml, ms) hell electrons with the same value of n ubshell electrons with the same values of n and l rbital electrons with the same values of n, l, and If n, l, and ml are fixed, then ms = or - An orbital can hold 2 electrons 11 Sub-levels = Specific Atomic Orbitals Each energy level has 1 or more sub-levels which describe the specific atomic orbitals for that level.

n = 1 has 1 sub-level (the s Blue = s block Yellow = p block Red = d block Green = f block orbital) n = 2 has 2 sub-levels (s and p) n = 3 has 3 sub-levels (s, p and d) n = 4 has 4 sub-levels (s, p, d and f) There are 4 types of atomic orbitals:

s, p, d and f Each of these sub-levels Orbitals The space where there is a high probability that it is occupiedd by a pair of electrons. s p In the s block, electrons are going into s orbitals. In the p block, the s orbitals are full. New electrons are going into the p orbitals. In the d block, the s and p orbitals are full. New electrons are going into the d orbitals. General Energy Ordering of Electrons in Atomic Orbitals

Azimuthal Quantum Number, l l = 0, 1...,n-1 Value of l 0 1 2 3 Type of orbital s p d f

So each of these letters corresponds to a shape of orbital. Arrangement of Electrons in Atoms Electrons are arranged around an atoms nucleus according to the Aufbau principle. Electrons enter the lowest energy level (n) and orbitals (l) available. n + l rule Electrons will enter lowest energy subshell (l) that is empty in that energy level (n). Example: 2s vs. 2p For 2s: n = 2 and l = 0 (s) So, (n + l) = 2 = 0 = 2

For 2p: n = 2 and l = 1 (p) So, (n + l) = 2 + 1 = 3 The electron goes into the empty 2s orbital, not the 2p. Electron Configuration According to quantum mechanics: Electron location around the atoms nucleus is described by the four quantum numbers: n (principle energy level) l (orbital type: s, p, d, f) ml (orientation of orbital) ms (spin of electron in orbital) No two electrons can have the same four

quantum numbers: Pauli exclusion principle Writing Atomic Electron Configurations Electron configuration for He, atomic number =2 number of electrons in the orbital 1 s2 orbital type (value of l) Energy level (value of n) Energy Level Sublevels Total Orbitals Total Electrons

Total Electrons per Level n=1 s 1 (1s orbital) 2 2 n=2 s p 1 (2s orbital) 3 (2p orbitals)

2 6 8 n=3 s p d 1 (3s orbital) 3 (3p orbitals) 5 (3d orbitals) 2 6 10 18

Complete the chart in your notes as we discuss this. n=4 1 (4s orbital) 2 32 The sp first level3(n=1) has an s orbital. (4p orbitals) 6 It has only 1. There d are no other 5 (4d orbitals orbitals) in the first 10 energy level. We call f 7 (4f orbitals) this orbital the 1s orbital. 14

Rules for Electron Configurations In order to write an electron configuration, we need to know the RULES. 3 rules govern electron configurations. Aufbau Principle Pauli Exclusion Principle Hunds Rule Using the orbital filling diagram at the right will help you figure out HOW to write them Start with the 1s orbital. Fill each orbital completely and then go to the next one, until all of the elements have been accounted for.

Filling Rules for Electron Orbitals Aufbau Principle: Electrons are added one at a time to the lowest energy orbitals available until all the electrons of the atom have been accounted for. Pauli Exclusion Principle: An orbital can hold a maximum of two electrons. To occupy the same orbital, two electrons must spin in opposite directions. Hunds Rule: Electrons occupy equal-energy orbitals so that a maxim number of unpaired electrons results. *Aufbau is German for building up Fill Lower Energy Orbitals FIRST Each line http://www.meta-synthesis.com/webbook/34_qn/qn3.jpg represents an orbital.

1 (s), 3 (p), 5 (d), 7 (f) High Energy Low Energy The Aufbau Principle states that electrons enter the lowest energy orbitals first. The lower the principal quantum number (n) the lower the energy. Within an energy level, s orbitals are the lowest energy, followed by p, d and then f. F orbitals are the highest energy for that level.

Orbital Diagrams Each box represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the spin of the electron. 1s22s1 Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s

5d 5p 4s Bohr Model 4d 4p 3s 4f 3d 3p N

2s 2p 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s

5d 5p 4s Bohr Model 4d 4p 3s Hydrogen 4f 3d 3p

N 2s 2p 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La H = 1s1 Energy Level Diagram 6s

6p Arbitrary Energy Scale 5s 5d 5p 4s Bohr Model 4d 4p 3s Helium

4f 3d 3p N 2s 2p 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La

He = 1s2 Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d 5p 4s Bohr Model 4d 4p

3s Lithium 4f 3d 3p N 2s 2p 1s Electron Configuration NUCLEUS

H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La Li = 1s22s1 Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d 5p 4s

Bohr Model 4d 4p 3s Carbon 4f 3d 3p N 2s 2p

1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La C = 1s22s22p2 Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d

5p 4s Bohr Model 4d 4p 3s Nitrogen 4f 3d 3p N

2s 2p Hunds Rule maximum number of unpaired orbitals. 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La N = 1s22s22p3

Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d 5p 4s Bohr Model 4d 4p 3s

Fluorine 4f 3d 3p N 2s 2p 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS

Fe La F = 1s22s22p5 Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d 5p 4s 4d

4p 3s 4f Aluminum Bohr Model 3d 3p N 2s 2p 1s Electron Configuration

NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Al = 1s22s22p63s23p1 Fe La Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d 5p 4s

4d 4p 3s 4f Argon Bohr Model 3d 3p N 2s 2p

1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Ar = 1s22s22p63s23p6 Fe La Energy Level Diagram 6s 6p Arbitrary Energy Scale 5s 5d

5p 4s Bohr Model 4d 4p 3s Iron 4f 3d 3p N

2s 2p 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe Fe = 1s La22s22p63s23p64s23d6 Energy Level Diagram 6s 6p

Arbitrary Energy Scale 5s 5d 5p 4s Bohr Model 4d 4p 3s Lanthanum 4f

3d 3p N 2s 2p 1s Electron Configuration NUCLEUS H He Li C N Al Ar F CLICK ON ELEMENT TO FILL IN CHARTS Fe La =

1s22s22p63s23p64s23d10 La 2 10 6 2 10 6 2 Electron configurations We fill orbitals in increasing order of energy. Different blocks on the periodic table,

Introduction Quantum theory enables us to understand the critical role that electrons play in chemistry. Studying atoms leads to the following questions: How many electrons are present in a particular atom? What energies do individual electrons possess? Where in the atom can electrons be found? The answer to these questions have a direct relationship to the behavior of all substances in chemical reactions. From Classical Physics to Quantum Theory The new era in physics started in 1900 with a

young German physicist named Max Planck. While studying the data on radiation emitted by solids heated to various temperatures, Planck discovered that atoms and molecules emit energy only in certain discrete quantities, or quanta. Physicists had always assumed that energy is continuous and that any amount of energy could be released in a radiation process. Plancks quantum theory turned physics upside down. 39 Waves A time Wave: some sort of periodic function

something that periodicaly changes vs. time. wavelength (): distance between equivalent points Amplitude: height of wave, maximum displacement of periodic function. Waves Higher frequency shorter wavelength lower frequency longer wavelength The number of waves passing a given point per unit of time is the frequency (). For waves traveling at the same velocity, the longer the

wavelength, the smaller the frequency. Properties of Waves Wavelength () is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency () is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = x 42 Wa ve s v = wavelength x frequency meters x (1/sec) = m/sec v =

James Clerk Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s All electromagnetic radiation lxn=c 44 Electromagnetic Radiation All electromagnetic radiation travels the speed of light (c), 3.00 108 m/s (in a vacuum).

Therefore: c = A photon has a frequency of 6.0 x 104 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? x=c = c/ = 3.00 x 108 m/s / 6.0 x 104 Hz = 5.0 x 103 m = 5.0 x 1012 nm 46 The three mysteries of 19th century physics Mystery #1: Blackbody radiation Why does metal

glow when heated? K.E. of electrons What light is given off? Mystery 1: Black body radiation Higher T leads to shorter wavelength of light More K.E., more E Must be relationship between E and wavelength Plank concluded that energy is quantized. It comes in packets (like fruit snacks) and is proportional to frequency: E = h where h is Plancks constant, 6.63 1034 J-s. The minimum packet of E.

Mystery # 1, Heated Solids Problem Solved by Max Planck in 1900 When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Radiant energy emitted by an object at a certain temperature depends on its wavelength. Energy (light) is emitted or absorbed only in discrete quantities, like small packages or bundles (quantum). Quantum: the smallest quantities of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. 49 What did Einstein get the Nobel Prize for? Mystery #2: The Photo-electric

effect Note, this is what a photo cell does Turn light into work (current) Einstein: Light is both a particle e- K.E. escape energy and a wave. Ephoton = 1/2mv2 + ho = Eelectron e- light comes in packets of energy. Each packet runs into one electron. Each packet must have enough E to break electron loose from metal. The rest of the energy goes into kinetic energy. Frequency tells us the E of each packet. I tells us how many packets/second we get. More packets, more current (more electrons knocked off).

emetal h The Nature of Energy Energy, , , related: c = E = h c= speed of light in vacuum, constant When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm. E=hx =hxc/ = 6.63 x 10-34 (Js) x 3.00 x 10 =

1.29 x 10 -15 8 (m/s) / 0.154 x 10- J 54 Mystery number 3: element line spectrum Hydrogen Neon Gas discharge tube (full of some elemental gas)

Gives off specific frequencies of light only. Different elements give off different colors. i.e. different energies. 1. Bohrs Model of the Atom e can only have (1913) specific (quantized) energy values 2. light is emitted as emoves from one energy level to a

lower energy level En = -RH( 1 n2 ) n (principal quantum number) = 1, 2, 3, RH (Rydberg constant) = 2.18 x 10-18J 56 E = h E = h 57 The Nature of Energy

Niels Bohr adopted Plancks assumption and explained these phenomena in this way: 1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies). The Nature of Energy Niels Bohr adopted Plancks assumption and explained these phenomena in this way: 2. Electrons in permitted orbits have specific, allowed energies;

The Nature of Energy Niels Bohr adopted Plancks assumption and explained these phenomena in this way: 3. Energy is only absorbed or emitted in such a way as to move an electron from one allowed energy state to another; the energy is defined by E = h The Nature of Energy The energy absorbed or emitted from electron promotion or demotion can be calculated by the equation:

where RH is the Rydberg constant, 2.18 1018 J, and ni and nf are integers, the initial and final energy levels of the electron. Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. Ephoton =DE = R(H 1 ni2 1 nf2 ) = 2.18 x 10-18 J x (1/25 - 1/9) = -1.55 x 10-19 J

Ephoton = h x c / = h x c / Ephoton = 6.63 x 10-34 (Js) x 3.00 x 108 (m/s)/1.55 x 1 = 1280 nm 62 Why is e- energy quantized? De Broglie (1924) reasoned that e- is both particle and wave. 2pr = n h =mu u = velocity of em = mass of e63

What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? = h/mu h in Js m in kg u in (m/s) = 6.63 x 10-34 / (2.5 x 10-3 x 15.6) = 1.7 x 10-32 m = 1.7 x 10-23 nm 64

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