Modern Atomic Theory

ELECTROMAGNETIC RADIATION

Electromagnetic radiation

Electromagnetic Radiation Most subatomic particles behave as PARTICLES and obey the physics of waves.

Electromagnetic Radiation wavelength Visible light Ultraviolet radiation Amplitude Node

Electromagnetic Radiation Wavelength, , is how long the wave is, from peak to peak Waves have a frequency, : how often the waves pass through a given point in a certain time All radiation travels at the same speed:  •  = c c = velocity of light = 3.00 x 108 m/sec = wavelength (meters)  = frequency (Hz or sec-1)

Electromagnetic Spectrum Long wavelength --> small frequency = low energy Short wavelength --> high frequency = high energy increasing frequency increasing wavelength

Electromagnetic Spectrum In increasing energy, ROY G BIV

Particle Nature of Light Light as a WAVE explains most everyday behavior, but not everything Light is also a PARTICLE Explains why only certain frequencies of light are observed when something is heated (example: iron) Matter can only gain or lose energy in small, specific amounts called quanta (plural) WHOA! This wave/particle duality of light was the beginning of quantum physics and leads to our current understanding of the atom https://www.youtube.com/watch?v=DfPeprQ7oGc

Planck’s equation Energy and frequency are directly related The higher the energy, the higher the frequency Each frequency carries a specific amount of energy Ephoton = h   Ephoton = the energy (in Joules) of a photon (a massless light particle carrying energy) h = Planck’s constant (6.626 x 10-34 J  s)  = frequency (in s-1)

Underline what you know Circle what you don’t know What is given in the problem? Circle what you don’t know What are you trying to find? List everything out and identify variables Write formula and solve for the unknown Substitute in values w/units Cancel units to see if everything is set up correctly Calculate and verify Round at end only (SIG FIGS) Does the answer have correct units and make sense?

What is the wavelength of electromagnetic radiation with a frequency of 5.00 x 1012 Hz?  What kind of radiation is this?

A photon has an energy of 2. 93 x 10 -25 J. What is its frequency A photon has an energy of 2.93 x 10 -25 J. What is its frequency? What type of radiation is this?

Atomic Line Emission Spectra and Niels Bohr Bohr’s greatest contribution: building a simple model of the atom. It was based on an understanding of the LINE EMISSION SPECTRA of excited atoms. Problem: only works for H Niels Bohr (1885-1962)

Atomic Spectra Thanks to Niels Bohr, atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit.

Line Emission Spectra of Excited Atoms Excited atoms emit light of only certain wavelengths The wavelengths of emitted light depend on the element

An excited lithium atom emitting a photon of red light to drop to a lower energy state.

An excited H atom returns to a lower energy level.

Spectrum of White Light

Spectrum of Excited Hydrogen Gas

Line Spectra of Other Elements

Atomic Spectra and Bohr Need a new theory — now called QUANTUM or WAVE MECHANICS. e- can only exist in certain discrete orbitals e- is restricted to QUANTIZED energy state (quanta = bundles of energy)

Quantum or Wave Mechanics Schrodinger applied idea of e- behaving as a wave to the problem of electrons in atoms. He developed the WAVE EQUATION Solution gives set of math expressions called WAVE FUNCTIONS,  Each describes an allowed energy state of an e- E. Schrodinger 1887-1961

Heisenberg Uncertainty Principle Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (= m•v) of an electron. We define e- energy exactly but accept limitation that we do not know exact position. W. Heisenberg 1901-1976

Bohr vs. Quantum Bohr: orbit Quantum: orbital Fixed path for e- Like a ring Quantum: orbital A region of space that says where I will probably find an e- Based on wave equations Like a box

QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 3 quantum numbers which describe the location of an electron within an atom or ion n (principal) ---> energy level, or shell l (angular) ---> sublevel, or subshell = shape of orbital ml (magnetic) ---> designates a particular orbital The fourth quantum number is not derived from the wave function s (spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)

QUANTUM NUMBERS 2 e- max. can be in an orbital The Pauli Exclusion Principle says that no two electrons within an atom (or ion) can have the same four quantum numbers. So… if two e- are in the same place at the same time, they must be repelling, so at least the spin quantum number is different! + 1/2 or - 1/2 for spin

Energy Levels Each energy level has a number called the PRINCIPAL QUANTUM NUMBER, n Currently n can be 1 thru 7, because there are 7 periods on the periodic table Higher energy, bigger orbitals

Relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen.

Energy Levels n = 1 n = 2 n = 3 n = 4

Sublevel: Shapes of Orbitals The most probable area to find electrons in an energy sublevel takes on a shape The angular quantum number (l) can be any integer between 0 and n - 1. So far, we have 4 shapes. They are named: s (l = 0), p (l = 1), d (l = 2), and f (l = 3). The angular quantum number (l) can be any integer between 0 and n - 1. If n = 1, then there is 1 sublevel (s). If n = 2, then 2 sublevels (s and p).

Shapes of Orbitals (l) s orbital p orbital d orbital

Magnetic Quantum Number (ml) The magnetic quantum number (ml) can be any integer between -l and +l. l = 0 for s orbitals s orbitals only have one direction they can be oriented in space, so ml = 0

p Orbitals 3py orbital (ml = -1, 0, 1) this is a p sublevel (l = 1) with 3 orbitals (ml = -1, 0, 1) These are called x, y, and z There is a PLANAR NODE thru the nucleus, which is an area of zero probability of finding an electron 3py orbital

p Orbitals The three p orbitals lie 90o apart in space

d Orbitals d sublevel (l = 2) has 5 orbitals ml = -2, -1, 0, 1, 2

The shapes and labels of the five 3d orbitals.

f Orbitals For l = 3, ---> f sublevel with 7 orbitals (ml = -3, -2, -1, 0, 1, 2, 3)

How many electrons can be in a sublevel? Remember: A maximum of two electrons can be placed in an orbital. s orbitals p orbitals d orbitals f orbitals Number of orbitals 7 1 3 5 Number of electrons 6 10 2 14

Aufbau Rule ___Aufbau_Principle_______ states that electrons fill from the lowest possible energy to the highest energy Aufbau = German word for “building up” Follow the arrows!

Diagonal Rule 1 2 3 4 5 6 7 s s 2p s 3p 3d s 4p 4d 4f s 5p 5d 5f 5g? Steps: Write the energy levels top to bottom. Write the orbitals in s, p, d, f order. Write the same number of orbitals as the energy level. Draw diagonal lines from the top right to the bottom left. To get the correct order, follow the arrows! s 2p s 3p 3d s 4p 4d 4f s 5p 5d 5f 5g? s 6p 6d 6f 6g? 6h? s 7p 7d 7f 7g? 7h? 7i?

Why are d and f orbitals always in lower energy levels? d and f orbitals require LARGE amounts of energy It’s better (lower in energy) to skip a sublevel that requires a large amount of energy (d and f orbitals) for one in a higher level but lower energy

Electron Configurations A list of all the electrons in an atom (or ion) Must go in order (Aufbau principle) 2 electrons per orbital, maximum 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

Electron Configurations 2p4 Number of electrons in the sublevel Energy Level Sublevel 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14… etc.

Let’s Try It! Write the electron configuration for the following elements: H Li B N Ne

Orbitals and the Periodic Table Orbitals grouped in s, p, d, and f orbitals (sharp, proximal, diffuse, and fundamental) s orbitals d orbitals p orbitals f orbitals

Orbital Diagrams Graphical representation of an electron configuration One “box” is one orbital One arrow represents one electron Shows spin and which orbital within a sublevel

Orbital Diagrams One additional rule: Hund’s Rule In orbitals of EQUAL ENERGY (p, d, and f), place one electron in each orbital before making any pairs All single electrons must spin the same way I nickname this rule the “Monopoly Rule” In Monopoly, you have to build houses EVENLY. You can not put 2 houses on a property until all the properties has at least 1 house.

Lithium Group 1A Atomic number = 3 1s22s1 ---> 3 total electrons

Carbon Group 4A Atomic number = 6 1s2 2s2 2p2 ---> 6 total electrons

Draw these orbital diagrams! Oxygen (O) Aluminum (Al) Chlorine (Cl)

Shorthand Notation A way of abbreviating long electron configurations Also called “noble gas” notation We want to identify valence electrons

Shorthand Notation Step 1: Find the closest noble gas (group 8) to the atom WITHOUT GOING OVER the number of electrons in the atom. Write the symbol in brackets [ ]. Step 2: Write the rest of the configuration by finding the next energy level on the periodic table.

Shorthand Notation [Ne] 3s2 3p5 Chlorine Longhand is 1s2 2s2 2p63s2 3p5 You can abbreviate the first 10 electrons with a noble gas, Neon. [Ne] replaces [1s2 2s2 2p6] [Ne] 3s2 3p5

Practice Shorthand Notation Write the shorthand notation for each of the following atoms: Mg K Co As Rb I Bi

Exceptions to the Aufbau Principle Remember d and f orbitals require LARGE amounts of energy If we can’t fill these sublevels, then the next best thing is to be HALF full (one electron in each orbital in the sublevel) There are many exceptions, but the most common ones are d4 and d9 For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d4 or d9 are exceptions to the rule.

Try These! Write the shorthand notation for: Cu W Au

Valence Electrons We need electron configurations so that we can determine the number of outermost electrons. These are called valence electrons. Electrons that are in the highest energy level, s and/or p sublevels ELECTRONS determine the chemical behavior of an atom, so…. Valence electrons determine how atoms will bond.

Valence Electrons Electrons are divided between core and valence electrons B 1s2 2s2 2p1 Core = [He] , valence = 2s2 2p1 Lewis Dot Structures Br [Ar] 4s2 3d10 4p5 Core = [Ar] 3d10 , valence = 4s2 4p5

Valence Electrons Write shorthand configurations and underline the valence electrons: Mg Ge I

Write longhand AND shorthand configs AND underline valence electrons--Any patterns? Group 1 Group 2 Group 3A Group 4A Group 5A Group 6A Group 7A Group 8A

Practice Wksh 4B-4 Write shorthand configurations AND draw the Lewis dot structure

What is the relationship between group number and the number of valence electrons in an atom? So, if group # = # of v.e; and v.e determine the chemical properties, then… Elements in the same group have similar chemical properties!