Quantum Theory and the Electronic Structure of Atoms Chapter 7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

What is light? A form of electromagnetic radiation: – energy that exhibits wavelike behavior as it travels through space

Light is organized on the Electromagnetic Spectrum LOW ENERGY HIGH ENERGY V I B G Y O R

Wave Properties Wavelength (λ) : distance between corresponding points on adjacent waves Unit: meters or nanometers Frequency (ν): number of waves that pass a given point per unit time (usually 1 sec) Unit: 1/s = s -1 = Hertz (Hz)

Properties of Light How are frequency and wavelength related? c = λν c : speed of light (m/s) c = 3.00 x 10 8 m/s λ : wavelength (m) ν : frequency of wave (s −1 = 1/s = Hz)

x = c = c/ = 3.00 x 10 8 m/s / 6.0 x 10 4 Hz = 5.0 x 10 3 m Radio wave A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? = 5.0 x nm

Max Planck proposed … Energy needed for electrons to move was quantized, or a quantum of energy is needed to move an electron. E = hν E : energy of light emitted (J) h : Planck’s constant (J·s) h = × 10 −34 J·s ν : frequency of wave (s −1 = 1/s = Hz)

E = h Electrons can only move with a quantum of energy. Every color represents a different amount of energy released.

E = h x E = 6.63 x (J s) x 3.00 x 10 8 (m/s) / x (m) E = 1.29 x J E = h x c /  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 nm.

Louis de Broglie proposed … that electrons be considered waves confined to the space around an atomic nucleus. – electron waves could exist only at specific frequencies (energy is still quantized!)

ELECTRON MOVEMENT

Electrons are always moving! The farther the electron is from the nucleus, the more energy it has. Electrons can change energy levels and emit a photon of light. – Photon: packet of energy – E photon = hν

Definitions Ground State: – ALL electrons are in the lowest possible energy levels Excited State: – Electrons absorb energy and are boosted to a higher energy level Emission: – when an electron falls to a lower energy level, a photon is emitted Absorption: – energy must be added to an atom in order to move an electron from a lower energy level to a higher energy level

1.e - can only have specific (quantized) energy values 2.light is emitted as e - moves from a higher energy level to a lower energy level Bohr’s Model of the Atom (1913)

Line Spectrum Every element has a different number of electrons. Every element will have different transitions of electrons between energy levels. Each element has their own unique bright line emission spectrum created from the release of photons of light. When are photons released?

Line Emission Spectrum of Hydrogen Atoms

E photon =  E = E f - E i n f = 1 n i = 2 n f = 2 n i = 3

E photon =  E = 10. x – 1.0 x E photon =  E = 9.0 x J = 6.63 x (Js) x 3.00 x 10 8 (m/s) 9.0 x J = 2.2 x m = 2.2 x 10 2 nm = 220 nm Calculate the wavelength (in nm) of a photon emitted from an electronic transition from the n = 4 state to the n = 2 state. E photon = h x c /  = h x c / E photon  E = E f - E i E photon =

Light and matter behave as both particles and waves “Dual Nature” of Light And Matter Light has both: 1.particle nature (energy released as a photon) 2.wave nature (energy has a specific wavelength and frequency that can be calculated) Even large objects have a wavelegnth!

Heisenberg Uncertainty Principle Electrons have a dual nature: – If it is a wave: then we know how fast it is moving – If it is a particle: then we know its position WE CANNOT KNOW AN ELECTRONS EXACT POSITION OR SPEED AT THE SAME TIME

Schrodinger Wave Equation equation that describes both the particle and wave nature of the electron We do not know the exact position or speed, but: 90% probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for other atoms.

What did your graph of electron density look like? Where 90% of the e - density is found for the 1s orbital

We do not know the exact location of an electron, but we do our best to DESCRIBE it’s location.

DO NOW Get 4 colors from the bin in front. Answer the question below. How would you describe your current location? Start off really broad, as in Earth, and describe your location to be more specific.

The first four principle energy levels in the atom.

ENERGY LEVEL SUB- LEVEL

The first four principle energy levels and their sub-levels.

SUB- LEVEL ORBITAL

The first four principle energy levels, their sub-levels, and orbitals. Energy 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d 4f

Aufbau Principle 4s 5s 1s 2s 3s 2p 3p 4p 3d 4d Energy 4f Electrons are added one at a time Starting at the lowest available Energy orbital. Electron Configuration for: Boron

m s = +½ or -½ How many electrons can an orbital hold? An orbital can hold 2 electrons

Pauli Exclusion Principle 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d Energy 4f Can not have same set of Quantum Numbers An orbital holds a max of 2 electrons. Must have opposite spins. - Paired electrons - Unpaired electron Electron Configuration for: Boron

Hund’s Rule 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d Energy 4f Electrons occupy equal energy orbitals So that a maximum number of unpaired Electrons results. Electron Configuration for: Oxygen

What is the electron configuration of Mg? Mg 12 electrons = 12 electrons Energy 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d

What is the electron configuration of Cl? Cl 17 electrons = 17 electrons 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d Energy

Sublevels on the Periodic Table

Exceptions Chromium Copper

Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

Outermost subshell being filled with electrons

Quantum Numbers

Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number: n n = 1, 2, 3, 4, …. distance of e - from the nucleus

 = fn(n, l, m l, m s ) angular momentum quantum number: l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 n = 4, l = 0, 1, 2, or 3 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation

 = fn(n, l, m l, m s ) magnetic quantum number: m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 0 (s orbital), m l = 0 if l = 1 (p orbital), m l = -1, 0, 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, 2 if l = 3 (f orbital), m l = -3, -2, -1, 0, 1, 2, 3 Schrodinger Wave Equation

m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2 m l = 0 m l = -2m l = -1m l = 0m l = 1m l = 2m l = -3m l = 3

 = fn(n, l, m l, m s ) spin quantum number: m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½ direction of electron spin

Summary

What are the possible magnetic quantum numbers for 2p? 2p n=2 l = 1 If l = 1, then m l = -1, 0, or +1 How many electrons can have the quantum numbers: n = 3 and m s = +1/2 ? If n = 3 then available orbitals are in 3s, 3p, and 3d How many electrons are only spin up in these orbitals?

What are all the possible quantum numbers for an electron in 4f? What are the possible quantum numbers for the last (outermost) electron in Cl? 1s 2 2s 2 2p 6 3s 2 3p 5 Last electron added to 3p orbital n = 3 l = 1m l = 0 m s = -½ n = 3l = 2m l = -2, -1, 0, +1, +2m s = +½ or -½