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 _____________________________ – energy that exhibits wavelike behavior as it travels through space

Wave Properties _____________________: distance between corresponding points on adjacent waves Unit: ____________________: number of waves that pass a given point per unit time (usually 1 sec) Unit:

Properties of Light How are frequency and wavelength related?

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?

Max Planck proposed … Energy needed for electrons to move was quantized, or a quantum of energy is needed to move an electron.

E = h

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.

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 __________________________ – –

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

Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 4 state to the n = 3 state.

“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

Schrodinger Wave Equation equation that describes both the particle and wave nature of the e - We do not know the exact position or speed, but: 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?

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

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

How many electrons can an orbital hold?

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. 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? Energy 1s 2s 3s 4s 5s 2p 3p 4p 3d 4d

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

Exceptions Chromium Copper

Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

Quantum Numbers

Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number: n n = 1, 2, 3, 4, …. n=1 n=2 n=3

 = 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 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 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

Summary

What are the possible magnetic quantum numbers for 2p? How many electrons can have the quantum numbers: n = 3 and m s = +1/2 ?

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?