Chapter 7 - Quantum Theory and Atomic Structure

conclusion from Heisenberg Uncertainty Principle

The more accurately we know a particle's position, the less accurately we can determine its momentum - and vice versa

d orbital

clover shaped

f orbital

daisy shaped

for a one e- hydrogen atom, orbitals w. the same n are . . .

degenerate or have the same energy

Quantum Theory of Energy

explained blackbody radiation by assuming that energy comes in packets called quanta (singular: quantum) energy is quantized: Atoms can gain or lose energy by absorbing or emitting energy only in whole quanta

ψ^2 The square of the wave function

gives the electron density, or probability of where an electron is likely to be found any given time

relationship between wavelength and frequency

inversely related

s orbital

spherical

amplitude

the maximum height of a wave

frequency v

the number of waves passing a fixed point each second (sec-1 or Hz)

orbital

the volume or space where an e- is likely to be found

Limitations of Bohr's Model

• Only works for hydrogen atoms • Treats electrons solely as particles •Does not explain why the electron does not continuously emit energy and fall into the nucleus

Quantum Mechanics

describes the energies and arrangements of e- mathematically - describes the size (distance from nucleus) and overall orbital energy level

p orbital

dumbbell

Electromagnetic radiation

carries energy through space (aka radiant energy)

Three observed properties associated with how atoms interact w/ electromagnetic radiation are NOT explainable by treating light as a wave

1) blackbody radiation: emission of light from hot objects 2) the photoelectric effect: emission of e- from metal surfaces on which light is shined 3) emission spectra: emission of light from electronically excited gas atoms

e- (1) emitted and (2) absorbed

1. ni > nf ΔE<0 2. ni < nf ΔE>0

Electromagnetic Radiation (EMR) is quantized properties???

EMR is both a wave and a stream of particles (photons) EMR has dual nature properties: •Particle-like •Wave-like

The Photoelectric Effect

Einstein explained this with quanta Each metal has a different energy at which it ejects electrons. At lower energy, electrons are not emitted. Light consists of particles (photons) each with a discrete amount of energy

ground state excited state

Electrons in their lowest possible energy levels Any higher energy state (further from the nucleus)

Heisenberg Uncertainty Principle

It's impossible to know both the exact position (x) and exact momentum (mv) of an e- at any given time

Bohr's Model

Niels Bohr adopted Planck's assumption and explained these phenomena in terms of a new model of the atom: Now called "quantum theory" 1. Electrons can only exist in certain discrete orbits - The energy of each orbit is QUANTIZED (can have only certain values of energy) 2. An electron in a permitted orbit is in an "allowed state" -Does not radiate energy 3. Energy is absorbed or emitted by the electron as a photon (E = hν) but only as the electron changes from one allowed energy state to another

wavelength 𝞴

The distance between corresponding points on adjacent waves