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Expectations Work with wavelength, frequency, and energy
of electromagnetic radiation. Know the order (energy and wavelength) of
the regions in the electromagnetic spectrum. Interpret line spectra of elements (lab). Understand electronic structure.
Quantum numbers Orbitals Electron configurations
6.1 The Wave Nature of Light Electromagnetic Radiation
A form of energy Light, heat, microwaves, radio waves Speed of light in a vacuum: c = 2.9979 x 108 m/s
Wave characteristics Wavelength (λ) in m or nm Frequency (ν) in s-1 or Hz Velocity (c) in m/s Amplitude – height of a wave Node – point where amplitude equals zero
Relating Wavelength and Frequency
All light travels at the same velocity:
As λ ↑, ν ↓. Electromagnetic spectrum (Fig. 6.4, p. 209)
Arranged by wavelength and frequency Visible portion: 350 – 760 nm Know order of spectrum!
νλc
6.2 Quantized Energy and Photons Matter (atoms) and energy (light) were thought to
be unrelated until 1900. Matter – consists of particles with mass and position Energy (waves) – massless with uncertain position
3 problems:1. Emission of light from hot objects (blackbody radiation)
2. Emission of electrons from a metal surfaces on which light shines (photoelectric effect)
3. Emission of light from electronically excited gas atoms (emission spectra)
What do these have in common?Color and intensity of light are temperature dependent.
Different colors of light are produced by each gaseous element.
Quantized Energy Max Planck (1900) – postulated that energy of
matter is quantized, that is, occurs only in certain discrete units of energy Equantum = hν h = 6.626 x 10-34 J·s
(Planck’s constant) E = nhν n = an integer
Quantized – restricted to certain quantities Quantum – fixed amount
Quantized Energy Einstein (1905) – explained that electro-
magnetic radiation is quantized Assumed light consists of tiny energy packets
called photons that behave like particles!?! Ephoton = hν
Some types of light have more energy than other types.
Energy ⇐ ? ⇒ Matter
Molybdenum requires a photon with a frequency of 4.41 x 1015 s-1 to emit electrons. Calculate (a) the energy of one photon and (b) of one mole of photons.
6.3 Line Spectra and the Bohr Model
Spectrum – radiation separated into different wavelengths Continuous – light of all
wavelengths Line – contains only
specific wavelengths
Different gases produce different line spectra.
Rydberg Equation
2217 11
m10096776.1λ
1
if nn
ni and nf are integers; ni > nf for emission
Used to calculate the wavelengths of the lines in the line spectrum of hydrogen
↑ RH
Bohr Model of the AtomPostulates:
1. Orbits have certain radii, which correspond to certain energy levels.
2. An electron in an orbit has a specified energy.
3. Energy is only emitted and absorbed by an electron as it moves from one energy state to another.
Energy States of the Hydrogen Atom Bohr calculated the energy of each orbit.
n is an integer (1…∞); the principal quantum number
Ground state (n = 1) – lowest energy state Excited state – higher energy state Energy values are negative, indicating stability
from the electron-nucleus attraction.
218 1
J)1018.2(n
E
Electronic Transitions
Ultraviolet (Lyman) ni → nf = 1
Visible (Balmer) ni → nf = 2
Infrared (Paschen) ni → nf = 3
e- transition practiceCalculate the wavelength, energy, and frequency for an electron transition from n = 5 to n = 3.
Limitations of the Bohr Model
Offered an explanation of the hydrogen atom, but failed for other atoms.
The electron does not orbit about the nucleus.
But,
1. Electrons do exist in energy levels.
2. Energy is involved in moving an electron between energy levels.
6.4 The Wave Behavior of Matter Louis de Broglie (1923) – discovered the
relationship between a particle’s mass and wavelength Diffraction of x-rays and electrons Tiny particles like electrons have wave-like
properties!?!
Sample Exercise 6.5: λ = 1.22 x 10-10 mmv
λh
v – velocity (m/s)
m – mass (kg)
Heisenberg Uncertainty Principle
It is impossible to know both the position and momentum of a particle at a given time.
Heisenberg may have been here!
Enter quantum mechanics, a way to deal with both the wavelike and particle-like behavior of the electron.
4(mv)x
h
6.5 Quantum Mechanics and Atomic Orbitals
Quantum (or wave) mechanics Schrödinger solved an equation.
Treated electron as wave Solved for energy of the wave Mathematical solution gives the size and
shape of a wave function or orbital.
Schrödinger solved an equation. Predicts the probability of finding an
electron (electron density) Node – where probability of finding an
electron is zero Each equation solution uses four variables
called quantum numbers.
6.5 Quantum Mechanics and Atomic Orbitals
So what are these orbitals anyway?
The Periodic Table gives us the answer.
A rule first:
Each orbital can hold only one pair of electrons – with spins of +½ and −½
↿⇂
Quantum Numbers (p. 220, 227)Quantum # Values Purpose Describes
Principal (n) 1, 2, 3, … ∞ size and energy
shell
Angular (ℓ) 0, 1, 2, 3, … (n−1)s, p, d, f
shape subshell
Magnetic (mℓ) −ℓ, … 0 …, +ℓ orientation in space
orbital
Spin magnetic (ms) +½, −½ spin of electron
electron
Each set of four quantum numbers defines individual electrons.
6.7 Many-Electron AtomsRules of Orbital Filling
1. Pauli Exclusion Principle – In a given atom, no two electrons can have the same set of four quantum numbers, i.e. only two electrons per orbital.
2. Aufbau Principle – Lowest energy orbitals are filled first.
3. Hund’s Rule – For degenerate orbitals, the lowest energy is attained with maximum number of unpaired electrons.
6.8 Electron Configurations Shows the number of electrons and type
of orbitals present in an atom or ion Orbital diagram – use boxes or lines Spectroscopic notation – 1s2 2s2 2p6 etc. Core electrons – electrons in filled shells Valence electrons – electron(s) in unfilled
shells
6.9 Electron Configurations and The Periodic Table
Remember: The Periodic Table is the answer. Use it!
Exceptions (p. 237):
24Cr
28Cu
Electron Configurations of Ions (pp. 262-263)
Cations: Remove electron(s) from the orbital(s) with
the highest n and highest l. For transition metals the s electrons are
removed first.
Anions: Add electron(s) to the empty or partially filled
orbitals with the lowest value of n.