Chapter 6: Electronic Structure of Atoms

Chapter 6: Electronic Structure of Atoms

electronic structure – the arrangement of electrons in an atom

6.1 The Wave Nature of Light

electronic radiation – radiant energy, carries energy through space
all electromagnetic radiation move through a vacuum at 3.00 x 10⁸ m/s

wavelength – the distance between successive peaks in a wave

electromagnetic radiation – 1) electric component

2) magnetic components

wave characteristics due to periodic oscillations of the two components
wavelength and frequency are related
n l = c (n =wavelength, l =frequency)
frequency expressed in cycles per second (hertz, Hz)

Unit	Symbol	Length(m)	Type of Radiation
Angstrom	Å	10^-10	X ray
Nanometer	nm	10^-9	Ultraviolet, visible
Micrometer	m m	10^-6	Infrared
Millimeter	mm	10^-3	Infrared
Centimeter	mm	10^-2	Microwave
Meter	M	1	TV, radio

6.2 Quantized Energy and Photons

German physicist, Max Planck – energy can be released by atoms only in "chunks" of some minimum size

Quantum – smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation
E=hv (h=planck’s constant=6.63 x 10^-34 J-s)

6.2.1 The Photoelectric Effect

photoelectric effect – when photons strike a metal surface, electrons are emitted

6.3 Bohr’s Model of the Hydrogen Atom
6.3.1 Line Spectra

monochromatic – radiation with a single wavelength
spectrum – created when radiation is divided up into its wavelengths
continuous wavelength – rainbow of colors containing light of all wavelengths
line spectrum – spectrum containing radiation of specific wavelengths
Johann Balmer:

n = C(1/2² – 1/n²) n = 3,4,5,6
C = 3.29 x 10¹⁵ s^-1

6.3.2 Bohr’s Model

electrons could circle the nucleus only orbits of specific radii
E_n = (-R_H)(1/n²) n = 1,2,3,4…
R_H = Rydberg constant = 2.18 x 10^-18 J
n = principle quantum number
gound state – lowest energy level
excited state – electrons in a higher energy level
E¥ = (-2.18 x 10^-18 J)(1/¥ ²) = 0
Electrons can jump to a higher energy state by absorbing energy
r E = E_f – E_I = hn

n_iandn_f are the principle quantum numbers of the initial and final states of the atom
n is positive when n_{i <}n_f (energy is absorbed)
v is negative when n_{i >}n_f(electron jumps from higher to lower state)
frequency of electromagnetic radiation must be a positive number
"-" sign indicates that light is emitted

6.4 The Wave Behavior of Matter

De Broglie: wavelength of the electron or any particle depends on its mass, m and velocity, v
l = h/mv
mv = momentum
matter waves – describe the waves characteristics of material particles

6.4.1 The Uncertainty Principle

it is impossible to know simultaneously both the exact momentum of the electron and its exact location in space

6.5 Quantum Mechanics and Atomic Orbitals

wave functions - y (has no physical meaning)

probability density - y ², probability that the electron will be found at the location proposed

electron density – regions where there is a high probability of finding the electron

6.5.1 Orbitals and Quantum Numbers

1) principal quantum number, n, can have integral values of 1,2,3,4…
n increases orbital becomes larger
2) azimuthal quantum number, l, can have integral values from 0 to n-1
defines the shape of the orbital
3) magnetic quantum number, m_l, can have integral values between l and –l, and 0
describes orientation of orbital

electron shell – collection of orbitals with the same value of n

subshell – orbitals that have the same n and l values
1) shell with principal quantum number n will consist of exactly n subshells
2) each subshell consists of a specific number of orbitals
3) the total number of orbitals in a shell is n², n = principle quantum number of shell

6.6 Representation of Orbitals

6.6.1 The s Orbitals

spherically symmetric

nodes – intermediate regions where y ² goes to zero
number of nodes increases as n increases

6.6.2 The p Orbitals

two lobes
orbitals of a given subshell have same size and shape but differ in spacial orientation

6.6.3 The d and f Orbitals

5 d orbitals, 4 of which are "4 leaf clover" shaped
one has two lobes and a "doughnut" shape in the middle
7 f orbitals

6.7 Orbitals in Many-Electron Atoms

6.7.1 Effective Nuclear Charge

effective nuclear charge – net positive charge attracting the electron
Z_eff = Z – S (Z_eff = effective nuclear charge, Z = number of protons, S = average number of electrons
Screening effect – inner electrons shield outer electrons from full charge of nucleus

6.7.2 Energies of Orbitals

In a many-electron atom, for a given value of n, Z_eff decreases with increasing value of l
in a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l

degenerate – orbitals with the same energy

6.7.3 Electron Spin and the Pauli Exclusion Principle

George Uhlenbeck and Samuel Boudsmit – proposed the electron spin
Electron spin quantum number, m_s – can only have values of +0.5 and –0.5
Pauli exclusion principle – no two electrons in an atom can have the same set of four quantum numbers n, l, m₁, and m_s
An orbital can hold a maximum of two electrons, and they must have opposite spins

6.8 Electron Configuration

electron configuration – the way electrons are distributed in orbitals

orbital diagram – a box with each electron represented by a half arrow (arrow pointing=electron with positive spin, arrow pointing down=electron with negative spin)

6.8.1 Periods 1,2, and 3

Hund’s rule – for degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized

Valence electrons – outer shell electrons

Core electrons – electrons in the inner shells

6.8.2 Period 4 and Beyond

transition elements or transition metals – 4^th row of the periodic table

lanthanide elements - elements 58-71 (rare-earth)

actinide elements – last row of periodic table

6.9 Electron Configurations and the Periodic Table

the periodic table is your best guide to the order in which orbitals are filled
chromium is [Ar]4s¹3d⁵ rather than [Ar]4s²3d⁴
copper [Ar]4s¹3d¹⁰rather than [Ar]4s²3d⁹