Download No Slide Title

Chapter 6
Electronic Structure of Atoms
David P. White
Prentice Hall © 2003
Chapter 6
The Wave Nature of Light
• All waves have a characteristic wavelength, l, and
amplitude, A.
• The frequency, f, of a wave is the number of cycles which
pass a point in one second.
• The speed of a wave, v, is given by its frequency
multiplied by its wavelength:
c = fλ
c is the speed of light
Prentice Hall © 2003
Chapter 6
Prentice Hall © 2003
Chapter 6
• Modern atomic theory involves interaction of radiation
with matter.
• Electromagnetic radiation moves through a vacuum with
a speed of 3.00  108 m/s.
Prentice Hall © 2003
Chapter 6
Electromagnetic spectrum
Example 1: A laser produces radiation with a
wavelength of 640.0 nm. Calculate the
frequency of this radiation.
Example 2: The YFM radio station broadcasts
EM radiation at 99.2 MHz. Calculate the
wavelength of this radiation (1 MHz = 106 s-1).
Prentice Hall © 2003
Chapter 6
Quantized Energy and
Photons
• Planck: energy can only be absorbed or released from
atoms in fixed amounts called quanta.
• For 1 photon (energy packet):
E = hf = hc/λ
where h is Planck’s constant (6.63  10-34 J.s).
Prentice Hall © 2003
Chapter 6
The Photoelectric Effect and Photons
• If light shines on the surface of a metal, there is a point
(threshold frequency) at which electrons are ejected from
the metal.
Prentice Hall © 2003
Chapter 6
Example 3: (a) A laser emits light with a frequency of
4.69 x 1014s-1. What is the energy of one photon of the
radiation from this laser? If the laser emits a pulse of
energy containing 5.0 x 1017 photons of this radiation,
what is the total energy of that pulse?
Prentice Hall © 2003
Chapter 6
Line Spectra and the Bohr
Model
Line Spectra
• Monochromatic light – one λ.
• Continuous light – different λs.
• White light can be separated into a continuous spectrum
of colors.
Prentice Hall © 2003
Chapter 6
A prism disperses light from a light bulb
• Balmer: discovered that the lines in the visible line
spectrum of hydrogen fit a simple equation.
• Later Rydberg generalized Balmer’s equation to:
1  RH

l  h
 1  1 
 2
 n1 n22 
where RH is the Rydberg constant (1.096776  107 m-1), h
is Planck’s constant, n1 and n2 are integers (n2 > n1).
Prentice Hall © 2003
Chapter 6
Bohr Model explains this equation
• Rutherford assumed the electrons orbited the nucleus
analogous to planets around the sun.
• However, a charged particle moving in a circular path
should lose energy, ie, the atom is unstable
• Bohr noted the line spectra of certain elements and
assumed the electrons were confined to specific energy
states called orbits.
Prentice Hall © 2003
Chapter 6
Colors from excited gases arise because
electrons move between energy states in the
atom.
Black regions show λs absent in the light
Prentice Hall © 2003
Chapter 6
Bohr Model
• Energy states are quantized, light emitted from excited
atoms is quantized and appear as line spectra.
• Bohr showed that

E   2.18  10
18

 1 
J 2
n 
where n is the principal quantum number (i.e., n = 1, 2, 3).
Prentice Hall © 2003
Chapter 6
• The first orbit has n = 1, is closest to the nucleus, and has
negative energy by convention.
• The furthest orbit has n close to infinity and corresponds
to zero energy.
• Electrons in the Bohr model can only move between
orbits by absorbing and emitting energy
∆E = Efinal – Einitial = hf
Prentice Hall © 2003
Chapter 6
• We can show that
 1

hc
1
E  hf 
  2.18  1018 J  2  2 
n

l
n
i 
 f


• When ni > nf, energy is emitted.
• When nf > ni, energy is absorbed
Prentice Hall © 2003
Chapter 6
Limitations of the Bohr Model
• Can only explain the line spectrum of hydrogen
adequately.
• Electrons are not completely described as small particles.
Prentice Hall © 2003
Chapter 6
The Wave Behavior of
Matter
• Explores the wave-like and particle-like nature of matter.
• Using Einstein’s and Planck’s equations, de Broglie
showed:
h
l
mv
• The momentum, mv, is a particle property, whereas l is a
wave property.
Prentice Hall © 2003
Chapter 6
The Uncertainty Principle
• Heisenberg’s Uncertainty Principle: on the mass scale
of atomic particles, we cannot determine exactly the
position, direction of motion, and speed simultaneously.
• For electrons: we cannot determine their momentum and
position simultaneously.
• If x is the uncertainty in position and mv is the
uncertainty in momentum, then
h
x·mv 
4
Prentice Hall © 2003
Chapter 6
Quantum Mechanics and
Atomic Orbitals
• Schrödinger proposed an equation that contains both
wave and particle terms.
• Solving the equation leads to wave functions, ψ
(orbitals).
• ψ2 gives the probability of finding the electron
• Orbital in the quantum model is different from Bohr’s
orbit
Prentice Hall © 2003
Chapter 6
Prentice Hall © 2003
Chapter 6
• Schrödinger’s 3 QNs:
1. Principal Quantum Number, n. - same as Bohr’s n. As n
becomes larger, the atom becomes larger and the electron is
further from the nucleus.
Prentice Hall © 2003
Chapter 6
2. Azimuthal Quantum Number, l. - depends on the value of n.
The values of l begin at 0 and increase to (n - 1). The letters
for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to
the s, p, d and f-orbitals.
3. Magnetic Quantum Number, ml. - depends on l. Has
integral values between -l and +l. Gives the 3D orientation of
each orbital. There are (2l +1) allowed values of ml and this
gives the no. of orbitals.
Total no. of orbitals in a shell = n2
Prentice Hall © 2003
Chapter 6
Prentice Hall © 2003
Chapter 6
• Orbitals can be ranked in terms of energy to yield an
Aufbau diagram.
Prentice Hall © 2003
Chapter 6
Single electron atom – orbitals with
the same value of n have the same
energy
Prentice Hall © 2003
Chapter 6
Representations of
Orbitals
The s-Orbitals
•
•
•
•
All s-orbitals are spherical.
As n increases, the s-orbitals get larger & no. of nodes
increase.
A node is a region in space where the probability of finding
an electron is zero, 2 = 0 .
For an s-orbital, the number of nodes is (n - 1).
Prentice Hall © 2003
Chapter 6
The p-Orbitals
•
•
•
•
There are three p-orbitals px, py, and pz.
The letters correspond to allowed values of ml of -1, 0, and
+1.
The orbitals are dumbbell shaped and have a node at the
nucleus.
As n increases, the p-orbitals get larger.
Prentice Hall © 2003
Chapter 6
Prentice Hall © 2003
Chapter 6
The d and f-Orbitals
• There are five d and seven f-orbitals.
• They differ in their orientation in the x, y,z plane
Prentice Hall © 2003
Chapter 6
Many-Electron Atoms
Orbitals and Their Energies
• Orbitals of the same energy are said to be degenerate.
• For n  2, the s- and p-orbitals are no longer degenerate
because the electrons interact with each other.
• Therefore, the Aufbau diagram looks different for manyelectron systems.
Prentice Hall © 2003
Chapter 6
Many electron atoms – electrons
repel and thus orbitals are at
different energies
Electron Spin and the Pauli Exclusion
Principle
• Line spectra of many electron atoms show each line as a
closely spaced pair of lines.
• Stern and Gerlach designed an experiment to determine
why.
Prentice Hall © 2003
Chapter 6
2 opposite directions of spin
produce oppositely directed
magnetic fields leading to the
splitting of spectral lines into
closely spaced spectra
• Since electron spin is quantized, we define ms = spin
quantum number = + ½ and - ½ .
• Pauli’s Exclusion Principle: no two electrons can have
the same set of 4 quantum numbers.
•
Therefore, two electrons in the same orbital must have
opposite spins.
Prentice Hall © 2003
Chapter 6
• In the presence of a magnetic field, we can lift the
degeneracy of the electrons.
Prentice Hall © 2003
Chapter 6
Electron Configurations
•
•
Hund’s Rule
Electron configurations - in which orbitals the electrons for an
element are located.
For degenerate orbitals, electrons fill each orbital singly before
any orbital gets a second electron.
Prentice Hall © 2003
Chapter 6
•
•
•
•
Condensed Electron Configurations
Neon completes the 2p subshell.
Sodium marks the beginning of a new row.
Na: [Ne] 3s1
Core electrons: electrons in [Noble Gas].
Valence electrons: electrons outside of [Noble Gas].
Prentice Hall © 2003
Chapter 6
Transition Metals
• After Ar the d orbitals begin to fill.
• After the 3d orbitals are full, the 4p orbitals begin to fill.
• Transition metals: elements in which the d electrons are
the valence electrons.
Prentice Hall © 2003
Chapter 6
•
•
•
•
•
Lanthanides and Actinides
From Ce onwards the 4f orbitals begin to fill.
Note: La: [Xe]6s25d14f0
Elements Ce - Lu have the 4f orbitals filled and are
called lanthanides or rare earth elements.
Elements Th - Lr have the 5f orbitals filled and are
called actinides.
Most actinides are not found in nature.
Prentice Hall © 2003
Chapter 6
Electron Configurations
and the Periodic Table
• The periodic table can be used as a guide for electron
configurations.
• The period number is the value of n.
• Groups 1A and 2A have the s-orbital filled.
• Groups 3A - 8A have the p-orbital filled.
• Groups 3B - 2B have the d-orbital filled.
• The lanthanides and actinides have the f-orbital filled.
Prentice Hall © 2003
Chapter 6