Transcript Chapter 1: Fundamental Concepts

Ch. 7 Atomic and Electronic Structure
Electromagnetic Radiation and Atomic Spectra
1. Electromagnetic Radiation -- Light
wavelength: l (m)
frequency: n (Hz = s–1)
ln = c = speed of light = 3.00 x 108 m/s
memorize!
memorize!
Wave/Particle Duality
•
Light was originally viewed as waves, since it displays diffraction
and interference properties. But, it also acts like particles, called
photons (hn), in some ways.
•
Electrons were originally viewed as particles, with a finite mass.
But they have interference and can diffract, so they have wavelike
properties too.
•
de Broglie wavelength:
l = h/mv
where l = wavelength, h = Planck’s constant
(6.626 x 10–34 J•s), m = mass,
v = velocity
memorize!
Radiation and the Atom
• Energy of electromagnetic radiation
– Radiation interacts with matter in discrete “packets” of energy called
“quanta” or “photons”
– E = hn
where h = Planck’s constant = 6.626 x 10–34 J s
– Atomic spectra:
Energetically excited atoms only emit radiation in discrete energies
corresponding to the atom’s electronic energy levels.
• Bohr model of H atom
– Energy levels
E = – b/n2
where b = 2.18 x 10–18 J
– Where n is a “quantum number”
with possible values of n = 1,2,3,4,…
– Increasing value of n indicates an
electron “orbit” farther from the nucleus
It is possible to calculate energy differences between levels (i.e. the
atomic spectrum) with different n values by using the Rydberg
Equation -- see textbook (but don’t memorize!)
Sample Questions
•
Calculate the wavelength of an FM radiowave at 100.2 MHz.
•
The energy required to ionize sodium is 496 kJ/mol. What is the
minimum frequency of light required to ionize sodium?
Sample Questions
•
Calculate the wavelength of an FM radiowave at 100.2 MHz.
2.99 m
•
The energy required to ionize sodium is 496 kJ/mol. What is the
minimum frequency of light required to ionize sodium?
1.24 x 1015 Hz
Electron Probability
Heisenberg’s Uncertainty Principle states
Dx • mDv = h/4p
(do not memorize)
where Dx is the uncertainty in the position and Dv is the uncertainty in the
velocity, m = mass, h = Planck’s constant
This says that electrons cannot be precisely located and their velocity
known at the same time. However, the probability of an electron
being in a location can be related to its energy using the
Schrodinger equation:
HY = EY
where H = hamiltonian operator, E = energy, and Y = wavefunction
•
Solutions to this equation generate the quantum numbers and
define the electron orbitals.
Electronic Quantum Numbers
• Electrons in multi-electron atoms can be classified into a
series of:
shells ---> subshells ---> orbitals
• Each orbital can be described mathematically by a “wave
function” that is characterized by a set of quantum
numbers.
• 1. Principal Quantum Number -- n
– Related to energy of shell and to distance from nucleus (size)
– Possible values of n = 1, 2, 3, 4, …
Electronic Quantum Numbers
• 2. Secondary Quantum Number -- l
– Related to shape of various subshells within a given shell
– Possible values of l = 0, 1, 2, 3, 4, … n-1
• Letter designation: s, p, d, f, g, …
Values of n
Values of l
subshells
1
0
1s
2
0, 1
2s, 2p
3
0, 1, 2
3s, 3p, 3d
Electronic Quantum Numbers
• 3. Magnetic Quantum Number -- ml
– related to spatial orientation of orbitals within a given subshell
– possible values of ml = –l, … 0, … +l
– the number of ml values = number of orbitals within a subshell
e.g. within a subshell having l = 2, there are 5 orbitals
corresponding to the 5 possible values of ml (-2, -1, 0, +1, +2)
Electronic Quantum Numbers
Summary -- electronic quantum numbers and orbitals
n
l
ml
subshell
# orbitals
1
0
0
1s
1
2
0
1
0
-1. 0, +1
2s
2p
1
3
3
0
1
2
0
-1, 0, +1
-2, -1, 0, +1, +2
3s
3p
3d
1
3
5
4
0
1
2
3
0
-1, 0, +1
-2, -1, 0, +1, +2
-3, -2, -1, 0, +1, +2, +3
4s
4p
4d
4f
1
3
5
7
Sample Questions
• For an electron in a 5f atomic orbital, give all possible
values of the quantum numbers.
• What is the maximum number of orbitals in the 5f subshell?
Sample Questions
• For an electron in a 5f atomic orbital, give all possible
values of the quantum numbers.
Answer:
n=5
l=3
ml = -3, -2, -1, 0, +1, +2, +3
• What is the maximum number of orbitals in the 5f subshell?
Answer: 7
Shapes of Atomic Orbitals
Atomic orbitals are best viewed as “clouds of electron density” and
represented as contour plots of the probability of finding the
electron.
nodal surface
an imaginary point, plane, or spherical
surface where the probability of finding the
electron is equal to zero
simplified pictures:
s orbitals are spherical shaped
Shapes of Atomic Orbitals
p orbitals are “bow tie” shaped and oriented along the coordinate
axes
y
z
x
px
py
pz
Shapes of Atomic Orbitals
d orbitals have more complex shapes
Orbital Phases –phases alternate just like in 2-D waves; always draw
orbitals with “shaded” and “unshaded” lobes. (will be important in
bonding)