Microsoft PowerPoint - Atomic structure.pptDevelopment of atomic
theory
The chapter presents the fundamentals needed to explain and atomic
& molecular structures in qualitative or semiquantitative
terms.
Sc Ti V Cr Mn Fe Co Ni Cu Zn
Li B B C N O F Ne
Thomson’s experiment
This deflection depends on: a. the strength of the deflecting
magnetic or
electric field b. the size of the negative charge on the electron
c. the mass of the electron * Charge-to-mass ratio, e/m of the
electron =
1.758 819 × 108 C/g.
Millikan’s experiment
Millikan’s experiment
Determined that the charge on a drop of oil was whole-number
multiple of e (e = 1.602 177 × 10-19 C).
Knowing the values for e/m and e for an electron, m can be
calculated (m = 9.109 390 × 10-28 g).
Rutherford’s experiment
In 1885, Balmer showed the energies of visible light emitted by the
H atom are given by the equation.
E=hν
The Balmer eq. was later made more general, as spectral lines in
the ultraviolet & infrared regions of the spectrum were
discovered, by replacing 22
by nl 2, with the condition that nl < nh.
The theory (Bohr’s quantum theory of atom) assumed that negative
electrons in atoms move in stable circular orbits around the
positive nucleus with no absorption or emission of energy (however,
electrons may absorb/emit light of specific energies).
E=hν
Classical physics : a particle in motion tends to move in a
straight line or in a circle by application of a force toward the
center of the circle. Since an electron revolving around the
nucleus constantly changes its direction, it is constantly
accelerating. Therefore, the electron should emit light & lose
energy, & must be drawn into the nucleus. This conclusion does
not correlate with the existence of stable atoms.
When applied to hydrogen, Bohr’s theory worked well; when atoms
with more electrons were consid- ered, the theory failed (i.e.,
elliptical rather than circular orbits).
410.1 nm
Particles massive enough to be visible have very short wavelengths,
too small to be measured. Electrons, on the other hand, have
observable wave properties because of their very small mass.
Hsisenberg’s uncertainty principle
states that there is a relationship between the inherent
uncertainty in the location & momentum of an electron moving in
the x direction :
The energy of spectral lines can be measured with great precision,
in turn allowing precise determination of the energy of electrons
in atoms. This precision in energy also implies precision in
momentum (Δpx is small); therefore according to Heisenberg, there
is a large uncertainty in the location of the electron (Δx is
large).
For an electron,
For a car,
These concept mean that we cannot treat electrons as simple
particles with their motions described precisely, but we must
instead consider the wave properties of electrons, characterized by
a degree on uncertainty in their location.
We must change :
Orbits (Bohr) → Orbitals (regions that describe the probable
location of electrons)
The probability of finding the electron at a particular point in
space (electron density - ψ2).
2-2 The SchrÖdinger Equation
The SchrÖdinger equation describes the wave properties of an
electron in terms of its position, mass, total energy, and
potential energy. The equation is based on the wave function, Ψ,
which describes an electron wave in space; in other words, it
describes an atomic orbital.
In the form used for calculating energy levels, the Hamiltonian
is
The potential energy, V, is a result of electrostatic attraction
between the electron & the nucleus.
Attractive forces, like those between a positive nucleus & a
negative electron, are defined by convention to have a negative
potential energy.
(1) Because every atomic orbital is described by a unique Ψ, there
is no limit to the # of solutions of the SchrÖdinger equation for
an atom. (2) Each Ψ describes the wave properties of a given
electron in a particular orbital. (3) The probability of finding an
electron at a given point in space is proportional to Ψ2.
A number of conditions are required for a physically realistic
solution for Ψ :
For complex and real numbers
2.2.1 The particle in a box
Ψ = Asin rx Apply x=0 & a, V=0.
Please see P. 24.
See Problem 6.
The Particle in a box as a model - A particle (m) is confined at 0
< x <L (V=0), but V=∞ at x=0 & L.
Hψ =Eψ (E=kinetic energy), H = -2/2m(d2/dx2)
-2/2m(d2ψ /dx2) = Eψ d2ψ /dx2 = -2mE/2(ψ) Our goal is to find
specific functions ψ(x) that satisfy the equation.
Figure 12.13: A schematic diagram of a particle in a
one-dimensional box with infinitely high
potential walls
d2ψ /dx2 = -2mE/2(ψ) ⇒ d2ψ /dx2 = (constant)ψ I.e., consider the
function Asin(kx), A, k : constants
Boundary conditions ?
The boundary conditions for the particle in a box enforce the
following facts :
1. The particle cannot be outside the box - it is bound inside the
box.
2. In a given state the total probability of finding the particle
in the box must be 1.
3. The wave function must be continuous.
Based on 1 :
Ηψ = Εψ, ψ=Asin(kx), so that ψ(0)=0 & ψ(L)=0
ψ(L)=Asin(kL)=0, k=nπ/L (n=1,2,3,…)
k = ?
A = ?
= L/2
Quantum numbers
Figure 12.14: The first three energy levels for a particle in a
one-dimensional box
ma hnE
=Ψ
The squared wave functions are the probability densities, and they
show the difference between classical and quantum mechanical
behavior.
Classical mechanics : the electron has equal probability of being
at any point in the box Quantum mechanics : different probabilities
at different locations in the box.
2.2.2 Quantum Numbers and Atomic Wave Functions
The particle-in-a-box example shows how a wave function operates in
one dimension. Mathematically, atomic orbitals are discrete
solutions of the 3-D Schrödinger equations. The same methods used
for the 1-D box can be expanded to the 3-D for atoms.
(s, p, d…)
(px, py, pz…)
Ψ(r, θ, φ)=R(r)Θ(θ)Φ(φ) = R(r)Υ(θ, φ)
x = r sinθ cosφ y = r sinθ sinφ z = r cosθ
Θ(θ)Φ(φ) : angular functions R(r) : radial functions
Nodal surfaces : Ψ=0, also R(r)=0 orΥ(θ, φ)=0
# of nodes ?
# of nodes ?
See figure 2-7
Node : 1 2 2
See P. 63
Each 2p orbital has two lobes. There is a planar node normal to the
axis of the orbital (so the 2px orbital has a yz nodal plane). Each
3p orbital has four lobes. There is a planar node normal to the
axis of the orbital (so the 3px orbital has a yz nodal plane, for
instance). Apart from the planar node there is also a spherical
node that partitions off the small inner lobes. Each 4p orbital has
six lobes. There is a planar node normal to the axis of the orbital
(so the 4px orbital has a yz nodal plane, for instance). Apart from
the planar node there are also two spherical node that partition
off the small inner lobes.
A gallery of atomic & molecular orbitals
http://winter.group.shef.ac.uk/orbitron/AOs/3p/index.html
2-2-3 The Aufbau Principle
1. Electrons are placed in orbitals to give the lowest total energy
to the atom.
2. Pauli exclusion principle. 3. Hund’s rule of maximum
multiplicity
Πc : Coulombic energy of repulsion Πe : exchange energy, which
arises purely from quantum mechanical considerations. This energy
depends on the number of possible exchanges between two electrons
with the same energy & spin.
The Coulombic energy, Πc, is positive & is nearly constant for
each pair of electrons. The exchange Energy, Πe, is negative &
is also nearly constant for each possible exchange of electrons
with the same spin. When the orbitals are degenerate (), both favor
the unpair configuration.
If there is a difference in energy between the levels involved,
this difference, in combination with the total pairing energy,
determines the final configu- ration (ligand-field theory, i.e.
Pt2+ - d8).
2-2-4 Shielding
In atoms with more than one electron, energies of specific levels
are difficult to predict quantitatively. A useful approach to such
predictions uses the concept of shielding : each electron acts as a
shield for electrons farther from the nucleus, reducing the
attraction between the nucleus & the more distant
electrons.
(a) 2s22p5 : for a particular 2p electron S = 6 x 3.5 = 2.10
(b) For the 3s electron of Na : the group (2s2, 2p6) has S = 8 x
0.85 = 6.80
Z* = Z - S
n-1 same n
The left same n
n-2 n-1 same n
Penetration effect : Note that although an electron in the 3s
orbital spends most of its time far from the nucleus & outside
the core electrons (the electrons in the 1s, 2s, & 2p
orbitals), which shields it from the nuclear charge, it has a small
but significant probability of being quite close to the
nucleus.
This effect also helps to explain why the 4s orbital fills before
the 3d orbital as the order : E4s < E3d. (Ens < Enp < End
< Enf)
Figure : The radial distribution of electron probability density
for the sodium atom.
E3s < E3p < E3d
Figure : Radial probability distributions
Note that the most probable distance of the electron from the
nucleus for the 3d orbital is less than that for the 4s orbital.
However, the 4s orbital allows more electron penetration close to
the nucleus & thus is preferred over the 3d orbital.
2-3 Periodic properties of atoms 2-3-1 Ionization energy
The ionization energy, also known as the ionization potential, is
the energy required to remove an e from a gaseous atom or ion
:
An+ (g) → A(n+1)+
(g) + e- ionization energy = ΔU Where n=0 (first ionization
energy), (second, third,…).
2-3-2 Electron affinity
Electron affinity can be defined as the energy required to remove
an e from a negative anion :
A- (g) → A(g) + e- electron affinity = ΔU (or EA)
[A(g) + e- → A- (g) electron affinity = EA]
Be : 1s22s2 B : 1s22s22p1
N : 1s22s22p3 O : 1s22s22p4
Richard F. Heck (University of Delaware, USA) Ei-ichi NegishiPurdue
(University, USA) Akira Suzuki (Hokkaido University, Japan)
The Nobel Prize in Chemistry 2010 was awarded jointly to Richard F.
Heck, Ei-ichi Negishi and Akira Suzuki "for
palladium-catalyzed cross couplings in organic synthesis".
The Nobel Prize in Chemistry 2010 Richard F. Heck, Ei-ichi Negishi,
Akira Suzuki
