CSO 203A: Inorganic Molecules, Materials &
Medicine
Lecture 1: Life
with Oxygen
Anantharaj Sengeni
Important
Announcements!
&
Heads Ups!
NO
Phone/Laptop/Tablet
During the Class!
Doors of the
classroom will
be shut at 9:05!
Maintaining
80%
Attendance Is
Mandatory!
There will be a lot of anime
references!
Overview!
Quiz-II and End-Sem Exam Will Be
Conducted as Scheduled in the FCH!
Grading Scheme!
Relative
Grading Will
Be Followed!
Let’s Begin!
CSO 203A: Inorganic Molecules, Materials &
Medicine
Lecture 1: Life
with Oxygen
Anantharaj Sengeni
Before Jumping Into
The World of O2, Let’s
Brush Up Some Basic
Concepts (most of) You
Probably Have
Forgotten!
What’s An Atom?
The basic unit of matter that defines the
chemical elements
Atomic
Models!
Atomic Models!
1. Dalton’s Atomic Model (1803) – Indivisible Atoms
• Atoms are indivisible and indestructible
particles.
• Atoms of the same element are identical;
different elements have different atoms.
• Atoms combine in fixed ratios to form
compounds.
• Limitations: Did not explain the existence of
subatomic particles (electrons, protons,
neutrons).
Atomic Models! 2. Thomson’s Plum Pudding Model (1897) – Discovery
of Electrons
• Atoms are a positively charged sphere with
negatively charged electrons embedded like
raisins in a pudding.
• Proposed after the discovery of the electron
(cathode ray experiment).
• Limitations: Couldn’t explain the existence of a
nucleus or atomic stability.
Atomic Models!
3. Rutherford’s Nuclear Model (1911) –
Discovery of Nucleus
• Based on the gold foil experiment.
• Atoms have a dense, positively
charged nucleus, with electrons
orbiting around it.
• Most of the atom is empty space.
• Limitations: Could not explain
electron stability (why electrons
don’t spiral into the nucleus).
Atomic Models!
4. Bohr’s Model (1913) – Quantized Orbits
• Electrons orbit the nucleus in fixed energy levels
(shells).
• Energy is absorbed/emitted when electrons move
between shells.
• Explained hydrogen’s atomic spectrum.
• Limitations: Failed for multi-electron atoms and
did not explain chemical bonding fully.
Atomic Models! 5. Quantum Mechanical Model (Schrödinger,
1926) – Probability Clouds
• Electrons are found in probability clouds
(orbitals) rather than fixed orbits.
• Uses wave equations to predict electron
behavior.
• Explains chemical bonding and the
periodic table structure.
• Most accurate model used today.
Wave
Equations?
• These describe the behavior of
electrons as probability waves
rather than fixed orbits.
• The most important wave equation
is the Schrödinger equation, which
determines the allowed energy
levels and shapes of orbitals.
Schrödinger Wave Equation (1926)
The time-independent form is:
Where:
= Hamiltonian operator (total energy operator: kinetic + potential energy)
= Wave function (describes electron probability distribution)
= Total energy of the system
Interpretation:
• The wave function gives a probability distribution of where an electron is likely to be
found.
• The square of the wave function gives the probability density.
Particle-in-a-Box Model
For a simple system like an electron in a 1D box of length L, the wave function is:
And the energy levels are:
This equation explains quantization—electrons can only have discrete energy levels.
The H Atom!
Hydrogen Atom &
Quantum Numbers!
Solving Schrödinger’s equation for hydrogen gives quantum numbers:
• n (Principal quantum number) → Energy level (shells: K, L, M...)
• l (Azimuthal quantum number) → Orbital shape (s, p, d, f...)
• ml (Magnetic quantum number) → Orbital orientation
• ms (Spin quantum number) → Electron spin (+1/2,−1/2+1/2, -
1/2+1/2,−1/2)
Why It’s Important?
• Predicts electron orbitals (s, p, d, f) accurately.
• Explains bonding, reactivity, and spectra of elements.
• Forms the foundation of quantum chemistry and modern physics.
An Exact Solution for
Schrödinger’s
Equation Is Possible
Only for H Atom!
Why?
Let’s Stick to H Atom for a While!
• Solving Schrodinger’s wave equation for H atom yields n, l, and ml
• For a given set of integers for n, l, and ml, a particular orbital in the H atom is
obtained.
• Plotting a wave function (ψ) completely requires a four-dimensional graph with ψ
as the fourth value
• Cartesian coordinates (x, y, z) or spherical coordinates (r, θ, φ) could help
• The latter is convenient
ψ(r, θ, φ) = R(r) ϴ(θ) Φ(φ)
• A solution to Schrödinger's equation, the fundamental
equation of motion.
• Provides a complete description of the quantum state of a
particle.
• Expresses position, momentum, and other physical properties
of the particle.
The Wave • It is complex in nature (i.e., has both real and imaginary parts).
Function (ψ) • Depends on the position of the particle in space (x, y, z or r, θ,
φ) and time (t).
• The square of absolute value of ψ (i.e., |ψ|2) gives the
probability density of the particle.
Particle = Electron
Probability Density = Orbital
The Three
Variables The radial part
Broken
Down from ψ(r, θ, φ) = R(r) ϴ(θ) Φ(φ)
ψ of the
The angular part
electron of (also expressed as “Yℓm(θ,ϕ)”)
the H Atom!
• r is the radial distance from the nucleus.
The Radial Functions
• a0 is the Bohr radius, approximately 0.52 Å.
of a First Few • In Bohr theory, a0 is immutable
Orbitals in H Atom! • In wave mechanics, a0 is just the most probable
• r is the radial distance from the nucleus.
The Radial Functions
• a0 is the Bohr radius, approximately 0.52 Å.
of a First Few • In Bohr theory, a0 is immutable
Orbitals in H Atom! • In wave mechanics, a0 is just the most probable
The radius of an orbital decreases exponentially
This decay slows down with the increasing n
Hence, the radius of orbital increases with the
increasing n
2s orbital has a node (i.e., when r = 2a0, R becomes
0 and the radial function changes its sign)
In general, s, p, d, and f-orbitals have n-1, n-2, n-3,
and n-4 nodes, respectively.
Radial Part of H’s
Eigen Functions
• For a given set of values of
“n”, it shows how Ψ changes
its sign
• The electron is in a shell of volume dV
extending from r to r + dr
But!
dV
Aren’t We Trying to Find the Probability of
An Electron In a Spherical Shell Around
the Nucleus of H? r dr
Assume the atom is like an onion where
shells = orbits
The volume of the sphere V is given by
𝟒𝝅𝒓𝟑
𝑽= 𝟑
The volume of the shell dV is given by
𝒅𝑽 = 𝟒𝝅𝒓𝟐 𝒅𝒓
• By squaring and multiplying the radial part (R) of the with 𝑑𝑉 = 4𝜋𝑟 2 𝑑𝑟 as
Radial Probability 𝑅 2 𝑑𝑉 = 4𝜋𝑟 2 𝑅 2 𝑑𝑟 one can get the radial probability function in that
Functions of An particular shell
• 4𝜋𝑟 2 𝑅 2 varies with r and provides the probability function for any given set
Electron in Different of eigen functions of “n”
Orbitals!
2s orbital 3s orbital
Key features of the 1s orbital’s
probability function:
• When r=0, 4𝜋𝑟 2 𝑅2 becomes zero
implying zero probability of finding an 3p orbital
electron at the nucleus 2p orbital
• At very large r values, R approaches zero
rapidly. Hence, an e- cannot wander far
away from the nucleus 3d orbital
• In between, both r and R are finite.
Hence, there exists a maximum in the
plot (This happens when r = a0)
Bohr’s radius
Radial Probability
Functions of An
Electron in Different
Orbitals!
• Key features of other orbital’s
probability function:
• Note that 2s, 3s, and 3p
orbitals have all +Ve
probability along with
nodes
• Nodes: A distance from
the nucleus at which
the probability of finding
an electron is ZERO!
The BIG Questions!
1. If the probability finding an
electron at nodes is zero,
how come an electron can
exist at distances above and
below the nodes?
2. Can these nodes affect
bonding?
3. How these sub-nodal
maxima affect the energy of
electrons in respective
orbitals?
Electrons in higher s orbitals are said to penetrate more than that of other orbitals. Why?
Angular Wave Functions!
ψ(r, θ, φ) = R(r) ϴ(θ) Φ(φ)
The angular part
• These define the most probable shape of an orbital
• It varies with the type of orbital under consideration (such as s, p, d, f,..)
• They are independent of principal quantum numbers (i.e., energy levels)
Angular Wave Functions of H-like s and p-Orbitals!
ϴΦ ϴΦ ϴ2Φ2
function for an s-orbital function for a p-orbital function for H-like p-orbitals
Do these represent the shape of atomic orbitals?
Shape of Orbitals:
A Meaningful
Expression!
• Contours are the best
• Essential in explaining
bonding and bond
strength
Symmetry of Orbitals:
The Significance of
Signs of Wave
Functions!
• Signs on the lobes are the
signs of the wave function
• Bonding happens only
between two lobes
bearing the same signs
from two atoms
• Orbitals of atoms have no absolute shape
• They are diffuse
• All that we have is just a fuzzy understanding based
on the probability of finding an electron
• Shape of orbitals of multi-electron atoms are
unknown
Key Points to • Use of H-like orbitals for all the atoms may become a
huge trouble
Remember! • All those pictures you saw as the shapes of orbitals
are NOT what they are shown to be so!
As we learned so much
about an atom, let’s move on
to bonding and molecules!
