# Atomic Orbitals and Hybrid Orbitals by gjjur4356

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Tabone
Uncertainty
 All measurements have a degree of uncertainty in
them

ocm      1cm        2cm       3cm

 We can tell that the blue bar is 2.3 cm for sure
 We can also estimate the next digit since the blue
bar is clearly between the 3 and 4 mm mark, but
this number is not 100% sure

 Therefore we say the blue bar is 2.35cm ± 0.02
 The 0.02 is the uncertainty in the measurement
Heisenberg Uncertainty Principle
 How do we observe anything?
 We often use light that bounces off an object to
determine its position and speed
 We do the same with particles

 It turns out that the higher energy (lower
wavelength) light we use, the more accurately we can
determine the position of a particle

 But we have learned that light can impart
momentum on particles...
Heisenberg Uncertainty Principle
 Since light imparts momentum on particles, the act
of observing them causes their behaviour to change

 The more accurately we try to determine their
position (by increasing the energy of the light) the
more momentum we give the particles.
 Meaning we know their momentum less accurately

 Heisenberg determined that there is always a
certain degree of uncertainty in our knowledge of the
behaviour of particles
Heisenberg Uncertainty Principle
 The product of the uncertainties in position (x) and
momentum (p) must always be larger than a
constant

ΔxΔp > h/4

 This means that even if we only think of electrons as
particles, we can never truly know everything about
what they are doing in an atom
 We must then think in probabilities
Schrödinger Wave Equation
 A physicist named Erwin Schrödinger developed an
equation that describes the states of electrons in
atoms and can be used to properly predict the
emission spectra of atoms

 It is based on Louis de Broglie’s work with electron
waves and utilizes the idea of probability in
describing the actions of electrons

 Ψ (psi) is the symbol for the wave function
 It represents the set of probabilities (ψ) that the atom
exists in different states
Schrödinger Wave Equation
 The electrons are viewed as standing waves, and
have only specific energies in each orbit due to their
wavelength

 The atom can exist in many different states, with the
electron in many different orbitals
Schrödinger Wave Equation
 The atom is said to simultaneously exist in all of the
possible states until one specific state “condenses”
 This idea is not very well understood, but it leads to
interesting technology like touch screens

 The idea of states existing simultaneously is called
“superposition”

 The superposition of states has famously been
described using the “Schrödinger’s Cat” paradox
Schrödinger’s Cat

Hammer
Fuzzy Cat

Geiger Counter

Poisonous Gas

Schrödinger’s Cat
 There is a 50% chance the radioactive material will
decay in 1 hour and a 50% chance that it will not
 Meaning for that hour there is an equal chance that the
cat is alive or dead – and we do not know which is true

 For that hour we say that the cat is

 The state condenses into one or the
other when we open the box and
make an observation
Electron Clouds
 Since we can’t know everything about the actions
of electrons, we view orbitals as clouds of negative
charge
 Each point in the orbital has a certain probability
that the electron will be there at any given moment
in time
 We picture orbitals as clouds of electron density
Atomic Orbitals
 If the electron density of different orbital types (s, p,
d, f) are graphed and modeled, we see that each type
has its own characteristic shape
 We can also see the differences between the degenerate
orbitals

 Degenerate orbitals often look similar but are
arranged differently in space

 3D Representations
Atomic Orbitals
Electron Density
Atomic Orbitals
Atomic Orbitals
 As n increases, the number of nodes in an orbital
increases
 A node is a region where there is zero electron density
 Ex: 1s – 0 nodes, 2s – 1 node, 3s – 2 nodes etc.

 As l increases, the number of nodes decreases
 3s – 2 nodes, 3p – 1 node, 3d – 0 nodes
Quantum Tunnelling
 Using the probabilistic approach to viewing matter,
every particle has a probability of existing anywhere
 But most of these probabilities are extremely small

 This can be used however to transport particles
through and across barriers
 Ex: an alpha particle (helium nucleus) within a larger
nucleus (like Ra) has a small probability of existing
outside of the nucleus
 This is how radioactive decay occurs
Ra-226  Rn-222 + He
Quantum Tunnelling
 Quantum tunnelling is also the phenomenon behind
touch screens

 The electrons in the screen have a small probability
of being located in the sensors below the screen.
 As the screen is pushed and the screen moves closer
the sensors beneath, the probability increases
 Eventually the probability is large enough that a
significant (though small) number of electrons “jumps”
from the screen to the sensors and starts an electric
current

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