Download The Current Model of the Atom Name This Element Building on Bohr

The Current Model of the Atom
Name This Element
Building on Bohr
Quantum Mechanics
• Uses mathematical equations to describe the
wave properties of subatomic particles
• It’s impossible to know the exact position,
speed and direction of an electron
(Heisenberg Uncertainty Principle)
• So Bohr’s “orbits” were replaced by orbitals
• The simple Bohr model
was unable to explain
properties of complex
atoms
• Only worked for
hydrogen
• A more complex model
was needed…
Orbits
– A wave function that predicts an electron’s
energy and location within an atom
– A probability cloud in which an electron is most
likely to be found
Orbitals
- Bohr
- Quantum Mechanics
- 2-dimensional ring
- 3-dimensional space
- Electron is a fixed
- Electrons are a variable
distance from nucleus
distance from nucleus
- 2, 8, or 18 electrons per - 2 electrons per orbital
orbit
Wave Particle Duality
• Experimentally, DeBroglie found
that light had both wave and
particle properties
• Therefore DeBroglie assumed
that any particle (including
electrons) traveled in waves
• Wavelengths must be quantized
or they would cancel out
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Heisenberg’s Uncertainty
Principle
• Due to the wave and particle nature of matter,
it is impossible to precisely predict the
position and momentum of an electron
• SchrÖdinger’s equation can be used to
determine a region of probability for finding
an electron (orbital)
• Substitute in a series of quantum numbers to
solve the wave function
Schroedinger’s Cat
• What’s up with the cat?
Quantum Numbers
• Four numbers used to describe a specific
electron in an atom
• Every electron in an atom has its own
specific set of quantum numbers
• Recall: Describes orbitals (probability
clouds)
Schroedinger's Equation
A description of each variable:
h - Planck's Constant - Usually (h/2π) is called hbar, and has a
value of 0.6582*10-15 eV·s
m -mass of the particle being examined.
Ψ - The wave function. This is what is usually being computed
using Schroedinger's Equation.
V - This is the potential energy of the described particle.
j - The imaginary number, being equal to √-1.
x - Position
t - Time
Defining the orbital
• Schroedinger’s calculations suggest the
maximum probability of finding an e- in a
given region of space with a particular quantity
of energy (orbital)
• Different orbitals are present in atoms having
different sizes, shapes and properties
• There are 4 parameters (called quantum
numbers) that define the characteristics of
these orbitals and the electrons within them
• This information provides the basis for our
understanding of bonding
Quantum Numbers
• Since an orbital is a 3-D space, we need
at least 3 variables to define it, though
there are 4 quantum numbers
• Each electron has a unique set of
numbers just as each point on a twodimensional graph has a unique set of two
numbers (x, y).
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The Pauli Exclusion Principle
• All four quantum numbers are needed for
a complete description of each electron in
an atom.
• The allowed values of the four quantum
numbersCan
areonly
restricted
be certainand
numbers
interdependent,
indicating
next number depends on the first the influence
of quantization.
• no two electrons in an atom can have the
same set of four quantum numbers,
• a complete set of four quantum numbers is
a unique description of a single electron in
a multielectron atom.
• “the address of the electron”
1. Principal Quantum Number (n)
Distance between energy levels
decreases as n increases
• the integer that Bohr used to label the
orbits and energy levels of an atom
• Tells us the size of the orbital
• n= 1, 2, 3…..∞, n € R
• The larger n is, the greater the
average distance from the nucleus
(less stable)
• The energy gap between successive
levels gets smaller as n gets larger
• The greatest number of electrons
possible in each energy level is 2n2
2. Angular momentum quantum
number (l)
• Is a sublevel of n that tells the shape of the
orbital
• The values of l depend on n
• For any given n, l = 0 to n-1
• The values of l are designated by the letters s,
p, d, f, g, h
• The number of sublevels is equal to the value
of n
– If n=1, l = 0
s
– If n=2, l = 0, 1
s, p
– If n=3, l = 0, 1, 2 s, p, d
Shape of orbitals
l
Name of
orbital
Shape
0
1
2
3
s
p
d
f
Sphere
(1 lobe)
2 lobes
4 lobes
8 lobes
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Shapes of s, p, and d-Orbitals
d-orbitals
Shapes of orbitals video
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 336
Shape of f orbitals
3. Magnetic quantum number (ml)
• This number indicates the orientation of
the orbital in 3-D space
• m has values related to l, ml = -l, 0, +l
– If n = 1, l = 0, ml = 0
– If n = 2, l = 0, 1, ml = -1, 0, +1 (this indicates
that there are 3 orbits that have the same
energy and shape, but differ only in their
orientation in space)
– Maximum number of orientations is n2
Principal Energy Levels 1 and 2
The First Three Quantum
Numbers
Quantum numbers video
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4. Spin quantum number (ms)
Quantum Numbers Summary Chart
Name
• The rotation of the electron in the orbital
is either clockwise or counterclockwise
• ms can have values of + ½ or – ½
• Qualitatively we refer to the spin as either
clockwise or counterclockwise or up or
down
Symbol Allowed Values
Property
Principal
n
positive integers
1,2,3…
Orbital size and
energy level
Secondary
l
Integers from
0 to (n-1)
Orbital shape
(sublevels/subshells)
Magnetic
ml
Integers –l to +l
Orbital orientation
Spin
ms
+½ or –½
Electron spin
Direction
Four numbers are required to describe
the energy of an electron in an atom
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