Download Recap – Last Lecture The Bohr model is too simple Wave

Recap – Last Lecture
The Bohr model is too simple
•  Bohr model of the atom: electrons occupy
orbits of certain energies.
•  Evidence of this from atomic spectra in which
wavelength of light is related to energy
difference between orbits.
Most atomic spectra are much more
complex than expected from a Bohr
model of electron arrangements.
E = hν = hc/λ
ΔE = -2.18 x 10-18 J (1/n2final - 1/n2initial) Z2
•  Theory and experiment agree closely…for
hydrogen.
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Wave – mechanical model
(http://chemistry.bd.psu.edu/jircitano/periodic4.html)
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Wave – mechanical model
•  Light has a dual nature and the de Broglie
equation relates wavelength to momentum
•  This can only be solved if various boundary
conditions are applied. That is, the waves
must be standing waves that are
λ  = h/mv
–  continuous
–  single valued
–  multiples of a whole number of half wavelengths
•  Heisenberg Uncertainty Principle – ‘fuzziness’
Δx Δv ≥ h/4πm
•  Schrödinger Equation – energy of electron waves
Ĥψ =
Eψ
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•  There are then discrete solutions that
represent the energy of each electron orbital.
The orbitals are described by quantum
numbers.
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Quantum Numbers
Quantum Numbers
•  The Principal Quantum Number : n
n = 1, 2, 3 …
•  The Angular Momentum Quantum Number : l
Energy
l = 0, 1, 2 … (n -1)
E=0
l=2
Energy
l =1
n=3
•  Describes the size of the orbital
n=3
l=0
n=2
•  The larger the value of n, the
bigger & the higher energy the
orbital
l =1
n=2
l=0
n =1
l=0
n =1
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Quantum Numbers
Quantum Numbers
•  The Magnetic Quantum Number : ml
ml = -l, -(l -1) … 0 … (l -1), l
l describes the shape of the orbital
d orbital
Quantum no
Orbital description
l=0
s orbital
l=1
p orbital
l=2
d orbital
l=3
f orbital
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l=2
Energy
p orbital
n=3
s orbital
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ml = -2,-1,0,+1,+2
l =1
ml = -1,0,+1
l=0
ml = 0
l =1
ml = -1,0,+1
n=2
l=0
ml = 0
n =1
l=0
ml = 0
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Quantum Numbers
Quantum Numbers
ml describes the orientation of the orbital
if l = 0; ml = 0
if l = 1; ml = -1, 0, +1
•  The Spin Quantum Number : ms
ms = + 1/2 , — ½
(1 x s orbital)
(3 x p orbitals)
•  Describes the spin of the electron
if l = 2; ml = -2, -1, 0, +1, +2
(5 x d orbitals)
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Quantum Numbers
Applications
•  Each orbital, uniquely described by n, l and
ml, may contain a maximum of two electrons,
one spin + 1/2, the other spin -1/2 .
l=2
Energy
n=3
n=2
n =1
Shell
ml = -2,-1,0,+1,+2
10e -
l =1
ml = -1,0,+1
6e-
l=0
ml = 0
2e-
l =1
ml = -1,0,+1
6e-
l=0
ml = 0
2e-
l=0
ml = 0
Sub-shell
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Orbital
18e -
•  Bohr model results in a periodic table with a 2, 8, 18 pattern
H
He
Li
Be
B
C
N
O
F
Ne
Na Mg Al
Si
P
S
Cl
Ne Sc
Ti
V
Cr Me Fe Co
Ni
Cu Zn
•  Actual periodic table needs to be explained!
8e-
2eElectrons
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Learning Outcomes:
• 
Questions to complete for next lecture:
1.  Provide a valid set of quantum numbers, n, l and ml, of an
electron in a 4p orbital? (Question form 2015 exam)
2.  Which of the following is a valid set(s) of quantum numbers
and identify the incorrect number in the other set(s)?
By the end of this lecture, you should be able to:
−  Explain the meaning of the orbital quantum
numbers, n l ml ms.
−  Understand the designation of orbitals such as
1s, 3d, 4p, 4f.
−  Recognise the shapes of s, p and d atomic
orbitals.
−  Determine the number of electrons in an orbital/
sub-shell/shell.
A. 
B. 
C. 
D. 
E. 
n
n
n
n
n
=1 l=1
=
=
=
=
3
2
2
3
l
l
l
l
=
=
=
=
1
0
2
2
ml
ml
ml
ml
ml
=0
=
=
=
=
+1
-1
+2
0
ms
ms
ms
ms
ms
= +1/2
=
=
=
=
+1/2
-1/2
-1/2
0
3.  Sketch the shape of a px orbital. How many electrons can it
accommodate?
4.  Which quantum number describes the shape of an orbital?
5.  How many sub-shells are there in the n = 3 shell?
−  be able to complete the worksheet (if you
haven’t already done so…)
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