quantum numbers structure 2
TRANSCRIPT
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Quantum Numbers andAtomic Structure
RefiningBohrs Model
By: Vishal Singh
XI-A
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What are Quantum Numbers?
Bohr defined the principal energy levels(n = 1,2,3,4)
experimental evidence indicated the need
for changes to this simple system quantum numbers are quantizedvalues
used to describe electrons in an atom
there are four quantum numbers
represented by the letters n(Bohrsnumber), l, ml
and ms
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The Principal Quantum Number, n(Bohr, 1913)
based on Bohrs observations of linespectra for different elements
n relates to the main energy of anelectron
allowable values: n= 1, 2, 3, 4,
electrons with higher n valueshave more energy
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The Secondary Quantum Number,l(Sommerfeld, 1915)
based on the observation (Michelson,1891) that lines on line spectra areactually groups of multiple, thin lines
l relates to the shape of the electronsorbits
allowable values: l= 0 to l= n - 1
i.e. for n = 4: l= 0, 1, 2, or 3
the l values 0, 1, 2, and 3 correspond to
the shapes we will call s, p, d and f,respectively
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The Magnetic Quantum Number, ml
(Sommerfeld and Debye, 1915)
based on the observation (Zeeman, 1897)that single lines on line spectra split into newlines near a strong magnet
ml relates to the direction/orientation of the
electrons orbits
allowable values: ml= - l to + l
i.e. for l= 2: ml= -2, -1, 0, 1, or 2
electrons with the same lvalue but different
ml values have the same energy but differentorientations
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The Spin Quantum Number, ms
(Pauli, 1925)
based on the observation that magnetscould further split lines in line spectra, andthat some elements exhibit paramagnetism
ms
relates to the spin of an electron allowable values: ms= - or +
i.e. for any possible set ofn, l, and ml
values, there are two possible msvalues
when two electrons of opposite spin arepaired, there is no magnetism observed; anunparied electron is weakly magnetic
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Defining Electrons Using
Quantum Numbers
Lets look at the energy level n = 2:
Possible lvalues: 0, 1
For l= 0, ml
= 0
For l= 1, ml
= -1, 0 or 1
For every value of ml, there are two
electrons (ms = and ms = - )
So, there would be 8 electrons foundin principal energy level 2 and theywould have the followingdesignations
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Electrons in energy level 2:
Electron n l ml
ms
1 2 0 (or s) 0
2 2 0 (or s) 0 -
3 2 1 (or p) -1
4 2 1 (or p) -1 -
5 2 1 (or p) 0
6 2 1 (or p) 0 -
7 2 1 (or p) 1
8 2 1 (or p) 1 -
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Orbits vs. Orbitals
initially, electrons were thought totravel in orbits (2D, travels aroundnucleus at fixed distance in acircular path, 2n2 electrons perorbit)
quantum theory describes electrons
as existing in orbitals (3D region,distance from nucleus varies, nopath, 2 electrons per orbital)
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For our purposes:
primary energy level (n) = shell
energy sublevel (l) = subshell
orbitals are named as a combinationof the n and lvalues
e.g.an electron may exist in a 2p orbital(n = 2, l= 1 or p)
shapes of these orbitals will bediscussed soon
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Energy-Level Diagrams
now we can be more specific
for every n, energy increases froms p d f
quantum number restrictions state thatthere can only be:
one s orbital (= 2 electrons) for any value ofn
three p orbitals (= 6 electrons) for n= 2,3,4,
five d orbitals (= 10 electrons) for n= 3,4,5,
seven f orbitals (=14 electrons) for n= 4,5,6,
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Relative Energies of Electron Orbitals
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When Placing Electrons in Orbitals
aufbau principle: fill lower-energyorbitals first
Hunds rule: within the same energylevel, give each orbital one electronbefore pairing up electrons
Pauli exclusion principle: two
electrons within the same orbitalmust have opposite spins
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Aufbau (building up) Diagram this diagram will help you remember the proper order for
filling orbitals
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
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Energy-Level Diagram for Vanadium
vanadium has 23electrons
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The Following is Just Beautiful
The quantum theory of the atomagrees completely with the periodictable, which had been around for 30years and was developed withoutany knowledge of electronarrangements.
Wait for it
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Relationship between the first two quantum numbers and
the periodic table:
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Referring to quantum theory and theperiodic table of the elements:
The unity of these concepts is a triumph
of scientific achievement that isunparalleled in the past of present.
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Electron Configurations
More concise than energy-leveldiagrams but provide sameinformation
e.g. for vanadium:
V: 1s2 2s2 2p6 3s2 3p6 4s2 3d3
Try chlorine right now
Cl: 1s2 2s2 2p6 3s2 3p5
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Shorthand Electron Configurations
use noble gases as a starting point
e.g. for vanadium: V: [Ar] 4s2 3d3
for chlorine: Cl: [Ne] 3s2 3p5
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The Power of What You Now Know
You have seen that the periodic table isexplained for you as never before
Charges of ions can be explained
e.g. lead Pb: 6s2 4f14 5d10 6p2
Pb2+ ion: remove two electrons from 6p
Pb4+ ion: remove two electrons from 6p
and two electrons from 6s
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