quantum numbers structure 2

8/22/2019 Quantum Numbers Structure 2

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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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quantum numbers structure 2

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