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QUANTUM MODEL OF AN ATOM
By , Lakshya
Prashant and
Sahil
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Quantum MechanicsQuantum Mechanics
In the quantum model, the nucleus is notIn the quantum model, the nucleus is notsurrounded by orbits, but by atomic orbitalsurrounded by orbits, but by atomic orbital
Atomic Orbital: a 3-d (three dimensional) regionAtomic Orbital: a 3-d (three dimensional) region
about the nucleus where a certain electron can beabout the nucleus where a certain electron can belocatedlocated
These orbital can be thought of as “clouds”These orbital can be thought of as “clouds”
The size and shape of the electron clouds dependThe size and shape of the electron clouds depend
on the occupying electrons’ energieson the occupying electrons’ energies
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Quantum Numbers specify the properties
of atomic orbital and their electrons
There are four quantum numbers:
principal quantum number
orbital quantum number
magnetic quantum number
spin quantum number
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The principal quantumThe principal quantum
number (number (nn
))
•It specifies the main energy levelsIt specifies the main energy levels
around the nucleusaround the nucleus
•AsAs nn increases, the distance from theincreases, the distance from the
nucleus increasesnucleus increases
•Currently the values forCurrently the values for nn are 1 to 7are 1 to 7
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Orbital Quantum Number (Orbital Quantum Number (l l ))
•It indicates the shape of the orbital where theIt indicates the shape of the orbital where the
electron can be foundelectron can be found
•These orbitals are called subshells or sublevelsThese orbitals are called subshells or sublevels
•The four most common orbital quantumThe four most common orbital quantum
numbers are given letter abbreviationsnumbers are given letter abbreviations
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““l l ” values range from” values range from
0 to (n-1)0 to (n-1)
Orbital QuantumOrbital QuantumNumbers:Numbers:
l l = 0, s orbital= 0, s orbital
l l = 1, p orbital= 1, p orbital
l l = 2, d orbital= 2, d orbital
l l = 3, f orbital= 3, f orbital
n l Subshell
Notation
1 0 1s
2 0 2s
2 1 2p
3 0 3s
3 1 3p
3 2 3d
4 0 4s
4 1 4p
4 2 4d
4 3 4f
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Magnetic Quantum Number (MMagnetic Quantum Number (Ml l ))
• Indicates the orientation of an orbital about the nucleusIndicates the orientation of an orbital about the nucleus
•It tells which axis that sublevel is located on (x, y, or zIt tells which axis that sublevel is located on (x, y, or zaxis)axis)
•ml ranges from -ml ranges from - l l toto l l
•For any subshell 2l + 1 values of ml are possible
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“s” orbital
As the value of l is 0 heretherefore m
l =0 and
2(0)+1=1 s orbital
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“p” orbital
Since the value of l is 1 here therefore the
value of ml =2(1)+1=3 p orbitals
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“d” orbital
Here the value of l =2 therefore ml = 2(2)+1= 5 d
orbitals
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“f” orbital Here ml = 2(3) +1 = 7 f orbitals
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Spin Quantum Number (MSpin Quantum Number (M s s):):
•It indicates the two possible states of anIt indicates the two possible states of an
electronelectron
•Values are + 1/2 or –1/2Values are + 1/2 or –1/2
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Energies of OrbitalsEnergies of Orbitals
•The energy of electron depends only on
the positively charged nucleus and thenegatively charged electron.
Therefore the energy of orbitals only
depend on the principal quantum number
and hence the energies of orbitals
increases as follows:
1s<2s=2p<3s=3p=3d<4s=4p=4d=4f <…..
•For mono electronic atom _ _ _ _ _ _ _ _
3s 3p 3d
_ _ _ _
2s 2p
_
1s
e n e r g y
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Energies of orbitalsEnergies of orbitals
The energy of orbitals of a multi-electron
atom is determined by the principal
quantum number and by the azimuthalquantum number. There are different
energies of the subshells because there is
attraction between the electron and the
nucleus as well as repulsion among the
other electrons present in the atom
•For multi-electronic atoms
_ _ _ _ _
3d
_
4s
_ _ _
3p
_
3s
_ _ _
2p
_
2s
_ 1s
e n e r g y
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•Lowest energy is determined by the n + l rule.
That is, the sum of those two quantum numbers
determines the lowest energy, the lower the sum
the lower the energy. If the sums are equal (theorbitals are called degenerate), the lowest value of
n determines the lowest energy.
n + l
1 + 0 = 1 1s
2 + 0 = 2 2s
2 + 1 = 3 2p3 + 0 = 3 3s
there is a tie, the 2p is lower than the 3s because
n=2 is less than n=3
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3 + 1 = 4 3p
3 + 2 = 5 3d
4 + 0 = 4 4s
4 + 1 = 5 4p
there are 2 ties, the 4s is higher than the 3p
because n=4 is GREATER than n=3 and the 4s
(sum = 4) comes before the 3d (sum = 5)
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The order is: 1s< 2s< 2p< 3s< 3p< 4s< 3d,< 4p< 5s< 4d<…
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Filling of orbitalsFilling of orbitals
To fill the orbitals of an atom there are certain set
of rules which have to be followed
Aufbau principle :- (means building-up in
German) in the ground state, the electrons will
fill the atomic orbital of lowest energy.
ORDER OF FILLING ENERGYORDER OF FILLING ENERGY
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ORDER OF FILLING ENERGYORDER OF FILLING ENERGY
LEVELSLEVELS
1s1s
2s2s 2p2p3s3s 3p3p
The diagramexplains that
the orbital
having thelowest energy
is filled first
and then the
electrons are
filled in the
other orbital.
The arrows mark the filling of
orbitals in their increasing order of
energy.
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Pauli Exclusion Principle :-
No two electrons in the same atom can have the same
set of all 4 quantum numbers.
Only two electrons may exist in the same orbital and
these electrons must have opposite spin.
This helped in formulating a new formula for
calculating the no. of electrons in a shell is 2n2
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Hund’s rule of maximum multiplicity :-
•Electrons occupy all the orbitals of a given
sublevel singly before pairing begins.
•Spins of electrons in different incomplete
orbitals are parallel in the ground state.
•The most stable arrangement of electrons in
the subshells is the one with the greatest
number of parallel spins.
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2px 2py 2pz
+1/2
-1/2
Diagram of hund’s rule
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Electron configurations – the
ground state
Element Electron configuration
1H 1s1
2He 1s2
3Li 1s22s1
4Be 1s22s2
5B 1s22s22p1
6C 1s22s22p2
7N 1s
2
2s
2
2p
3
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8O 1s22s22p4
9F 1s22s22p5
10 Ne 1s22s22p6
11 Na 1s22s22p63s1
12
Mg 1s22s22p63s2
13 Al 1s22s22p63s23p1
14 Si 1s22s22p63s23p2
15 P 1s2
2s2
2p6
3s2
3p3
16 S 1s22s22p63s23p4
17 Cl 1s22s22p63s23p5
18 Ar 1s2
2s2
2p6
3s2
3p6
K 1 22 22 63 23 64 1
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19 K 1s22s22p63s23p64s1
20 Ca 1s22s22p63s23p64s2
21 Sc 1s22s22p63s23p64s23d1
22 Ti 1s22s22p63s23p64s23d2
23 V 1s
2
2s
2
2p
6
3s
2
3p
6
4s
2
3d
3
24 Cr 1s22s22p63s23p64s13d5
There is a tendency toward half-filled and completely filled dsubshells. This is a consequence of the closeness of the 3d and the 4s
orbital energies. The half filled and fully filled orbitals have a
symmetry in the electrons and are more stable because they have
maximum no. parallel spins and there for have less interaction
between them.
24 Cr 1s22s22p63s23p64s23d4
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29Cu 1s22s22p63s23p64s13d10 Another example is Cu where electron from lowerenergy level jumps to the higher energy level to
attain stability by filling the d orbital completely
and thus attaining stability.
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Orbital diagram and noble gasOrbital diagram and noble gas
configurationsconfigurations
In the orbital diagrams each orbital of the subshell
is represented by a box and the electron is
represented by an arrow a positive spin or anarrow a negative spin.
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1s 2s 2p
To simplify the process of writing the electronic
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To simplify the process of writing the electronic
configurations we can represent the total no. of first
two shells by the name of the element [Ne] because the
elements between Na and Ar the first two shells will
have the same configuration as Ne as it is a noble gas.
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ELECTRON
CONFIGURATIONS OF IONSElectrons do not come out the same way as we
put them in according to the Aufbau Principle.
Electrons leave the outer most shell first.
Let's look at V vs V2+
23 V 1s
2
2s
2
2p
6
3s
2
3p
6
4s
2
3d
3
23 V2+ 1s22s22p63s23p63d3