Present as at Ion 1

8/6/2019 Present as at Ion 1

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QUANTUM MODEL OF AN ATOM

By , Lakshya

Prashant and

Sahil



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



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



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



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



““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



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



“s” orbital

As the value of l is 0 heretherefore m

l =0 and

2(0)+1=1 s orbital



“p” orbital

Since the value of l is 1 here therefore the

value of ml =2(1)+1=3 p orbitals



“d” orbital

Here the value of l =2 therefore ml = 2(2)+1= 5 d

orbitals



“f” orbital Here ml = 2(3) +1 = 7 f orbitals



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



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



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



•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



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)



The order is: 1s< 2s< 2p< 3s< 3p< 4s< 3d,< 4p< 5s< 4d<…



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



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.



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



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.



2px 2py 2pz

+1/2

-1/2

Diagram of hund’s rule



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



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



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



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.



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.



1s 2s 2p

To simplify the process of writing the electronic



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.



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

Present as at Ion 1

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