Quantum numbers

1. Quantum numbers
Course: B.Sc. Microbiology
Sem II
Sub: Inorganic Chemistry
Unit 1.1

2. The Three Physicists
• Louie de Broglie
• Erwin Schrodinger
• Werner Karl Heisenberg
Quantum Mechanical Model

3. The Quantum Mechanical
Model
ELECTRON
CLOUDS
The probability of finding an electron in the
region around the nucleus of an atom can
be represented in many ways.

4. Number of sublevels in a main
energy level is the same as the
assigned main energy level.
SHELLS
Energy levels
The Atom a.k.a The Condo

5. Main Energy Level Number of
Sublevels
1 (lowest energy) 1
2 2
3 3
4 4

6. Sublevel Number of
Orbitals
s 1
p 3
d 5
f 7
g 9

7. Sublevel Number of
Orbitals
s 1
p 3
d 5
DEGENERATE ORBITALS
Orbitals of the same energy

8. Quantum Numbers
• According to Heisenberg’s Uncertainty
Principle, it is not possible to give the
exact position of an electron and its
energy at the same time.
• But the probability of finding an electron in
an orbital of given energy can be
determined.

9. • In atom : large of orbitals are possible.
• Orbitals : differ in size, shape & orientation
in space around the nucleus.
• State of e in atom: its location with respect
to the nucleus & its energy.
• Permissible state of an e : orbitals
• Quantum numbers.

10. The 4 Quantum Numbers
• Principal Quantum Number, n
• Azimuthal Quantum Number, l
• Magnetic Quantum Number, ml
• Spin Quantum Number, ms

11. Principal Quantum Number
• Determines Main energy level of an orbital
- shell
• An increase in n also means increase in
the energy of the electron in the orbital.
• n= 1, 2, 3….
• Maximum no.of electrons = 2n^2

12. Azimuthal Quantum Number
• Also called Angular Momentum Number
• Defines the shape of the orbital
• Values range from 0 to n-1

13. Azimuthal Quantum Number
l Sublevel Orbital Shape
0 s(harp) Spherical
1 p(rincipal) dumbbell-
shaped
2 d(iffused) Cloverleaf
3 f(undamental) Too complex

14. Azimuthal Quantum Number
• A sublevel in a particular main energy
level is defined by its n and its l values.
n l Kind of
Sublevel
1 0 1s
3 1 3p

15. Magnetic Quantum Number, ml
• Charged particle – in motion: produce magnetic field
• Magnetic field value represented by,ml
• Describes the orientation of the orbital in space
• Values are –l to +l
• Values per sublevel = 2l +1

16. • two orbitals in same shell-identical value, but they
must have different values of m.
• -nce of magnetic field – all orbitals having same
value of n & l, but different values of m: same
energies.
• Moving e- : small magnetic field
• When external magnetic field is applied, interaction
occur & e- : orient themselves.
• This changes energies slightly.

17. Magnetic Quantum Number, ml
Sublevel Type l ml
s 0 0
p 1 -1,0,+1
d 2 -2,-1,0,1,2

18. Spin Quantum Number, ms
• Spin of the electron
• e- two types of motion.
• 1. orbital & 2. axial motion
• Values are +1/2 and -1/2
• Clockwise and Counterclockwise
• Opposite spins because of Pauli Exclusion Principle

19. nn shellshell ll subshellsubshell mmll
#orbitals#orbitals
#e#e––
11 KK 00 ss 00 11 22
22 LL 00 ss 00 11 22
11 pp ––1,0,11,0,1 33 66
33 MM 00 ss 00 11 22
11 pp ––1,0,11,0,1 33 66
88
22 dd -2,-1,0,1,2-2,-1,0,1,2 55 1010
1818
44 NN 00 ss 00 11 22
11 pp ––1,0,11,0,1 33 66
22 dd -2,-1,0,1,2-2,-1,0,1,2 55 1010
33 ff -3,-2,-1,0,1,2,3-3,-2,-1,0,1,2,3 77 1414
3232
n2
1
4
9
16
Max

20. Shapes of atomic orbitals
• Atomic orbitals
• Probability(Ψ2) : distribution of e- cloud in
the space.
• Density of e- cloud = probability of finding
e-
• Probability of finding e- : not same
• Orbitals : not have a rigid boundary
• Atom : definite size.

21. S orbital

22. Shapes of S-orbitals:sphere
• For s-orbitals, l=0 (ns)
• Distribution of e- density = symmetrical
• Probability of finding an e- : same at all angles.
• Sphere-no exact radius
• n increases : s orbital –larger
• Total no. of concentric sphere = n.
• For e.g., 1s = 1 sphere
2s = 2 sphere
Energy of s-orbital increses = n

23. P-orbitals(dumb-bell)
• l=1, m=-1, 0, +1
• Distribution of e- density: not spherical
• Same shape but directions are different.
• For 2p orbitals, e- density is maximum along the orbital
axis.
• e- density at nucleus = zero.
• Node & nodal plane.
• Size of p-orbital is increses with n.
• Lobes of 3p is bigger than 2p.

24. Shapes of d-orbitals
• l=2
• d = not show spherical
• Five different space orientation.

25. References
• Essentials of Physical chemistry by Bahl Arun, S Chand, 2012
• General chemistry by Ebbing Darrell D, 5th
, A I T B S Publishers,
2002