THE QUANTUM NUMBERS
&
SHAPES OF ORBITALS
CHAPTER # 2
ATOMIC STRUCTURE
DRAWBACKS OF BOHR’S
ATOMIC MODEL
• Objections were being made on Bohr’s
atomic model about:
– the movement of electrons in 3D space
– spectra of poly electronic atoms.
• Bohr’s atomic model failed to justify
these objections.
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Erwin Rudolf Schrödinger
o In 1926, Erwin Rudolf
Schrödinger, gave the
idea that of wave
motion of electron
o Nobel Prize in Physics
in 1933
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Schrödinger Equation
o He formulated an equation called “the
Schrödinger equation”, in which electrons
are treated as moving with wave like
motion in 3D space around the nucleus.
o The solution of Schrödinger Equation
gave a set of numerical values.
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“The Quantum Numbers”
o Explained the arrangement and
movement of electrons, spectral lines of
poly electronic atoms and gave an
acceptable model of an atom.
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The 4 Quantum Numbers An Electron’s Address
o Principal Quantum Number (n)
oSpecifies the main energy level (orbit)
o Azimuthal Quantum Number (l)
oInformation about the sub energy level
(orbital)
o Magnetic Quantum Number (m)
oSpatial orientations of an orbital
o Spic Quantum Number (s)
oSpin movement of electrons
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Principal Quantum Number (n)
o Size & Energy of an
orbit/shell
o n=1, 2, 3, 4,….
o Greater value of n
represents Bigger orbits
with high energies
o Distance from the
nucleus also increases.
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Principle Quantum Number (n)
Total No. of Electrons in an orbit = 2n2
Value of n
Name of
Shell
Total No. of Electrons
2n2
n=1
K
2(1)2 =
2
n=2
L
2(2)2 =
8
n=3
M
2(3)2 =
18
n=4
N
2(4)2 =
32
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Azimuthal Quantum Number (l)
o Each energy level is divided into sub
levels.
o l defines the shape of sub energy
level/orbital
l
0
1
2
3
Sub
level
s
p
d
f
Name
Sharp
Principal
Diffused
Fundamental
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No. of
electrons
2
6
10
14
Relationship between n & l
l = 0  (n-1)
Orbit
n
l
Orbitals
No. of
electrons
K
1
0
1s
2
L
2
0, 1
2s, 2p
2+6 = 8
M
3
0, 1, 2
3s, 3p, 3d
2+6+10= 18
N
4
0, 1, 2, 3 4s, 4p, 4d, 4f 2+6+10+14=32
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Increasing Energy & Size
n
l
4f (14 electrons)
n=4 , N shell
4d (10 electrons)
4p (6 electrons)
4s (2 electrons)
n=3 , M shell
n=2 , L shell
n=1 , K shell
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3d (10 electrons)
3p (6 electrons)
3s (2 electrons)
2p (6 electrons)
2s (2 electrons)
1s (2 electrons)
Magnetic Quantum Number (m)
o Explains the effect of an orbital in
magnetic field i.e. the orientation of an
orbital
o Orbitals split up into degenerate
orbitals (having same energy & size) in a
magnetic field
o Each degenerate orbital can hold up to 2
electrons
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Relationship between l & m
m = -l  0  +l
l
m
l = 0, s
l = 1, p
0
-1, 0, +1
-2, -1, 0, +1,
+2
l = 2, d
l = 3, f
Degenerate
orbitals
No. of
electrons
1
3
2
2+2+2 = 6
2+2+2+2+
2 = 10
2+2+2+2+
2+2+2 =
14
-3, -2, -1, 0,
+1, +2, +3
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5
7
Increasing Energy & Size
n
n=4 , N shell
l=3, 4f
l=2, 4d
l=1, 4p
l=0, 4s
n=3 , M shell
l=2, 3d
l=1, 3p
l=0, 3s
n=2 , L shell
n=1 , K shell
m
l
l=1, 2p
l=0, 2s
l=0, 1s
m=-3 m=-2 m=-1 m=0 m=+1 m=+2 m=+3
m=-2 m=-1 m=0 m=+1 m=+2
m=-1 m=0 m=+1
m=0
m=-2 m=-1 m=0 m=+1 m=+2
m=-1 m=0 m=+1
m=0
m=-1 m=0 m=+1
m=0
m=0
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Spin Quantum Number (s)
o Direction of spin of an electron
o Electron which rotates around the
nucleus also rotates around its own axis
o This is called self rotation
o Either Clockwise (50%) or anticlockwise
(50%)
o s = -1/2 (↑) for clockwise
o s = +1/2 (↓) for anticlockwise
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Spin of electron
Associated with magnetic field
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Orbital Diagrams
o We often represent an orbital as a square
and the electrons in that orbital as arrows.
o The direction of the arrow represents the spin of
the electron.
Unoccupied
orbital
Orbital with
1 electron
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Orbital with
2 electrons
4f14
4d10
4p6
4s2
Increasing Energy
N shell
3d10
M shell
2p6
2s2
L shell
K shell
1s2
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3p6
3s2
Orbit
o The circular path of
an electron around
the nucleus is called
an orbit.
o The orbit or shells
are denoted by K, L,
M, N etc
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Electron Cloud
A cloud showing
the probability of
finding the
electron in terms
of charged cloud
around the nucleus
is called Electron
Cloud.
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Atomic Orbitals: s, p, d, f
o Atomic orbitals are regions of space
where the probability of finding an
electron about an atom is highest.
o s orbital
o p orbital
o d orbital
o f orbital




spherical shape
dumb-bell shape
clover leaf shape
double clover leaf
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s orbital - spherically symmetric
l= 0 and m =
0
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p orbital - dumbbell shaped
l = 1 m = -1,0,+1
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d orbital shapes
l= 2 m = -2,-1,0,+1,+2
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l=3
f orbital shapes
m = -3,-2,-1,0,+1,+2, +3
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The End
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