1) Erwin Schrodinger developed quantum mechanics and formulated the Schrodinger equation in 1926, which treats electrons as waves rather than particles. 2) The Schrodinger equation led to the discovery of quantum numbers that describe electron behavior and allowed for a more accurate model of atomic structure. 3) There are four quantum numbers - the principal quantum number (n) describes the electron shell or energy level, the azimuthal quantum number (l) describes the subshell shape, the magnetic quantum number (m) describes spatial orientation, and the spin quantum number (s) describes electron spin.

1. THE QUANTUM NUMBERS
&
SHAPES OF ORBITALS
CHAPTER # 2
ATOMIC STRUCTURE

2. 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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3. 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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4. 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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5. “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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6. The 4 Quantum Numbers -
An Electron’s Address
oPrincipal Quantum Number (n)
oSpecifies the main energy level (orbit)
oAzimuthal Quantum Number (l)
oInformation about the sub energy level
(orbital)
oMagnetic Quantum Number (m)
oSpatial orientations of an orbital
oSpic Quantum Number (s)
oSpin movement of electrons
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7. 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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8. 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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9. Azimuthal Quantum Number (l)
o Each energy level is divided into sub
levels.
o l defines the shape of sub energy
level/orbital
l
Sub
level
Name
No. of
electrons
0 s Sharp 2
1 p Principal 6
2 d Diffused 10
3 f Fundamental 14
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10. 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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11. n=1 , K shell
n=2 , L shell
n=3 , M shell
n=4 , N shell
1s (2 electrons)
2s (2 electrons)
2p (6 electrons)
3s (2 electrons)
3p (6 electrons)
3d (10 electrons)
4s (2 electrons)
4p (6 electrons)
4d (10 electrons)
4f (14 electrons)
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n l

12. 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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13. Relationship between l & m
m = -l  0  +l
l m
Degenerate
orbitals
No. of
electrons
l = 0, s 0 1 2
l = 1, p -1, 0, +1 3 2+2+2 = 6
l = 2, d
-2, -1, 0, +1,
+2
5
2+2+2+2+
2 = 10
l = 3, f
-3, -2, -1, 0,
+1, +2, +3
7
2+2+2+2+
2+2+2 =
14
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14. n=1 , K shell
n=2 , L shell
n=3 , M shell
n=4 , N shell
l=0, 1s
l=0, 2s
l=1, 2p
l=0, 3s
l=1, 3p
l=2, 3d
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m=0
m=0
m=0
m=0
m=-1 m=+1m=0
m=-1 m=+1m=0
m=-1 m=+1m=0
m=-1 m=+1m=0m=-2 m=+2
m=-1 m=+1m=0m=-2 m=+2
m=-1 m=+1m=0m=-2 m=+2m=-3 m=+3
l=0, 4s
l=1, 4p
l=2, 4d
l=3, 4f
n l m

15. 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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16. Spin of electron
Associated with magnetic field
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17. 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.
Orbital with
1 electron
Unoccupied
orbital
Orbital with
2 electrons
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18. Prepared By: Sidra Javed
IncreasingEnergy
1s2
2s2
3s2
4s2
2p6
3p6
4p6
3d10
4d10
4f14
K shell
N shell
M shell
L shell

19. 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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20. 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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21. 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  spherical shape
o p orbital  dumb-bell shape
o d orbital  clover leaf shape
o f orbital  double clover leaf
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22. s orbital - spherically symmetric
l= 0 and m =
0
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23. p orbital - dumbbell shaped
l = 1 m = -1,0,+1
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24. d orbital shapes
l= 2 m = -2,-1,0,+1,+2
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25. f orbital shapes
l = 3 m = -3,-2,-1,0,+1,+2, +3
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26. The End
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