The document outlines the different quantum numbers that describe the characteristics of electrons in an atom, including principal (n), angular momentum (l), magnetic (ml), and spin (ms) quantum numbers. Each quantum number provides specific information about the electron's energy level, subshell, orbital orientation, and spin direction. The document includes details on the maximum number of electrons in shells and subshells, as well as the shapes of orbitals associated with each quantum number.

2. • Principal Quantum Number (n)
• Angular Momentum Quantum Number (l)
• Magnetic Quantum Number (ml)
• Spin Quantum Number (ms)
Quantum Numbers
Describes the location and energy of an electron
in an atom.

3. Principal Quantum Number
(n)
• Represents the Shells of an Electron.
• Determines Energy Level of an Electron.
• Maximum Number of Electrons in a given Shell = 2n2
• n (shell number) = 1, 2, 3, 4…
Shell (n) Maximum no. of Electrons
1 2
2 8
3 18
4 32

4. Angular Momentum Quantum
Number
• Represents the Subshells of an Electron.
• Determines the Angular Momentum of an Electron.
• Number of Sub-Shells (l) = n
• l (sub-shell) = 0, 1, 2, 3……(n-1)
n l Number of Sub-Shells
1 0 1
2 0, 1 2
3 0, 1, 2 3
4 0, 1, 2, 3 4
(l)

5. Orbitals
• Maximum Number of Electrons in a given Sub-
Shell = 2 x (2l + 1)
l Orbital Number of
electrons
0 s 2
1 p 6
2 d 10
3 f 14
A region of probability where an electron can
be found.

6. Magnetic Quantum Number
• Determines the Number of Types/Orientation of Orbitals.
• Number of Orientation of Orbitals (ml) = (2l+1)
• ml = -l,……..0……,+l
l ml Number of Orbitals
0 (s) 0 1
1(p) -1, 0, 1 3
2(d) -2, -1, 0, 1, 2 5
3(f) -3, -2, -1, 0, 1, 2, 3 7
(ml)

7. Orbitals
• Number of Orbitals for a given Shell = n2
Shell (n) Number of Orbitals Set of Orbitals
1 1 1s
2 4 2s 2px, 2py, 2pz
3 9 3s 3px, 3py, 3pz 3dxy, 3dyz,
3dxz, 3dz
2
, 3dx2-y2

8. Shapes of Orbitals

9. Spin Quantum Number
• Represents the Direction of Spin of an Electron
on its own Axis.
• Electrons can Spin either Clockwise ↑ or
Anticlockwise ↓ Direction.
• ms =-1/2 or +1/2
(ms)

10. Principal
Q.N. (n)
Angular
Momentum Q.N.
(l)
Magnetic Q.N. (ml) Spin
Q.N.
(ms)
Designation
of Orbital
1 0 0 ± ½ 1s
2 0
1
0
-1, 0, +1
± ½
± ½
2s
2p
3 0
1
2
0
-1, 0, +1
-2, -1, 0, +1,+2
± ½
± ½
± ½
3s
3p
3d
4 0
1
2
3
0
-1, 0, +1
-2, -1, 0, +1,+2
-3, -2, -1, 0, +1,+2, +3
± ½
± ½
± ½
± ½
4s
4p
4d
4f
Permissible Values of Q.N.