Quantum Numbers, Electrons, Quantum State, Principal Quantum Number, Orbital Quantum Number

1. Pauli’s Exclusion Principle
Dr.M.Sankareswari
Assistant Professor of Physics
VVVanniaperumal College for Women
Virudhunagar

2. Pauli’s Exclusion Principle
Statement:
No two electrons in an atom exist in the same quantum state.
The state of an electron can be completely determined by four
quantum numbers n, l, ml, ms.
“No two electrons in an isolated atom may have the same four
quantum numbers”
Explanation
If two electrons of an atom have identical quantum numbers (n,
l, ml, ms), then one of those electrons would be excluded from
entering into the constitution of the atom. Hence it is called as
“exclusion principle”.

3. Pauli’s Exclusion Principle
Application:
This principle enables us to calculate the number of electrons in
a subshell.
1) Consider the K-shell with n = 1, l = 0 hence ml= 0.
Since S = ½ ; ms can be either +1/2 or -1/2.Hence K shell can
have 2 electrons; one electron with quantum numbers n = 1, l =
0, ml = 0, ms = +1/2 and another electron with quantum numbers
n = 1, l = 0, ml = 0, ms = -1/2
K-shell is completed with 2 electrons.

4. Pauli’s Exclusion Principle
2) Consider the L-shell with n = 2, l = 0 or 1. For l = 0, ml= 0, ms
can be either +1/2 or -1/2. There are two electrons in this sub
shell.
With n = 2, l = 1, ml= -1, 0, +1. For each of these ml value,
ms can be either +1/2 or -1/2. There are six electrons in this sub
shell.
Hence L-shell is completed with 8 electrons.

5. Pauli’s Exclusion Principle
3) Consider the M-shell with n = 3, l = 0, 1, 2. For l = 0, ml= 0, ms
can be either +1/2 or -1/2. There are two electrons in this sub
shell.
With n = 3, l = 1, ml= -1, 0, +1. For each of these ml value,
ms can be either +1/2 or -1/2. There are six electrons in this sub
shell.
With n = 3, l = 2, ml= -2, -1, 0, +1, +2. For each of these ml
value, ms can be either +1/2 or -1/2. There are ten electrons in
this sub shell.
Hence M-shell is completed with 18 electrons.

6. Pauli’s Exclusion Principle
3) Consider the N-shell with n = 4, l = 0, 1, 2, 3. For l = 0, ml= 0,
ms can be either +1/2 or -1/2. There are two electrons in this sub
shell.
With n = 4, l = 1, ml= -1, 0, +1. For each of these ml value,
ms can be either +1/2 or -1/2. There are six electrons in this sub
shell.
With n = 4, l = 2, ml= -2, -1, 0, +1, +2. For each of these ml
value, ms can be either +1/2 or -1/2. There are ten electrons in
this sub shell.
With n = 4, l = 3, ml= -3, -2, -1, 0, +1, +2, +3. For each of
these ml value, ms can be either +1/2 or -1/2. There are fourteen
electrons in this sub shell.
Hence M-shell is completed with 18 electrons.

7. Pauli’s Exclusion Principle
Conclusions:
i) The maximum number of electrons in a sub-shell with a
given value of l is 2(2l + 1). The sub shells are denoted by s,
p, d, f, g ---
ii) The number of electrons that can be accommodated in a
shell with principal quantum number = Sum of the
electrons in the constituent n subshells = 2n2.
The shells are denoted by K, L, M, N, O---

8. Pauli’s Exclusion Principle
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