Planck S Quantum Theory

The statement "No two electrons in an atom can have the same set of four quantum numbers" is known as the:

Pauli's Exclusion Principle

This principle was formulated by Wolfgang Pauli in 1925 and is fundamental to understanding electron configurations in atoms.

According to this principle, each electron in an atom is described by a unique set of four quantum numbers:

• n: Principal quantum number
• l: Azimuthal (angular momentum) quantum number
• m_l: Magnetic quantum number
• m_s: Spin quantum number

Correct Answer: (C) Pauli's exclusion principle

We are given the principal quantum number n = 3 and spin quantum number m_s = +1/2.

For n = 3, the possible values of the azimuthal quantum number l are:

• l = 0 (s-subshell)
• l = 1 (p-subshell)
• l = 2 (d-subshell)

Each subshell has the following number of orbitals:

• s: 1 orbital
• p: 3 orbitals
• d: 5 orbitals

Total orbitals for n = 3: 1 + 3 + 5 = 9

Each orbital can hold 2 electrons, one with spin +1/2 and one with spin -1/2.

So, the number of electrons with m_s = +1/2 will be:

9 orbitals × 1 electron per orbital = 9 electrons

Correct Answer:

Correct Answer: (A) 9

Step 1: The azimuthal quantum number determines the shape of the subshell.
Step 2: For example, corresponds to an -orbital (spherical), corresponds to a -orbital (dumbbell-shaped), and so on.
Step 3: Thus, the shape of the subshell is determined by the azimuthal quantum number.