Quantum Mechanical Model Of Atom

Answer: Option 4: spin quantum number

Explanation:

According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of all four quantum numbers. When two electrons occupy the same atomic orbital, they share the same:

• Principal quantum number (n): same energy level
• Azimuthal quantum number (l): same subshell (s, p, d, f)
• Magnetic quantum number (m_l): same orbital orientation

The only quantum number that differs between them is the spin quantum number (m_s), which can have values of +½ or –½. This opposite spin allows both electrons to exist in the same orbital.

The energy of an electron is primarily determined by the principal quantum number (n) and then the azimuthal quantum number (l). Lower n and l values correspond to lower energy.
For the same n, lower l has lower energy. If n and l are same, then energy depends on spin, lower energy for -1/2.
Let’s analyze the electrons:
I. (n=4, l=2)
II. (n=3, l=2)
III. (n=4, l=1)
IV. (n=3, l=1)
Thus, I > III and II > IV based on n and l. Also, I > II and III > IV as n is higher for I and III respectively. Thus, I>III>II>IV