Question

Identify the degenerated orbitals

• A. \(2p_x\ 2p_y\  2p_z\)
• B. \(2s, 3s, 4s\)
• C. \(3p_x\ 3p_y\  3p_z\)
• D. Both (1) and (3)

Answer 1

The Correct Option is D

The term "degenerated orbitals" refers to orbitals that have the same energy level. In an atomic subshell, orbitals like \(p_x\), \(p_y\), and \(p_z\) are examples of degenerated orbitals as they are energetically equivalent when not in the presence of an external field. Let us evaluate the given options:

\(2p_x, 2p_y, 2p_z\): These orbitals are within the same 2p subshell and hence have the same energy in an isolated atom situation, making them degenerate.

\(2s, 3s, 4s\): These are different energy levels; as s orbitals in different principal quantum numbers (n) are not degenerate.

\(3p_x, 3p_y, 3p_z\): Similar to the 2p case, these are within the same 3p subshell, thus they are degenerate.

Both (1) and (3): Both sets of \(p\) orbital triplets are degenerate under normal atom conditions without external fields or inter-electronic interactions involving differences in symmetry.

Hence, the correct answer is "Both (1) and (3)" because both the \(2p\) and \(3p\) subshell orbitals are degenerate.

Answer 2

Orbitals are said to be degenerate if they have the same energy level.

In a given subshell, the orbitals like \( p_x \), \( p_y \), and \( p_z \) are degenerate because they differ only in orientation, not in energy.

• \(2p_x, 2p_y, 2p_z\) → same energy ⇒ degenerate
• \(2s, 3s, 4s\) → different energy levels ⇒ not degenerate
• \(3p_x, 3p_y, 3p_z\) → same energy ⇒ degenerate

Correct Answer: Both (1) and (3)