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In a 3d subshell, all the five oprbitals...

In a 3d subshell, all the five oprbitals are degenerate. What does it mean?

A

All the orbitals have the same3 orientation.

B

All the orbitals have the same shape.

C

All the orbitals have the same energy.

D

All the orbitals are unoccupied.

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The correct Answer is:
To understand the concept of degeneracy in the context of the 3d subshell, let's break it down step by step. ### Step-by-Step Solution: 1. **Identify the Subshell and Orbitals**: - The question refers to the 3d subshell, which contains five d orbitals. These orbitals are designated as \(d_{xy}\), \(d_{xz}\), \(d_{yz}\), \(d_{x^2-y^2}\), and \(d_{z^2}\). 2. **Understand Quantum Numbers**: - Each orbital is defined by quantum numbers: the principal quantum number \(n\) and the azimuthal quantum number \(l\). - For the 3d subshell: - The principal quantum number \(n = 3\). - The azimuthal quantum number \(l = 2\) (since d orbitals correspond to \(l = 2\)). 3. **Calculate the \(n + l\) Value**: - The \(n + l\) value for the 3d subshell is calculated as follows: \[ n + l = 3 + 2 = 5 \] 4. **Degeneracy of Orbitals**: - Orbitals are said to be degenerate when they have the same energy level. Since all five d orbitals in the 3d subshell have the same \(n + l\) value of 5, they are considered degenerate. - This means that all five d orbitals have the same energy. 5. **Conclusion**: - Therefore, the term "degenerate" in the context of the 3d subshell means that all five d orbitals have the same energy. ### Final Answer: In a 3d subshell, all five orbitals are degenerate, meaning they have the same energy. ---
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