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

Options

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.

Answer

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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