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In the absence of external magnetic fiel...

In the absence of external magnetic field, d-orbital is

A

`3-`fold degenerate

B

Non-degenerate

C

`5-`fold degenerate

D

`7-`fold degenerate

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**Step-by-Step Solution:** 1. **Understanding d-Orbitals**: - The d-orbitals consist of five different types: \(d_{xy}\), \(d_{yz}\), \(d_{xz}\), \(d_{x^2-y^2}\), and \(d_{z^2}\). 2. **Effect of Magnetic Field**: - When an external magnetic field is applied, these d-orbitals become non-degenerate, meaning they split into different energy levels. This is due to the interaction of the magnetic field with the electrons in the d-orbitals. 3. **Absence of Magnetic Field**: - In the absence of an external magnetic field, the d-orbitals do not experience this splitting. Therefore, they all remain at the same energy level. 4. **Degeneracy of d-Orbitals**: - Since all five d-orbitals are at the same energy level in the absence of a magnetic field, they are said to be degenerate. Specifically, they are referred to as "5-fold degenerate" because there are five orbitals. 5. **Conclusion**: - Therefore, in the absence of an external magnetic field, the d-orbitals are 5-fold degenerate. **Final Answer**: In the absence of external magnetic field, d-orbital is 5-fold degenerate. ---

**Step-by-Step Solution:** 1. **Understanding d-Orbitals**: - The d-orbitals consist of five different types: \(d_{xy}\), \(d_{yz}\), \(d_{xz}\), \(d_{x^2-y^2}\), and \(d_{z^2}\). 2. **Effect of Magnetic Field**: - When an external magnetic field is applied, these d-orbitals become non-degenerate, meaning they split into different energy levels. This is due to the interaction of the magnetic field with the electrons in the d-orbitals. ...
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