To identify the correct ascending order of energies of orbitals, we need to understand the principles governing the energy levels of atomic orbitals. This involves the concepts of principal quantum number ( ) and penetration effect.
Step 1: Understanding Orbital Energies
The energy of an orbital depends primarily on two factors:
1. Principal Quantum Number ( ): Orbitals with a lower value have lower energy.
2. Penetration Effect: Within the same shell ( ), the energy of orbitals depends on their angular momentum quantum number ( ). The order of increasing energy for orbitals within a shell is .
However, when comparing orbitals from different shells, the overlap of energy levels can occur due to the penetration effect. Specifically:
- For , the and orbitals are lower in energy than the orbital.
- The orbitals have higher energy than the orbital but lower energy than the orbitals.
Step 2: Analyzing the Given Orbitals
We are tasked with ordering the following orbitals in ascending order of energy:
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Key Points:
1. : Within the same shell ( ), orbitals are always lower in energy than orbitals.
2. : Due to the penetration effect, the orbital has lower energy than the orbitals. This is because the electrons penetrate closer to the nucleus compared to the electrons.
3. : The orbital is lower in energy than the orbitals but higher in energy than the orbitals.
Step 3: Correct Order
Based on the above reasoning, the correct ascending order of energies is:
$ {3s < 3p < 4s < 3d} $