Question

Identify the correct ascending order of energies of forbitals.

• A. \(3s < 3p < 3d < 4s\)
• B. \(3s <4s < 3p < 3d\)
• C. \(3s < 3p < 4s < 3d\)
• D. \(3s <3d < 3p < 4s\)

Answer 1

The Correct Option is C

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 ($n$) and penetration effect.

Step 1: Understanding Orbital Energies
The energy of an orbital depends primarily on two factors:
1. Principal Quantum Number ($n$): Orbitals with a lower $n$ value have lower energy.
2. Penetration Effect: Within the same shell ($n$), the energy of orbitals depends on their angular momentum quantum number ($l$). The order of increasing energy for orbitals within a shell is $s < p < d < f$.

However, when comparing orbitals from different shells, the overlap of energy levels can occur due to the penetration effect. Specifically:
- For $n = 3$, the $3s$ and $3p$ orbitals are lower in energy than the $4s$ orbital.
- The $3d$ orbitals have higher energy than the $4s$ orbital but lower energy than the $4p$ orbitals.

Step 2: Analyzing the Given Orbitals
We are tasked with ordering the following orbitals in ascending order of energy:
- $3s$
- $3p$
- $3d$
- $4s$

Key Points:
1. $3s < 3p$: Within the same shell ($n = 3$), $s$ orbitals are always lower in energy than $p$ orbitals.
2. $3d > 4s$: Due to the penetration effect, the $4s$ orbital has lower energy than the $3d$ orbitals. This is because the $4s$ electrons penetrate closer to the nucleus compared to the $3d$ electrons.
3. $3p < 4s$: The $4s$ orbital is lower in energy than the $3d$ orbitals but higher in energy than the $3p$ orbitals.

Step 3: Correct Order
Based on the above reasoning, the correct ascending order of energies is:
$$ 3s < 3p < 4s < 3d $$

Final Answer: $ {3s < 3p < 4s < 3d} $