VIPSolutionsgive answer in 3steps with explanation at the end of each step and final answer at the end
Question:
give answer in 3steps with explanation at the end of each step and final answer at the end
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Asked by: aarti
Created at: 2025-06-01 04:02:21
Asked by: aarti
Created at: 2025-06-01 04:02:21
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Let's solve each part in **3 steps** with explanations:
---
### 1. **5d<sub>y²</sub>**
**Step 1:**
Identify what 5d<sub>y²</sub> means:
- “5” is the principal quantum number (n = 5).
- “d” means ℓ = 2.
- d<sub>y²</sub> is one specific d orbital (there are 5 d orbitals in total).
**Step 2:**
Each orbital can hold a maximum of 2 electrons (one with spin up, one with spin down).
**Step 3:**
So, the maximum number of electrons in 5d<sub>y²</sub> = **2**.
---
### 2. **4f**
**Step 1:**
“4f” means n = 4, ℓ = 3 (f-subshell). The f-subshell has 7 orbitals.
**Step 2:**
Each orbital can hold 2 electrons, so 7 orbitals × 2 = 14 electrons.
**Step 3:**
Maximum number of electrons in 4f = **14**.
---
### 3. **3d<sub>xy</sub>**
**Step 1:**
“3d” means n = 3, ℓ = 2. "d<sub>xy</sub>" is one specific d orbital.
**Step 2:**
One d orbital = 2 electrons max.
**Step 3:**
Maximum number of electrons in 3d<sub>xy</sub> = **2**.
---
### 4. **2d<sub>xy</sub>**
**Step 1:**
"2d" would mean n = 2, ℓ = 2. But for n = 2, ℓ can only be 0 (s) or 1 (p). There is **no d orbital in n = 2**.
**Step 2:**
So, the maximum number of electrons = **0**.
**Step 3:**
Maximum number of electrons in 2d<sub>xy</sub> = **0**.
---
### 5. **7d<sub>z</sub>**
**Step 1:**
"7d" means n = 7, ℓ = 2 (d-subshell). "d<sub>z</sub>" is an individual d orbital.
**Step 2:**
One d orbital can hold 2 electrons.
**Step 3:**
Maximum number of electrons in 7d<sub>z</sub> = **2**.
---
## **Final Answers:**
| Designation | Max Number of Electrons |
|:--------------:|:----------------------:|
| 5d<sub>y²</sub> | **2** |
| 4f | **14** |
| 3d<sub>xy</sub> | **2** |
| 2d<sub>xy</sub> | **0** |
| 7d<sub>z</sub> | **2** |
Question:
tell concept used in answering the question in paragraph form in very brief in large
This is AI generated Response.
Asked by: aarti
Created at: 2025-06-01 04:04:44
Asked by: aarti
Created at: 2025-06-01 04:04:44
Final Answer:
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The concept used in answering these questions revolves around atomic orbital theory and quantum numbers, which describe the arrangement of electrons within an atom. Each atomic orbital is characterized by a principal quantum number (n), an azimuthal quantum number (ℓ), and a magnetic quantum number (mℓ). The principal quantum number (n) indicates the energy level or shell, while ℓ defines the type of orbital (s, p, d, f) with specific shapes and capacities. For each type of orbital, the maximum number of electrons it can hold is determined by the degeneracy of that orbital, where each orbital can accommodate up to two electrons with opposite spins. When considering specific orbitals such as d<sub>y²</sub> or d<sub>xy</sub>, we recognize that they are particular orientations within the d subshell, which contains five orbitals in total. The maximum electron capacity for each subshell is calculated by multiplying the number of orbitals in that subshell by two. Additionally, the presence of certain orbitals depends on the principal quantum number; for instance, there are no d orbitals in the n=2 shell because the d subshell begins at n=3. Understanding these quantum numbers, subshell capacities, and the nature of orbitals allows us to determine the maximum number of electrons that can occupy each specified orbital or subshell.
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