`{:(" List-I"," List-II"),("(Orbital)"," (Radial nodes)"),((P) 3p," (1) "0),((Q)5d," (2) "1),((R)4f," (3) 2"),((S)4s," (4) 3"):}`

Options

A. P `to` 2,Q `to` 3,R `to` 1,S `to` 4
B. P `to` 4,Q `to` 2,R `to` 3,S `to` 1
C. P `to` 1,Q `to` 2,R `to` 4,S `to` 3
D. P `to` 3,Q `to` 2,R `to` 4,S `to` 1

Answer

To solve the problem of matching the orbitals with their corresponding radial nodes, we will use the formula for calculating radial nodes, which is given by:

**Radial Nodes = n - l - 1**

Where:
- **n** is the principal quantum number.
- **l** is the azimuthal quantum number (which corresponds to the type of orbital: s, p, d, f).

### Step-by-Step Solution:

1. **Identify the values of n and l for each orbital:**
- For **3p**:
- n = 3 (principal quantum number)
- l = 1 (for p-orbital)
- Radial Nodes = 3 - 1 - 1 = 1

2. **Match 3p with radial nodes:**
- 3p corresponds to **1 radial node**. So, **P matches with (1)**.

3. **Calculate for 5d:**
- For **5d**:
- n = 5
- l = 2 (for d-orbital)
- Radial Nodes = 5 - 2 - 1 = 2

4. **Match 5d with radial nodes:**
- 5d corresponds to **2 radial nodes**. So, **Q matches with (2)**.

5. **Calculate for 4f:**
- For **4f**:
- n = 4
- l = 3 (for f-orbital)
- Radial Nodes = 4 - 3 - 1 = 0

6. **Match 4f with radial nodes:**
- 4f corresponds to **0 radial nodes**. So, **R matches with (0)**.

7. **Calculate for 4s:**
- For **4s**:
- n = 4
- l = 0 (for s-orbital)
- Radial Nodes = 4 - 0 - 1 = 3

8. **Match 4s with radial nodes:**
- 4s corresponds to **3 radial nodes**. So, **S matches with (3)**.

### Final Matching:
- P (3p) matches with (1)
- Q (5d) matches with (2)
- R (4f) matches with (0)
- S (4s) matches with (3)

### Conclusion:
The correct matches are:
- P → 1
- Q → 2
- R → 0
- S → 3