The correct order of closeness of 3s,3p,3d orbitals of nucleus is :

Options

A. `3dgt3pgt3s`
B. `3sgt3pgt3d`
C. `3sgt3dgt3p`
D. `3dgt3sgt3p`

Answer

To determine the correct order of closeness of the 3s, 3p, and 3d orbitals to the nucleus, we need to analyze their energy levels using the n + l rule. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Quantum Numbers
- Each orbital is defined by two quantum numbers: the principal quantum number (n) and the angular momentum quantum number (l).
- For the 3s, 3p, and 3d orbitals:
- 3s: n = 3, l = 0
- 3p: n = 3, l = 1
- 3d: n = 3, l = 2

### Step 2: Calculate n + l Values
- The closeness of orbitals to the nucleus can be determined by calculating the n + l value for each orbital. The lower the n + l value, the closer the orbital is to the nucleus.
- For 3s: n + l = 3 + 0 = 3
- For 3p: n + l = 3 + 1 = 4
- For 3d: n + l = 3 + 2 = 5

### Step 3: Compare n + l Values
- Now, we compare the n + l values:
- 3s: n + l = 3
- 3p: n + l = 4
- 3d: n + l = 5

### Step 4: Determine the Order of Closeness
- Since 3s has the lowest n + l value, it is the closest to the nucleus.
- Next is 3p, and farthest is 3d.
- Therefore, the order of closeness to the nucleus is:
- 3s < 3p < 3d

### Final Answer
The correct order of closeness of the 3s, 3p, and 3d orbitals to the nucleus is:
**3s < 3p < 3d** (or simply 3s, 3p, 3d).

---