The radii of maximum probability for 3s,3p, and 3d electrons are in the order :

Options

A. (a) `(r_(max))3dgt(r_(max))3pgt(r_(max))3s`
B. (b) `(r_(max))3dgt(r_(max))3sgt(r_(max))3p`
C. (c) `(r_(max))3sgt(r_(max))3pgt(r_(max))3d`
D. (d) None of these

Answer

To determine the order of the radii of maximum probability for 3s, 3p, and 3d electrons, we can follow these steps:

### Step 1: Understand the Principal Quantum Number (n)
The principal quantum number (n) indicates the energy level of the electron. In this case, we are given n = 3 for all three types of orbitals (3s, 3p, and 3d).

**Hint:** The principal quantum number defines the shell in which the electrons reside.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) determines the shape of the orbital and can take values from 0 to (n-1). For n = 3:
- For 3s, l = 0
- For 3p, l = 1
- For 3d, l = 2

**Hint:** The value of l corresponds to the type of orbital: s (l=0), p (l=1), d (l=2).

### Step 3: Relationship Between l and Radius of Maximum Probability
For orbitals with the same principal quantum number (n), the radius of maximum probability for finding an electron decreases with increasing values of l. This means that:
- The 3s orbital (l = 0) has the largest radius of maximum probability.
- The 3p orbital (l = 1) has a smaller radius than 3s.
- The 3d orbital (l = 2) has the smallest radius among the three.

**Hint:** The order of maximum probability radius is inversely related to the azimuthal quantum number (l).

### Step 4: Order the Orbitals
Based on the above understanding, we can list the orbitals in order of their radii of maximum probability:
1. 3s (largest radius)
2. 3p (medium radius)
3. 3d (smallest radius)

Thus, the order of the radii of maximum probability for 3s, 3p, and 3d electrons is:
**3s > 3p > 3d**

**Final Answer:** The radii of maximum probability for 3s, 3p, and 3d electrons are in the order: **3s > 3p > 3d**.