.What designations are given to the orbitals having (i) n = 2, l = 1 (ii) n = 2, l = 0 (iii) n = 4, l = 3 (iv) n = 4, l = 2 (v) n = 4, l = 1?

Answer

To determine the designations of the orbitals based on the given quantum numbers (n and l), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number (n) indicates the shell or energy level of the electron.
- The azimuthal quantum number (l) indicates the subshell or type of orbital. The values of l correspond to specific orbitals:
- l = 0: s orbital
- l = 1: p orbital
- l = 2: d orbital
- l = 3: f orbital

2. **Case (i): n = 2, l = 1**:
- Here, n = 2 indicates the second shell.
- l = 1 indicates a p orbital.
- Therefore, the designation is **2p**.

3. **Case (ii): n = 2, l = 0**:
- Here, n = 2 indicates the second shell.
- l = 0 indicates an s orbital.
- Therefore, the designation is **2s**.

4. **Case (iii): n = 4, l = 3**:
- Here, n = 4 indicates the fourth shell.
- l = 3 indicates an f orbital.
- Therefore, the designation is **4f**.

5. **Case (iv): n = 4, l = 2**:
- Here, n = 4 indicates the fourth shell.
- l = 2 indicates a d orbital.
- Therefore, the designation is **4d**.

6. **Case (v): n = 4, l = 1**:
- Here, n = 4 indicates the fourth shell.
- l = 1 indicates a p orbital.
- Therefore, the designation is **4p**.

### Final Designations:
- (i) 2p
- (ii) 2s
- (iii) 4f
- (iv) 4d
- (v) 4p