The electrons identified by the following quantum numbers `n` and `l: (i) n = 4, l = 1, (ii) n = 4, l = 0, (iii) n = 3, l = 2`, and (iv) `n = 3, l = 1` can be placed in the order of increasing enegry from the lowest to the highest as

Options

A. (iv) < (ii) < (iii) < (i)
B. (ii) < (iv) < (i) < (iii)
C. (i) < (iii) < (ii) < (iv)
D. (iii) < (i) < (iv) < (ii)

Explanation

To determine the order of increasing energy for the given quantum numbers, we will analyze each set of quantum numbers and identify the corresponding orbitals. Then, we will arrange them based on their energy levels.

### Step-by-Step Solution:

1. **Identify the Orbitals**:
- For (i) \( n = 4, l = 1 \):
- Here, \( l = 1 \) corresponds to the **p orbital**. Thus, this is the **4p orbital**.
- For (ii) \( n = 4, l = 0 \):
- Here, \( l = 0 \) corresponds to the **s orbital**. Thus, this is the **4s orbital**.
- For (iii) \( n = 3, l = 2 \):
- Here, \( l = 2 \) corresponds to the **d orbital**. Thus, this is the **3d orbital**.
- For (iv) \( n = 3, l = 1 \):
- Here, \( l = 1 \) corresponds to the **p orbital**. Thus, this is the **3p orbital**.

2. **List the Orbitals**:
- (i) 4p
- (ii) 4s
- (iii) 3d
- (iv) 3p

3. **Determine the Energy Order**:
- According to the Aufbau principle, orbitals are filled in order of increasing energy. The general order of filling is:
- 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p
- Based on this order, we can arrange the identified orbitals:
- 3p (lower energy)
- 4s
- 3d
- 4p (highest energy)

4. **Final Arrangement**:
- The order of increasing energy from lowest to highest is:
- 3p < 4s < 3d < 4p

### Final Answer:
The order of increasing energy from lowest to highest is:
**3p < 4s < 3d < 4p**