the electrons identified by quantum number 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 order of increasing energy from the lowest to the highest as

Options

A. `(iv)lt(ii)lt(iii)lt(i) `
B. `(ii)lt(iv)lt(i)lt(iii)`
C. `(i)lt(iii)lt(ii)lt(iv)`
D. `(iii)lt(i)lt(iv)lt(ii)`

Answer

To solve the question of ordering the electrons identified by the quantum numbers \( n \) and \( l \) in terms of increasing energy, we will follow these steps:

### Step 1: Identify the orbitals based on the quantum numbers

1. **For (i) \( n=4, l=1 \)**:
- \( l=1 \) corresponds to the **p orbital**.
- Therefore, this is the **4p orbital**.

2. **For (ii) \( n=4, l=0 \)**:
- \( l=0 \) corresponds to the **s orbital**.
- Therefore, this is the **4s orbital**.

3. **For (iii) \( n=3, l=2 \)**:
- \( l=2 \) corresponds to the **d orbital**.
- Therefore, this is the **3d orbital**.

4. **For (iv) \( n=3, l=1 \)**:
- \( l=1 \) corresponds to the **p orbital**.
- Therefore, this is the **3p orbital**.

### Step 2: List the orbitals identified

- (i) 4p
- (ii) 4s
- (iii) 3d
- (iv) 3p

### Step 3: Determine the order of increasing energy

Using the Aufbau principle, we can determine the order of energy levels. The general order of filling is:

1. 1s
2. 2s
3. 2p
4. 3s
5. 3p
6. 4s
7. 3d
8. 4p

From this order, we can see that:

- **3p** (from (iv)) has lower energy than **4s** (from (ii)).
- **4s** (from (ii)) has lower energy than **3d** (from (iii)).
- **3d** (from (iii)) has lower energy than **4p** (from (i)).

### Step 4: Arrange the orbitals in order of increasing energy

Thus, the order of increasing energy from lowest to highest is:

1. 3p (iv)
2. 4s (ii)
3. 3d (iii)
4. 4p (i)

### Final Answer

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

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