The electrons identified by quantum numbers n and l :-
(a) n=4, l=1 (b) n=4, l=0 (c ) n=3, l=2 (d) n=3, l=1
Can be placed in order of increasing energy as

Explanation

To determine the order of increasing energy for the given quantum numbers, we will use the n + l rule. This rule states that the energy of an electron in an atom is primarily determined by the sum of its principal quantum number (n) and azimuthal quantum number (l). The higher the value of n + l, the higher the energy of the electron. If two orbitals have the same n + l value, the one with the higher n value will have higher energy.

Let's analyze each pair step by step:

### Step 1: Calculate n + l for each pair
1. **(a) n = 4, l = 1**
- n + l = 4 + 1 = **5**

2. **(b) n = 4, l = 0**
- n + l = 4 + 0 = **4**

3. **(c) n = 3, l = 2**
- n + l = 3 + 2 = **5**

4. **(d) n = 3, l = 1**
- n + l = 3 + 1 = **4**

### Step 2: Compare the n + l values
- From the calculations:
- (a) has n + l = 5
- (b) has n + l = 4
- (c) has n + l = 5
- (d) has n + l = 4

### Step 3: Determine the order based on n + l values
- The pairs with the lowest n + l values will have the lowest energy:
- (b) and (d) both have n + l = 4.
- (b) has n = 4 and (d) has n = 3. Since n is lower for (d), it will have lower energy than (b).

- For (a) and (c), both have n + l = 5. We need to compare their n values:
- (a) has n = 4 and (c) has n = 3. Therefore, (a) has higher energy than (c).

### Step 4: Final order of increasing energy
Now we can summarize the order based on our findings:
1. **(d)**: n = 3, l = 1 (n + l = 4)
2. **(b)**: n = 4, l = 0 (n + l = 4)
3. **(c)**: n = 3, l = 2 (n + l = 5)
4. **(a)**: n = 4, l = 1 (n + l = 5)

Thus, the order of increasing energy is:
**(d) < (b) < (c) < (a)**

### Final Answer:
The increasing order of energy is: **(d), (b), (c), (a)**.