Correct energy value order is

Options

A. ns np nd(n - 1)f
B. ns np(n - 1)d (n - 2)f
C. ns np(n - 1)d (n - 1)f
D. ns(n - 1)d (n - 1)f

Explanation

To determine the correct order of energy levels in atomic orbitals, we can use the (n + l) rule. This rule states that the energy of an orbital increases with increasing values of n + l. If two orbitals have the same n + l value, the one with the higher n value has higher energy.

### Step-by-Step Solution:

1. **Identify the Orbitals**: We will consider the following orbitals:
- 1s (n=1, l=0)
- 2s (n=2, l=0)
- 2p (n=2, l=1)
- 3s (n=3, l=0)
- 3p (n=3, l=1)
- 3d (n=3, l=2)
- 4s (n=4, l=0)
- 4p (n=4, l=1)
- 4d (n=4, l=2)
- 4f (n=4, l=3)

2. **Calculate n + l for Each Orbital**:
- For 1s: n + l = 1 + 0 = 1
- For 2s: n + l = 2 + 0 = 2
- For 2p: n + l = 2 + 1 = 3
- For 3s: n + l = 3 + 0 = 3
- For 3p: n + l = 3 + 1 = 4
- For 3d: n + l = 3 + 2 = 5
- For 4s: n + l = 4 + 0 = 4
- For 4p: n + l = 4 + 1 = 5
- For 4d: n + l = 4 + 2 = 6
- For 4f: n + l = 4 + 3 = 7

3. **Order the Orbitals by n + l Values**:
- 1s (1)
- 2s (2)
- 2p (3)
- 3s (3)
- 4s (4)
- 3p (4)
- 3d (5)
- 4p (5)
- 4d (6)
- 4f (7)

4. **Determine the Energy Order**:
- The order of increasing energy based on n + l values is:
1s < 2s < 2p < 3s < 4s < 3p < 3d < 4p < 4d < 4f

5. **Final Energy Order**:
- The correct order of energy levels is:
- 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 4d < 4f