4d, 5p, 5f and 6p orbitals are arranged in the order of decreasing energy. The correct option is :

Options

A. 5f > 6p > 5p > 4d
B. 5f >6p >5p > 4d
C. 6p > 5f > 5p > 4d
D. 6p > 5f >4d > 5p

Explanation

To determine the order of decreasing energy for the orbitals 4d, 5p, 5f, and 6p, we can use the n + l rule. This rule states that the energy of an orbital increases with increasing values of n + l, where n is the principal quantum number and l is the azimuthal quantum number.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n) and Azimuthal Quantum Number (l)**:
- For the 4d orbital:
- n = 4, l = 2 (since d corresponds to l = 2)
- For the 5p orbital:
- n = 5, l = 1 (since p corresponds to l = 1)
- For the 5f orbital:
- n = 5, l = 3 (since f corresponds to l = 3)
- For the 6p orbital:
- n = 6, l = 1 (since p corresponds to l = 1)

2. **Calculate n + l for Each Orbital**:
- For 4d: n + l = 4 + 2 = 6
- For 5p: n + l = 5 + 1 = 6
- For 5f: n + l = 5 + 3 = 8
- For 6p: n + l = 6 + 1 = 7

3. **Order the Orbitals Based on n + l Values**:
- The calculated n + l values are:
- 4d: 6
- 5p: 6
- 5f: 8
- 6p: 7
- The order of increasing n + l values is:
- 4d (6) = 5p (6) < 6p (7) < 5f (8)

4. **Resolve the Tie Between 4d and 5p**:
- Since both 4d and 5p have the same n + l value (6), we look at the principal quantum number (n). The orbital with the lower n value has lower energy.
- Therefore, 4d (n = 4) is lower in energy than 5p (n = 5).

5. **Final Order of Decreasing Energy**:
- The final order from highest energy to lowest energy is:
- 5f > 6p > 5p > 4d

### Conclusion:
The correct order of the orbitals in terms of decreasing energy is:
**5f > 6p > 5p > 4d**