Among 4p,4s,3p and 3d orbital has the least energy

Answer

To determine which of the orbitals among 4p, 4s, 3p, and 3d has the least energy, we can apply the n + l rule. This rule helps us understand the relative energy levels of different orbitals based on their principal quantum number (n) and azimuthal quantum number (l).

### Step-by-Step Solution:

1. **Identify the Quantum Numbers:**
- For each orbital, identify the principal quantum number (n) and the azimuthal quantum number (l).
- The values of l for the orbitals are:
- s: l = 0
- p: l = 1
- d: l = 2
- f: l = 3

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

3. **Compare the n + l Values:**
- 4p: n + l = 5
- 4s: n + l = 4
- 3p: n + l = 4
- 3d: n + l = 5

4. **Determine the Orbital with the Least Energy:**
- The lower the n + l value, the lower the energy of the orbital.
- Here, both 4s and 3p have the same n + l value of 4, which is lower than that of 4p and 3d.
- Between 4s and 3p, the orbital with the lower principal quantum number (n) will have lower energy.
- Since 3p has n = 3 (lower than n = 4 for 4s), it has the least energy.

### Conclusion:
The orbital with the least energy among 4p, 4s, 3p, and 3d is **3p**.