Which of the following statement in relation to the hydrogen atom is correct?

Options

A. 3s, 3p and 3d- orbitals all have the same energy
B. 3s and 3p- orbitals is lower energy than 3d- orbtial
C. 3p-orbital is ower in energy than 3d- orbital
D. 3s-orbital is lower in energy than 3p - orbital

Answer

To determine which statement regarding the hydrogen atom is correct, we will analyze the energy levels of the orbitals given in the options.

### Step-by-Step Solution:

1. **Identify the Orbitals**: The orbitals mentioned are 3s, 3p, and 3d. We need to calculate their energy levels using the n + l rule.

2. **Calculate n + l for Each Orbital**:
- For the **3s** orbital:
- n = 3, l = 0 (since s = 0)
- n + l = 3 + 0 = 3
- For the **3p** orbital:
- n = 3, l = 1 (since p = 1)
- n + l = 3 + 1 = 4
- For the **3d** orbital:
- n = 3, l = 2 (since d = 2)
- n + l = 3 + 2 = 5

3. **Determine Energy Order**: According to the n + l rule, the energy of orbitals increases with increasing values of n + l. Therefore, the order of energy for the orbitals is:
- 3s (n + l = 3) < 3p (n + l = 4) < 3d (n + l = 5)

4. **Evaluate the Statements**:
- **Option 1**: 3s, 3p, and 3d orbitals have the same energy. **(Incorrect)**
- **Option 2**: 3s and 3p orbitals have lower energy than 3d. **(Correct)**
- **Option 3**: 3p orbital is lower in energy than 3d. **(Correct)**
- **Option 4**: 3s orbital is lower in energy than 3p. **(Correct)**

5. **Conclusion**: The correct statements regarding the hydrogen atom are options 2, 3, and 4.