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

Options

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

Answer

To determine which statement is correct in relation to the hydrogen atom, we need to analyze the electronic configuration and energy levels of the hydrogen atom. Here’s a step-by-step solution:

### Step 1: Identify the Electronic Configuration of Hydrogen
- The hydrogen atom has only one electron. Therefore, its electronic configuration is represented as \(1s^1\).

### Step 2: Understand the Concept of n + l Rule
- The n + l rule is used to determine the energy levels of orbitals. Here, 'n' represents the principal quantum number, and 'l' represents the azimuthal quantum number (which is 0 for s, 1 for p, 2 for d, etc.).

### Step 3: Calculate n + l for Hydrogen's Orbitals
- For the 1s orbital:
- \(n = 1\) and \(l = 0\) (since it is an s orbital).
- Therefore, \(n + l = 1 + 0 = 1\).

### Step 4: Consider Higher Energy Levels (3s, 3p, 3d)
- For the 3s orbital:
- \(n = 3\) and \(l = 0\) → \(n + l = 3 + 0 = 3\).
- For the 3p orbital:
- \(n = 3\) and \(l = 1\) → \(n + l = 3 + 1 = 4\).
- For the 3d orbital:
- \(n = 3\) and \(l = 2\) → \(n + l = 3 + 2 = 5\).

### Step 5: Analyze Energy Levels for Hydrogen
- In hydrogen, all orbitals of the same principal quantum number (n) have the same energy due to the lack of electron-electron repulsion. Thus, the 3s, 3p, and 3d orbitals are degenerate (have the same energy).

### Conclusion
- Therefore, the correct statement regarding the hydrogen atom is that the 3s, 3p, and 3d orbitals all have the same energy.

### Final Answer
The correct statement is: **3s, 3p, and 3d orbitals all have the same energy for the hydrogen atom.**

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