How many of the following atomic orbitals of H atom are degenerate?
`3s, 3p_(x), 3p_(z), 3d_(xy), 3d_(xz), 3d_(x^(2)-y^(2)), 3d_(z^(2)).`

Explanation

To determine how many of the given atomic orbitals of the hydrogen atom are degenerate, we need to follow these steps:

### Step 1: Understand Degeneracy
Degenerate orbitals are those that have the same energy level. For a hydrogen atom, which is a single-electron system, the energy of an orbital depends only on the principal quantum number (n).

### Step 2: Identify the Principal Quantum Number (n)
For the given orbitals:
- **3s**: n = 3
- **3p_x**: n = 3
- **3p_z**: n = 3
- **3d_xy**: n = 3
- **3d_xz**: n = 3
- **3d_(x²-y²)**: n = 3
- **3d_(z²)**: n = 3

All the orbitals listed have the same principal quantum number, n = 3.

### Step 3: Determine the Azimuthal Quantum Number (l)
The azimuthal quantum number (l) for each type of orbital is as follows:
- **3s**: l = 0
- **3p_x**: l = 1
- **3p_z**: l = 1
- **3d_xy**: l = 2
- **3d_xz**: l = 2
- **3d_(x²-y²)**: l = 2
- **3d_(z²)**: l = 2

### Step 4: Identify Degenerate Orbitals
In hydrogen, since it is a single-electron atom, all orbitals with the same principal quantum number (n) will be degenerate regardless of their azimuthal quantum number (l).

### Conclusion
Since all the given orbitals (3s, 3p_x, 3p_z, 3d_xy, 3d_xz, 3d_(x²-y²), 3d_(z²)) have the same principal quantum number (n = 3), they are all degenerate.

**Final Answer**: All 7 orbitals are degenerate.

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