Not considering the electronic spin, the degenracy of the second excited state of `H^(-)` is

Explanation

To solve the problem of finding the degeneracy of the second excited state of \( H^- \) (hydride ion), we will follow these steps:

### Step 1: Understand the Concept of Degeneracy
Degeneracy refers to the number of different quantum states of a system that have the same energy level. In the context of atomic orbitals, it means that multiple orbitals can have the same energy.

**Hint:** Remember that orbitals of the same type (like p orbitals) can have the same energy in multi-electron atoms.

### Step 2: Identify the Electrons in \( H^- \)
The hydride ion \( H^- \) has two electrons. This means we are dealing with a multi-electron atom, which influences the energy levels of the orbitals.

**Hint:** Count the total number of electrons in the ion to understand how they will fill the orbitals.

### Step 3: Determine the Ground State Configuration
For \( H^- \), the ground state configuration will fill the lowest energy orbital first. The configuration will be:
- 1 electron in the 1s orbital
- 1 electron in the 2s orbital

This gives us the configuration: \( 1s^2 \).

**Hint:** Start filling the orbitals from the lowest energy level according to the Aufbau principle.

### Step 4: Identify the Excited States
The first excited state of \( H^- \) will involve promoting one of the electrons from the 1s orbital to the next available orbital, which is the 2p orbital. Thus, the first excited state configuration can be written as:
- \( 1s^2 \) (2 electrons in 1s)
- \( 2s^0 \) (0 electrons in 2s)
- \( 2p^1 \) (1 electron in 2p)

The second excited state configuration will promote another electron, resulting in:
- \( 1s^2 \)
- \( 2s^0 \)
- \( 2p^2 \)

**Hint:** Keep track of how electrons are promoted to higher energy levels to find the excited states.

### Step 5: Determine the Degeneracy of the Second Excited State
In the second excited state, we have 2 electrons in the 2p orbital. The 2p subshell has three orbitals: \( 2p_x, 2p_y, \) and \( 2p_z \). Since these orbitals are degenerate (they have the same energy), the degeneracy of the second excited state is determined by the number of orbitals available in the 2p subshell.

Thus, the degeneracy is 3.

**Hint:** Count the number of orbitals in the subshell that have the same energy to find the degeneracy.

### Conclusion
The degeneracy of the second excited state of \( H^- \) is 3.

**Final Answer:** 3