An ionised H-molecules consists of an electron and wo protons. The protons are seperated by a small distance of the order of angstrom. In the ground state,

Options

A. the electrons would not move iin circular orbits
B. the energy would be `(2)^(4)` times that of a H-atom
C. the electrons, orbits would go around the protons
D. the molecule will soon decay in a proton and a H-atom

Explanation

To solve the problem regarding the ionized hydrogen molecule (H₂⁺) consisting of an electron and two protons, we need to analyze the behavior of the electron in the presence of two protons and determine the validity of the given statements.

### Step-by-Step Solution:

1. **Understanding the System**:
- An ionized hydrogen molecule (H₂⁺) consists of one electron and two protons. The protons are separated by a small distance on the order of angstroms (10^-10 m).
- In this system, the electron is influenced by the electric fields of both protons.

2. **Electron Motion**:
- In a hydrogen atom, according to Bohr's model, the electron moves in a circular orbit around a single proton. However, in H₂⁺, the presence of two protons means that the electron cannot simply move in a circular orbit around one proton.
- The electron will experience a more complex potential due to the two protons, leading to a different type of motion.

3. **Energy Calculation**:
- The energy levels of a hydrogen atom are given by the formula \( E_n = -\frac{13.6 \, \text{eV}}{n^2} \). For hydrogen, \( Z = 1 \).
- In the case of H₂⁺, the energy levels will not follow the same formula as in hydrogen. The energy will depend on the configuration of the electron in relation to both protons.
- The statement claiming that the energy would be \( 2^4 \) times that of a hydrogen atom is incorrect, as the energy levels must be derived from solving the Schrödinger equation for this system.

4. **Electron's Orbit**:
- The electron's orbit in H₂⁺ will not be a simple circular orbit. Instead, it can take on various shapes (elliptical or otherwise) due to the influence of both protons.
- Thus, the statement that the electron's orbit would go around the protons is true, as the electron will be influenced by both protons.

5. **Stability of the Molecule**:
- The stability of the H₂⁺ molecule depends on the conditions and the energy states involved. It is possible for the molecule to be stable, meaning it may not decay into a proton and a hydrogen atom immediately.
- Therefore, the statement about the molecule decaying is not necessarily true.

### Conclusion:
Based on the analysis:
- **True Statements**:
- The electrons would not move in circular orbits (True).
- The electron's orbit would go around the protons (True).
- **False Statements**:
- The energy would be \( 2^4 \) times that of a hydrogen atom (False).
- The molecules will soon decay into a proton and a hydrogen atom (False).