Question

If one of the two electrons of a H₂ molecule is removed, we get a hydrogen molecular ion. In the ground state of an, the two protons are separated by roughly 1.5 Å, and the electron is roughly 1 Å from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

Answer 1

The system of two protons and one electron is represented in the given figure.

Charge on proton 1, q₁ = 1.6 ×10⁻¹⁹ C

Charge on proton 2, q₂ = 1.6 ×10⁻¹⁹ C

Charge on electron, q₃ = −1.6 ×10⁻¹⁹ C

Distance between protons 1 and 2, d₁ = 1.5 ×10⁻¹⁰ m

Distance between proton 1 and electron, d₂ = 1 ×10⁻¹⁰ m

Distance between proton 2 and electron, d₃ = 1 × 10⁻¹⁰ m

The potential energy at infinity is zero.

Potential energy of the system,

Therefore, the potential energy of the system is −19.2 eV.