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Class 12
Physics
Electrostatic Potential and Capacitance
if one of the two electrons of a h2 molecule is re...

Question:
If one of the two electrons of a H₂ molecule is removed, we get a hydrogen molecular ion H₂⁺. In the ground state of an H₂⁺, 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:

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.

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