The potential energy of two electric charges Q₁and Q₂in a vacuum is

where r₁₂ is the distance between the charges and ε₀ is a constant called the permittivity of a vacuum, equal to 8.854187817 × 10^ˆ’12 F m^ˆ’1 = 8.854187817 × 10^ˆ’12 C² N^ˆ’1 m^ˆ’2. The potential energy of a hydrogen molecules is given by

where A and B represent the nuclei and 1 and 2 represent the electrons, and where the two indexes indicate the two particles whose interparticle distance is denoted. If a hydrogen molecule is placed so that the origin is midway between the two nuclei and the nuclei are on the z axis show that the inversion operator î and the reflection operator σ̂_h do not change the potential energy if applied to the electrons but not to the nuclei.

Transcribed Image Text:

Q1Q2 4πε0Γ12 e2 4πε0Γ2 e2 e2 e2 Ξ ν. 4περΓΑΒ 4περΓ1Β ΑπερΓ1Α e2 4πε0Γ12 e? 4περΓ2Β