Explain briefly how the relative mass of the proton relative

Explain briefly how the relative mass of the proton relative to the electron leads to the Born-Oppenheimer approximation. 4

Solution

The Idea for the Born-Oppenheimer approximation is the fact that the mass of the nucleus in a molecule is greater the mass of an electron (more than 1000 times). Due to this difference, the nuclei move very slowly than the electrons. And due to their opposite charges, there is a mutual attractive force of Ze²/r²acting on an atomic nucleus and an electron. This force causes both particles to be accelerated. Since the magnitude of the acceleration is inversely proportional to the mass, the acceleration of the electrons is large and the acceleration of the atomic nuclei is small; the difference is a factor of more than 1000. Hence, the electrons are moving and responding to forces very quickly, and the nuclei are not. So a good approximation is to describe the electronic states of a molecule by thinking that the nuclei aren\'t moving, i.e. that they are stationary.