Question

Estimate the total ground state energy in eV of the system obtained if all the electrons in the Carbon atom were replaced by π⁻ particles. (You are given that the ground state energy of the hydrogen atom is −13.6 eV and that the π⁻ is a particle with charge −1, spin 0 and mass 270 m_e

Answer 1

A carbon atom has 6 electrons. If all these electrons are replaced by π⁻ mesons then two differences would arise 

(i) As π⁻ mesons are bosons (spin 0) Pauli’s principle does not operate so that all of them can be in the K-shell (n = 1) 

(ii) The total energy is enhanced because of the reduced mass μ.