What is the ground state energy of positronium? (The ground state energy of hydrogen is −13.6eV)−3.4eV−6.8eV−13.6eV−27.2eV

The ground state energy of positronium is -6.8eV.

Here's why:

Positronium is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom. The mass of the positron is the same as that of the electron, unlike in hydrogen where the proton is much heavier than the electron.

The ground state energy of a system like this is given by the formula E = -13.6eV * (mu/m_e), where mu is the reduced mass of the system, and m_e is the mass of the electron.

For hydrogen, mu is approximately equal to the mass of the electron, because the proton is so much heavier. So the ground state energy is -13.6eV.

For positronium, mu is half the mass of the electron, because the two particles are identical. So the ground state energy is -13.6eV * (0.5) = -6.8eV.