Positronium is just like a H-atom with the proton replaced by the positively charged antiparticle of the electron (called the positron which is as massive as the electron). What would be the ground state energy of positronium?

Explanation

Here, positronium atom is a binary system, made up of positron and electron. In this system, both of these particles revolve around their common centre of mass.
Now, if above system is to be replaced by a single particle then mass of this single particle is to be taken equal to reduced mass of a binary system. In the present case, its value is
`mu=(m_(1)m_(2))/(m_(1)+m_(2))=(m_(e)xxm_(e))/(m_(e)+m_(e))=(m_(e))/(2)=(m)/(2)....(1)`
(where `m_(e)=m` mass of electron)
`rArr` Now, ground state energy of electron in H-atom,
`E_(1).=((mu)e^(4))/(8 epsi_(0)^(2)h^(2))=-(((m)/(2))e^(4))/(8 epsi_(0)^(2)h^(2))( :. "Here" mu=(m)/(2))`
`:.E_(1).=(1)/(2)(E_(1))=(1)/(2)(-13.6eV)=-6.8eV`