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

Options

A. `3.4eV`
B. `-5.2eV`
C. `-6.8eV`
D. `-10.2eV`

Answer

C

Explanation

Bohr's formula for ground state energy ,
`E=(me^(4))/(8epsilon_0^2h^2)` (`because n=1`)....(i)
Here, m is reduced mass of electron and position in positronium
`therefore m(m_em_p)/(m_e+m_p)=(m_e)/(2)`(`becausem_e=m_p`)
`therefore` Ground state energy of positronium
`E=-(((m_e)/(2))e^4)/(8epsilon_0^(2)h^2)=-(1)/(2)((m_ee^4)/(8epsilon_0^(2)h^2))("using"(i))`
`=-(1)/(2)xx13.6eV" "[(m_ee^4)/(8epsilon_0^(2)h^2)=13.6eV]`
`=-6.8eV`.