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  • Positronium is just like an 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?

Positronium is just like an 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?

 

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The total energy of the electron in the stationary states of the hydrogen atom is given by

E_{n}=-\left \{ \frac{\mu}{2h^{2}}\left (\frac{e^[2]}{4\pi\epsilon _{0}} \right )^{2} \right \}\frac{1}{n^{2}}

\mu that occurs in the Bohr formula is the reduced mass of electron and proton For hydrogen atom :

\mu=\frac{m_{e}m_{p}}{m_{e}+m_{p}}=\frac{m_{e}m_{p}}{m_{p}}=m_{e}(As m_{p}>>m_{e})

me  mp are the mass of electron and proton which are the same for positronium:

\mu=\frac{m_{e}m_{p}}{m_{e}+m_{p}}=\frac{m_{e}^{2}}{2m_{e}}=\frac{m_{e}}{2}

(As mass of positron is equal to the mass of electron)

E_{n}=\frac{1}{2}\left \{ \frac{m_{e}}{2h^{2}\left ( \frac{e^{2}}{4 \pi \varepsilon _{0}} \right )^{2}} \right \}\frac{1}{n^{2}}-\frac{13.6eV}{2}\frac{1}{n^{2}}=\frac{-6.8eV}{n^{2}}

The energy is half of the hydrogen level.

the lowest energy level of positronium (n=1)is -6.8 electron volts(eV).

The next highest energy level (n=2) is 1.7 eV the negative sign implies a bound state

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infoexpert24

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