Ncert Exercises & Solutions

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?

Hint: The energy of a H-like atom depends on the reduced mass.

Step 1: Find the energy of the H-atom in the ground state.

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

E_{n} = - \frac{{me}^{4}}{8 n^{2} ε_{0}^{2} h^{2}}

where signs are as usual and 'm' that occurs in the Bohr formula is the reduced mass of electron and proton. Also, the total energy of the electron in the ground state of the hydrogen atom is -13.6 eV.

Step 2: Find the energy of Positronium in the ground state.

For H-atom reduced mass = m_e. Whereas for positronium, the reduced mass is

m \approx \frac{m_{e}}{2}

Hence, the total energy of the electron in the ground state of the positronium atom is

\frac{- 13.6 ev}{2} = - 6.8 eV

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