Question

Consider a positronium atom consisting of a positron and an electron each having mass $m$(equal to mass of electron) in the orbit around its centre of mass. This structure lasts for 10${}^{-6}s$ only. Find the energy levels for this model.

Answer 1

In Bohr, mazz zof proton was assumed infinite and the relation for binding energy is

$E_n$ = $\frac{m{e}^4}{{\epsilon }_0^2{n}^2{h}^2}$.

In the new system (positrinium atom) masses are equal.

Therefore, we use reduced mass, $m_{reduced}=\frac{m_1{m}_2}{m_1+m_2}=\frac{m}{2}$