Positronium consists of an electron and a positron (same mass opposite charge) orbiting around their common center of mass .The spectrum is, therefore expected to be hydrogen like , the difference arising from the mass difference .Calculate the wavelength of the first three line of the balmer series of positronium.

Explanation

To calculate the wavelengths of the first three lines of the Balmer series of positronium, we will follow these steps:

### Step 1: Understand the System
Positronium consists of an electron and a positron, both having the same mass but opposite charges. The spectrum of positronium is similar to that of hydrogen, but we need to account for the reduced mass in our calculations.

### Step 2: Calculate the Reduced Mass
The reduced mass \( \mu \) of the positronium system is given by:
\[
...