Nuclear & Particle Physics - Positronium

The positronium “atom” consists of an electron and a positron bound together by their mutual Coulomb attraction and moving about their center mass, which is located halfway between them. Thus the positronium “atom” is somewhat analogous to a hydrogen atom. The ground-state binding energy of hydrogen is 13.6 electron volts. What is the ground-state binding energy of positronium. 

A. (½)2× 13.6 eV 
B. ½ × 13.6 eV 
C. 13.6 eV 
D. 2 × 13.6 eV 
E. (2)2× 13.6 eV 
 (GR8677 #99)
Solution

Hydrogen: proton and electron
Positronium: positron (anti electron) and electron

By definition of particles and antiparticles, the mass of the electron and the positron are the same.
→ The reduced mass Positronium:



→ Energy levels of Positronium is half those of Hydrogen

En(H)  = −13.6 / n²
En(Ps) ½ En(H) 

For the ground-state → E(Ps)  − ½ × 13.6 eV 

Answer: B

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