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)
SolutionHydrogen: 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 n = 1 → E(Ps) = − ½ × 13.6 eV
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