Question

Given that the Bohr energy of a hydrogen atom is proportional to the reduced mass of the system. Then

the ground state energy of the positronium (positron-electron system) is approximately equal to​

Answer 1

Answer:

Bohr’s Model of the Atom: Positronium

Problem 3.35, page 141

Positronium is a hydrogen-like atom consisting of a positron (a positively charged electron) and an electron

revolving around each other.

• Using the Bohr model, find the allowed radii (relative to the center of mass of the two particles) and the

allowed energies of the system. Use the concept of reduced mass in solving the problem.

Solution

Eqs. (22) and (23) with m = mN = me and Z = 1 give the Bohr model values for the allowed radii rn and

energies En of positronium:

rn = 105.8n

2 pm

En = −

6.79

n2

eV