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Exercise 1: A positronium is a bound electron positron state, where the electron is rotating around...

Exercise 1: A positronium is a bound electron positron state, where the electron is rotating around a positron rather than a proton. Prove that in a positronium bound state:

a) The transition energy levels are halved compared with those of the Hydrogen Atom.

b) The electron radii are expanded to double the corresponding radii of the Hydrogen Atom.

Expert Solution

(a) Energy Levels,

Where, is the reduced mass of the system.

Considering all the remaining variables as constant, the energy for transition levels varies as,

In the case of Hydrogen atom,

In the case of Positronium,

Here, mass of electron is equal to the mass of the positron.

Since, the reduced mass is halved the energy levles also bcomes halved in positronium when compared to that of the Hydrogen atom.

(b) Electron radii for each energy level is given by,

Again, by considering all the remaining variables as constant except reduced mass, the radii for transition levels varies as,

Since reduced mass for positronium is half of that of Hydrogen atom, the radii of positronium will be expanded to double to that of the Hydrogen atom.

genius_generous answered 1 year ago

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