Positronium atom transition - energy of photon

In summary, positronium is an atom consisting of an electron and a positron, similar to a hydrogen atom with the positron replacing the proton. When a positronium atom transitions from state n=3 to n=1, the energy of the emitted photon is closest to 6 eV. This is due to the two-body problem of the electron and positron revolving around their common center of mass, with a reduced mass of half that of the electron. This results in a halving of the Rydberg constant.
  • #1
quietrain
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2

Homework Statement


Positronium is an atom formed by an electron and a positron. It is similar to the
hydrogen atom, with the positron replacing the proton. If a positronium atom
makes a transition from the state n = 3 to a state with n = 1, the energy of the
photon emitted in this transition is closest to

The Attempt at a Solution



what will my proton number Z be in this case?

E = -13.6eV x Z2 / n2

but a hydrogen atom's Z = 1, what about the positronium atom? 0?

state n=3 has -1.511 eV while state 1 has -13.6 eV.

but the answer is 6 eV? how is that obtained? i have no idea . thanks for help!
 
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  • #2


The positron and electron have about the same mass. The electron does not revolve around the positron, but both revolve around their common centre of mass. This two-body problem can be treated as the motion of a single body with the reduced mass: mp*me/(mp+me) which is half the mass of the electron. The Rydberg constant is proportional to the mass of the electron: Now it is halved.

ehild
 
  • #3


ah isee.. thank you very much ehild!
 

1. What is a positronium atom transition?

A positronium atom transition refers to the process in which a positron (a positively charged subatomic particle) and an electron (a negatively charged subatomic particle) combine to form a short-lived, neutral atom called positronium. This atom then undergoes a transition to a lower energy state, releasing a photon (a particle of light) in the process.

2. How is the energy of a photon determined in a positronium atom transition?

The energy of a photon in a positronium atom transition is determined by the difference in energy between the initial and final energy states of the atom. This energy difference is known as the transition energy and is equal to the energy of the emitted photon.

3. Can the energy of a photon in a positronium atom transition be calculated?

Yes, the energy of a photon in a positronium atom transition can be calculated using the Rydberg formula, which takes into account the charge of the particles involved and the distance between them. This formula is often used in quantum mechanics to calculate the energy of emitted photons in various atomic processes.

4. How does the energy of a photon in a positronium atom transition compare to other atomic transitions?

The energy of a photon in a positronium atom transition is relatively low compared to other atomic transitions. This is because positronium is a very light atom and its energy levels are closer together, resulting in lower energy transitions and correspondingly lower energy photons being emitted.

5. What are the applications of studying positronium atom transitions?

Studying positronium atom transitions can provide valuable insights into the behavior of matter and antimatter, as well as the fundamental laws of quantum mechanics. It also has potential applications in areas such as positron emission tomography (PET) imaging and precision measurements of atomic properties.

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