Positronium is an atom formed by an electron and a positron (anti electron), it is similar to the hydrogen atom with proton being replaced by a positron. If this positronium atom makes a transition fromn= 3ton= 1the corresponding photon energy would be :a)13.6eVb)6.0eVc)6.8eVd)12.2eVCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Positronium Transition and Photon Energy

Introduction:
Positronium is an atom composed of an electron and a positron (also known as an anti-electron). It is similar to the hydrogen atom, with the proton being replaced by a positron. Like the hydrogen atom, positronium can undergo transitions between different energy levels, resulting in the emission or absorption of photons.

Transition from n=3 to n=1:
In the given question, the positronium atom is said to undergo a transition from the n=3 energy level to the n=1 energy level. This means that the electron in the positronium atom moves from a higher energy state (n=3) to a lower energy state (n=1).

Energy Difference:
The energy difference between the initial and final energy levels can be calculated using the formula:

ΔE = E_final - E_initial

In the case of positronium, the energy of an electron in a given energy level is given by the formula:

E = -13.6 eV / n^2

where n is the principal quantum number.

Substituting the values for the initial and final energy levels, we can calculate the energy difference:

ΔE = (-13.6 eV / 1^2) - (-13.6 eV / 3^2)
= (-13.6 eV) - (-13.6 eV / 9)
= -13.6 eV + 1.51 eV
= -12.09 eV

Photon Energy:
According to the conservation of energy, the energy difference between the initial and final energy levels is equal to the energy of the emitted or absorbed photon. Therefore, the corresponding photon energy for the given transition is 12.09 eV.

Correct Answer:
The correct answer given is option 'B' (6.0 eV). However, this answer is incorrect based on the calculations performed above. The correct answer should be -12.09 eV (as calculated).

Note: It is possible that there might be an error or typo in the answer options provided. It is always important to double-check the answer choices and perform the calculations independently to ensure accuracy.

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