JEE Advanced 2025 — Paper 2 — Question 10

A hydrogen atom, initially at rest in its ground state, absorbs a photon of frequency $v_{1}$ and ejects the electron with a kinetic energy of 10 eV . The electron then combines with a positron at rest to form a positronium atom in its ground state and simultaneously emits a photon of frequency $v_{2}$. The center of mass of the resulting positronium atom moves

with a kinetic energy of 5 eV . It is given that positron has the same mass as that of electron and the positronium atom can be considered as a Bohr atom, in which the electron and

the positron orbit around their center of mass. Considering no other energy loss during the whole process, the difference between the two photon energies (in eV ) is $\qquad$