Q. A hydrogen-like atom (atomic number $Z$ ) is in a higher excited state of quantum number $n$ . By successively emitting two photons of energies $10.20eV$ and $17.00eV$ respectively this excited atom can transition to the first excited state. By successively emitting two photons of energies $4.25eV$ and $5.95eV$ respectively the atom can also transition to the second excited state. If the value of $\frac{Z}{n}$ is $\frac{3}{x}$ then find $x$ . (ionization energy of hydrogen atom $=13.6eV$ )
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