A hydrogen-like atom (atomic number Z ) is in a higher excited...

A hydrogen-like atom (atomic number $Z$) is in a higher excited state of quantum number $n$. This excited atom can make a transition to the first excited state by successively emitting two photons of energies $\text{10.20}eV$ and $\text{17.00}eV$ respectively. Alternatively, the atom from the same excited state can make a transition to the second excited state by successively emitting two photons of energy $\text{4.25}eV$ and $\text{5.95}eV$ respectively. Determine the value of $Z$. [Ionization energy of hydrogen atom $= \text{13.6}eV]$