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