The electron in H-atom makes a transition from $n_1 \to n_2$ where $n_1$ and $n_2$ are the principal quantum numbers of the states. Assume Bohr's model to be valid. The time period of the electron in initial state is $27$ times that in final state. Find the possible value of $n_1$ and $n_2$ if only the first $10$ states are in the visible range of the instrument