Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency.

Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is ( $h=$ Planck's constant, $\mathrm{I}=$ moment of inertia of diatomic molecule)

Which of the following transitions in hydrogen atom emit photons of highest frequency? ( $\mathrm{n}=$ principle quantum number)

Two radioactive materials $A$ and $B$ having decay constant ' $7 \lambda$ ' and ' $\lambda$ ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is