Answer
(a) $B\lt A\lt C$
(b) $C\lt A\lt B$
Work Step by Step
We know that
$\Delta E_B=|E_2-E_7|$
$\implies\Delta E_B= |\frac{-13.6}{2^2}-\frac{-13.6}{7^2}|$
This simplifies to:
$\Delta E_B=3.12eV$
$\Delta E_A=|E_2-E_5|$
$\Delta E_A=13.6(\frac{1}{4}-\frac{1}{25})=2.856eV$
and $\Delta E_C=13.6(\frac{1}{36}-\frac{1}{49})=0.1eV$
As $\Delta E_B\gt \Delta E_A\gt \Delta E_C $, therefore $\lambda_B\lt \lambda_A\lt \lambda_C$
(b) We know that the frequency is directly proportional to energy, therefore, the increasing order of transition in frequency is given as $C\lt A\lt B$
