Answer :

Correct answer is : 7

Longest wavelength ⇒ Minimum energy

$\frac{1}{\mathrm{\lambda <!--\; \lambda \; -->}}=R[\frac{1}{3^2}-<!--\; -\; -->\frac{1}{4^2}]$

$=\frac{7R}{144}$

$\mathrm{\Rightarrow \; \lambda <!--\; \lambda \; -->}=\frac{144R}{7}$