Answer
$2.25\Big(\frac{h}{8mL^2}\Big)$
Work Step by Step
The frequency $(v)$ that corresponds to photon energy $(E)$ is given by
$v=\frac{E}{h}$
From the section $(a)$ of this problem, we can say that the third highest frequency occurs at $E_{2,1}\leftrightarrow E_{1,2}$ tranision. The corresponding frequency is
$v=\frac{\Delta E}{h}=2.25\Big(\frac{h}{8mL^2}\Big)$
