Answer
49.4 nm
Work Step by Step
The longest wavelength photon has an energy equal to the sum of the ionization energy (13.6 eV) and the kinetic energy (11.5 eV).
$$ E_{total} =hf = \frac{hc}{\lambda}$$
In this problem, the value of hc is useful. Use the result stated in Problem 29, $hc=1240\;eV \cdot nm$.
$$ \lambda=\frac{hc}{E_{total}}=\frac{1240\;eV \cdot nm }{13.6eV+11.5eV}=49.4 nm$$