In the case of hydrogen like atom, the maximum energy liberated by the Balmer series is,

$n_1=2, n_2=\infty$

We know that energy is given by,

$\Rightarrow E=13.6\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) \mathrm{eV}$
$\Rightarrow E=13.6\times \frac{1}{4} \mathrm{eV}$
$\Rightarrow E=3.4 \mathrm{eV}$

Thus, $3.4 \mathrm{eV}$ is the maximum work function of the metal.