Light from the Balmer series of hydrogen is capable of ejecting...

The Balmer series of hydrogen corresponds to electron transitions from higher energy levels $n \ge 3$ to $n = 2$.

The energy of the emitted photon is given by $E = 13.6 \left( \dfrac{1}{2^2} - \dfrac{1}{n^2} \right) \text{ eV}$.

The maximum energy of a photon in the Balmer series is obtained for the transition from $n = \infty$ to $n = 2$.

E_{\text\max} = 13.6 \left( \dfrac{1}{4} - 0 \right) = 3.4 \text{ eV}.

For the photoelectric effect to occur, the energy of the incident photon must be greater than or equal to the work function $\Phi$ of the metal, which implies \Phi \le E_{\text\max}.

Therefore, the maximum possible work function of the metal is $3.4 \text{ eV}$.