The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause electron emission from the material is (approximately)

310 nm

The correct answer is Option (4) → 310 nm

Photoelectric effect: $E_\text{photon} = h \nu = \phi$ for threshold wavelength

Energy of photon: $E = \frac{hc}{\lambda}$

Given: $\phi = 4.0 \, \text{eV} = 4.0 \times 1.6 \times 10^{-19} \, \text{J} = 6.4 \times 10^{-19} \, \text{J}$

Planck's constant: $h = 6.63 \times 10^{-34} \, \text{Js}$, $c = 3 \times 10^8 \, \text{m/s}$

$\lambda_\text{max} = \frac{hc}{\phi} = \frac{6.63 \times 10^{-34} \cdot 3 \times 10^8}{6.4 \times 10^{-19}}$

$\lambda_\text{max} \approx \frac{1.989 \times 10^{-25}}{6.4 \times 10^{-19}} \approx 3.11 \times 10^{-7} \, \text{m}$

Longest wavelength ≈ 311 nm