The work function of a substance is $$3.0 \text{ eV}$$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately:

The photoelectric effect equation at threshold (minimum frequency / maximum wavelength) is:

$$E = \phi = \frac{hc}{\lambda_{max}}$$

where $$\phi$$ is the work function, $$h$$ is Planck's constant, $$c$$ is the speed of light, and $$\lambda_{max}$$ is the longest wavelength that can cause photoemission.

Solving for $$\lambda_{max}$$:

$$\lambda_{max} = \frac{hc}{\phi}$$

Using the standard value $$hc = 1240 \text{ eV} \cdot \text{nm}$$:

$$\lambda_{max} = \frac{1240}{3.0} = 413.3 \text{ nm} \approx 414 \text{ nm}$$

The correct answer is $$414 \text{ nm}$$.