Final answer:
The longest wavelength of light that can eject a photoelectron from a metal with a work function of 2.18 eV is approximately 568 nm, which is in the visible range.
Step-by-step explanation:
The question is asking for the longest wavelength of light that can eject a photoelectron from a metal with a work function of 2.18 eV. To find the longest wavelength (λ), we use the energy equation for photons: E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10-34 J·s), and c is the speed of light in a vacuum (3 x 108 m/s). The energy of the photon needs to be at least equal to the work function of the metal for photoemission to occur. Converting 2.18 eV to joules (1 eV = 1.602 x 10-19 J), we get E = 2.18 eV * 1.602 x 10-19 J/eV = 3.489 x 10-19 J. Now we solve for λ: λ = hc/E = (6.626 x 10-34 J·s * 3 x 108 m/s) / (3.489 x 10-19 J) ≈ 568 nm, which is in the visible spectrum.
Therefore, the longest wavelength of light that can eject a photoelectron from the metal is approximately 568 nm.