Question

The work function of a material is 2.21 eV. Which of the following cannot produce photoelectrons from it?

• A. Red light
• B. Blue light
• C. Violet light
• D. Green light

Hint:

Use \( E = \frac{1240}{\lambda} \) to quickly estimate photon energy in eV. Red light has the longest wavelength and lowest photon energy among visible light.

Answer 1

The Correct Option is A

To eject photoelectrons, the energy \( E \) of the incident photon must be greater than or equal to the work function \( \phi \). The energy of a photon is given by: \[ E = \frac{hc}{\lambda} = \frac{1240\ \text{eV·nm}}{\lambda\ (\text{nm})} \] Work function \( \phi = 2.21\ \text{eV} \) Now we compare photon energies of different visible lights: - Red light: \( \lambda \approx 700\ \text{nm} \Rightarrow E \approx \frac{1240}{700} \approx 1.77\ \text{eV} \) - Green light: \( \lambda \approx 550\ \text{nm} \Rightarrow E \approx \frac{1240}{550} \approx 2.25\ \text{eV} \) - Blue light: \( \lambda \approx 470\ \text{nm} \Rightarrow E \approx \frac{1240}{470} \approx 2.64\ \text{eV} \) - Violet light: \( \lambda \approx 400\ \text{nm} \Rightarrow E \approx \frac{1240}{400} \approx 3.10\ \text{eV} \) Only red light has energy less than the work function and therefore cannot emit photoelectrons.