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

Photoelectron emission requires incident photon energy \( E \) to be at least equal to the work function \( \phi \). Photon energy is calculated as: \[E = \frac{hc}{\lambda} = \frac{1240\ \text{eV·nm}}{\lambda\ (\text{nm})}\]Given the work function \( \phi = 2.21\ \text{eV} \), we compare photon energies for visible light wavelengths: - Red light: \( \lambda \approx 700\ \text{nm} \Rightarrow E \approx 1.77\ \text{eV} \) - Green light: \( \lambda \approx 550\ \text{nm} \Rightarrow E \approx 2.25\ \text{eV} \) - Blue light: \( \lambda \approx 470\ \text{nm} \Rightarrow E \approx 2.64\ \text{eV} \) - Violet light: \( \lambda \approx 400\ \text{nm} \Rightarrow E \approx 3.10\ \text{eV} \)Only red light, with energy below the work function, cannot emit photoelectrons.