The work function of a photosensitive material is \( 4.0\,\mathrm{eV} \). The longest wavelength of light that can cause electron emission from the material is (approximately)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 310\,\mathrm{nm} \)
Electrons are emitted only if the photon energy is at least the work function. The longest wavelength that works is the threshold wavelength, where the photon energy just equals the work function.
\( \displaystyle \phi_0 = \frac{h c}{\lambda_{\max}} \;\Rightarrow\; \lambda_{\max} = \frac{h c}{\phi_0} \)
\( \displaystyle hc \approx 1240\,\mathrm{eV\,nm} \;\Rightarrow\; \lambda_{\max} = \frac{1240\,\mathrm{eV\,nm}}{4.0\,\mathrm{eV}} = 310\,\mathrm{nm} \)
Note: A similar question was also asked in CUET (UG) 2023 on 08-06-2023 (Slot 3).