The work function for a metallic surface is 4.0 eV. The longest wavelength of light that can cause photoelectron emission is approximately
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 310 nm
Photoelectrons are emitted only if the photon energy is at least the work function. Light of any wavelength shorter than the threshold wavelength \( \lambda_0 \) works, so the longest wavelength is the one whose photon energy just equals the work function.
\( \displaystyle \frac{hc}{\lambda_0} = \phi_0 \Rightarrow \lambda_0 = \frac{hc}{\phi_0} \)
\( \phi_0 = 4.0\,\mathrm{eV} = 4.0\times1.6\times10^{-19}\,\mathrm{J} = 6.4\times10^{-19}\,\mathrm{J} \)
\( \displaystyle \lambda_0 = \frac{6.63\times10^{-34}\times3\times10^{8}}{6.4\times10^{-19}}\,\mathrm{m} \approx 3.1\times10^{-7}\,\mathrm{m} = 310\,\mathrm{nm} \)
Shortcut: Use \( hc \approx 1240\,\mathrm{eV\,nm} \), so \( \lambda_0(\mathrm{nm}) = 1240/\phi_0(\mathrm{eV}) = 1240/4.0 = 310\,\mathrm{nm} \).
Note: A similar question was also asked in CUET (UG) 2025 on 19-05-2025 (Slot 1).