The work functions of Cesium and Platinum are 1.9 eV and 5.7 eV, respectively. The ratio of their threshold wavelengths, respectively is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 3:1 \)
The threshold wavelength is the longest wavelength that can eject electrons, given by \( \phi_0 = hc/\lambda_0 \), so \( \lambda_0 \propto 1/\phi_0 \). The smaller the work function, the longer the threshold wavelength.
\( \displaystyle \frac{\lambda_{\mathrm{Cs}}}{\lambda_{\mathrm{Pt}}} = \frac{\phi_{\mathrm{Pt}}}{\phi_{\mathrm{Cs}}} = \frac{5.7}{1.9} = 3 \)
So the ratio is \( 3:1 \).