Arrange the following photosensitive metals (work function given in brackets) according to their threshold wavelengths in decreasing order of their values.
A. K (Φ = 2.3 eV)
B. Na (Φ = 2.75 eV)
C. Cs (Φ = 2.14 eV)
D. Ca (Φ = 3.2 eV)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → C, A, B, D
The threshold wavelength is the longest wavelength whose photons can just eject electrons, \( hc/\lambda_0 = \Phi \). So
\( \displaystyle \lambda_0 = \frac{hc}{\Phi} \)
and the threshold wavelength is inversely proportional to the work function. Decreasing \( \lambda_0 \) means increasing \( \Phi \):
\( \text{Cs (C)}: 2.14\,\mathrm{eV} \;\lt\; \text{K (A)}: 2.3\,\mathrm{eV} \;\lt\; \text{Na (B)}: 2.75\,\mathrm{eV} \;\lt\; \text{Ca (D)}: 3.2\,\mathrm{eV} \)
Decreasing order of threshold wavelength: C, A, B, D.