The work functions of cesium (\(\text{Cs}\)) and lithium (\(\text{Li}\)) metals are \(1.9\text{ }\text{eV}\) and \(2.5\t…
The work functions of cesium (\(\text{Cs}\)) and lithium (\(\text{Li}\)) metals are \(1.9\text{ }\text{eV}\) and \(2.5\text{ }\text{eV}\), respectively. If light of wavelength 550 nm is incident on these two metal surfaces, for which metal(s) will the photoelectric effect occur? (Planck’s constant \(h=6.63\times 1{0}^{−34}\text{ }\text{Js}\), Speed of light \(c=3\times 1{0}^{8}\text{ }\text{m/s}\).)
[JEE Main 2025, 22 Jan (Shift 1)]
Cs only
\(\mathrm{Energy}\mathrm{associated}\mathrm{to}\lambda =550\mathrm{nm}\mathrm{is}\\ \mathrm{E}=\frac{\mathrm{h}\mathrm{c}}{\lambda }\\ \mathrm{E}=\frac{6.63\times {10}^{-34}\times 3\times {10}^{8}}{550\times {10}^{-9}}=3.61\times {10}^{-19}\mathrm{J}\\ \mathrm{E}=\frac{3.61\times {10}^{-19}}{1.6\times {10}^{-19}}=2.25\mathrm{eV}\)
This energy is more than the work function of cesium and less than the work fucntion of lithium. So photoelectric emission is possible for cesium only.
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