# The surface of a metal is illuminated alternatively with photons of energies E=4eV and E=2.5eV resp. The ratio of maximum speeds of the photoelectrons emitted is the two cases is 2. The work function of  the metal in eV is ...... Option: 1 2.5 Option: 2 5 Option: 3 7.5 Option: 4 10

$\mathrm{E}_{1}=\phi+\mathrm{K}_{1} \ldots(1) \\ \mathrm{E}_{2}=\phi+\mathrm{K}_{2} \ldots(2) \\ E_{1}-E_{2}=K_{1}-K_{2} \\ Now \frac{V_{1}}{V_{2}}=2 \\ \frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}=4 \\ \mathrm{K}_{1}=4 \mathrm{~K}_{2} \\ Now from equation (2) \Rightarrow 4-2.5=4 \mathrm{~K}_{2}-\mathrm{K}_{2} \\ 1.5=3 \mathrm{~K}_{2} \\\ \mathrm{K}_{2}=0.5 \mathrm{eV} \\ Now putting This Value in equation (2) \\ 2.5=\phi+0.5 \mathrm{eV} \\ \phi=2 \mathrm{ev}$

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