JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 17)
A metal exposed to light of wavelength $$800 \mathrm{~nm}$$ and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $$500 \mathrm{~nm}$$ is used. The workfunction of the metal is : (Take hc $$=1230 \,\mathrm{eV}-\mathrm{nm}$$ ).
1.537 eV
2.46 eV
0.615 eV
1.23 eV
Explanation
$$\because$$ $${K_m} = {{hc} \over \lambda } - \phi $$
$$ \Rightarrow K = {{1230} \over {800}} - \phi $$
and, $$2K = {{1230} \over {500}} - \phi $$
$$ \Rightarrow 2 \times {{1230} \over {800}} - 2\phi = {{1230} \over {500}} - \phi $$
$$ \Rightarrow \phi = 0.615\,eV$$
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