A) \[<2.8\times {{10}^{-9}}m\]
B) \[\ge 2.8\times {{10}^{-9}}m\]
C) \[\le 2.8\times {{10}^{-12}}m\]
D) \[<2.8\times {{10}^{-10}}m\]
Correct Answer: B
Solution :
[b] Work function \[\phi \] of metal = 2.28 eV Wavelength of light \[X=500nm=500\times {{10}^{-9}}m\]\[\lambda =500nm=500\times {{10}^{-9}}m\] \[K{{E}_{\max }}=\frac{hc}{\lambda }-\phi \] \[K{{E}_{\max }}=\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{5\times {{10}^{-7}}\times 1.6\times {{10}^{-19}}}-2.28\] \[K{{E}_{\max }}=2.48-2.20.2ev\] \[{{\lambda }_{\min }}=\frac{h}{p}=\frac{h}{\sqrt{2m{{\left( KE \right)}_{\max }}}}\] \[{{\lambda }_{\min }}=\frac{25}{9}\times {{10}^{-9}}=2.80\times {{10}^{-9}}nm\]\[\therefore \lambda \ge 2.8\times {{10}^{-9}}m\]
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