A) \[9\times {{10}^{3}}\,\,Hz\]
B) \[\lambda \,~\text{is greater than 2d}\]
C) \[\lambda \,quals2d\]
D) \[\lambda \,\text{is smaller than or equal to 2d}\]
Correct Answer: C
Solution :
The energy of incident photon of wavelength 400 nm is \[p{{K}_{b}}\] \[{{C}_{2}}{{H}_{5}}N{{H}_{2}}.{{C}_{6}}{{H}_{5}}NHC{{H}_{3}},{{({{C}_{2}}{{H}_{5}})}_{2}}NH\]Number of such photons in a beam of light of power \[1.55\text{ }mW\] \[{{C}_{6}}{{H}_{5}}N{{H}_{2}}\] \[{{\left( {{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}} \right)}_{\text{2}}}\text{NH}>{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}>{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{NHC}{{\text{H}}_{\text{3}}}>{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}\] This implies, number of photons that were used to produce photoelectron per second \[{{\left( {{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}} \right)}_{\text{2}}}\text{NH}>{{\text{C}}_{6}}{{\text{H}}_{\text{5}}}\text{NHC}{{\text{H}}_{\text{3}}}>{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}>{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}\] Hence, the current due to such photoelectron per second \[{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}>{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{NHC}{{\text{H}}_{\text{3}}}>{{\left( {{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}} \right)}_{\text{2}}}\text{NH}>{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}\] \[{{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}>{{\left( {{\text{C}}_{\text{2}}}{{\text{H}}_{\text{5}}} \right)}_{\text{2}}}\text{ NH }>{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{NHC}{{\text{H}}_{\text{3}}}>{{\text{C}}_{\text{6}}}{{\text{H}}_{\text{5}}}\text{N}{{\text{H}}_{\text{2}}}\]
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