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Question

Light of frequency 8.41×1014Hz is incident on a metal surface. Electrons with a maximum speed of 7.5×105 ms1 are ejected from the surface. Calculate the threshold frequency for photo emission of electrons. Also find the work function of the metal in electron volt (eV). Given, Planck's constant h=6.625×1034Js1 and mass of the electron 9.1×1031Kg.

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Solution

v=8.41×1014Hz
Vmax=7.5×105ms1
h=6.625×1034Js1
m=9.1×1031kg
hv=ϕ0+Kmax
hv=hv0+12mV2max
hvhv0=12mV2max
(vv0)=12hmV2max=12×6.625×1034×9.1×1031×(7.5×105)2
(vv0)=3.8632×1014
v0=8.41×10143.8632×1014=4.5468×1014Hz
ϕ0=hv0=6.625×1034×4.5468×1014=3.01226×1019
ϕ0=3.01226×10191.6×1019=1.8826eV

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