Light of frequency 8.41×1014Hz is incident on a metal surface. Electrons with a maximum speed of 7.5×105 ms−1 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=6.625×10−34Js−1 and mass of the electron 9.1×10−31Kg.
v=8.41×1014Hz
Vmax=7.5×105ms−1
h=6.625×10−34Js−1
m=9.1×10−31kg
hv=ϕ0+Kmax
hv=hv0+12mV2max
hv−hv0=12mV2max
(v−v0)=12hmV2max=12×6.625×10−34×9.1×10−31×(7.5×105)2
(v−v0)=3.8632×1014
v0=8.41×1014−3.8632×1014=4.5468×1014Hz
ϕ0=hv0=6.625×10−34×4.5468×1014=3.01226×10−19
ϕ0=3.01226×10−191.6×10−19=1.8826eV