To calculate the threshold frequency of the metal we use the formula,
[tex]E=h\nu_{o}[/tex]
Also, [tex]\nu_{o}=\frac{E}{h}[/tex]
Here, E is the energy of electron per atom, h is plank constant.
Given, binding energy of electron [tex]E=192kJ/mol[/tex] or for one electron,[tex]E=\frac{192 kJ/mol}{N}[/tex], here N is the Avogadro constant and its value is [tex]6.023\times10^{23}[/tex], so [tex]E=\frac{192\times10^3 J}{6.023\times10^{23}}=3.19\times10^{-19} J[/tex] and plank constant, [tex]h=6.626\times10^{-34} Js[/tex]
Substituting these values in above relation we get,
[tex]\nu _{o} =\frac{3.19 \times10^{-19J} }{6.626 \times 10^{-34}Js } =4.81\times 10^{14} Hz[/tex].
Thus, the threshold frequency of the metal is [tex]4.81 \times 10^{14} Hz[/tex].
