What frequency of light is needed to eject an electron from a metal whose threshold energy is #"201 kJ/mol"#?
1 Answer
This sounds like it's about the photoelectric effect.
The binding energy
It is also defined as the threshold that needs to be overcome in order to eject a specific number of electron(s). Hence, its associated frequency IS the threshold frequency.
If you supply more energy than the required threshold to eject a specific quantity of electrons, the difference in the supplied energy and the binding energy gives the remaining kinetic energy that goes into the ejected electrons.
Therefore, the equation becomes:
#bb(stackrel("leftover kinetic energy")overbrace(K_e) = stackrel("supplied")overbrace(E_"photon"))# #-bb()# #bb(stackrel("required threshold")overbrace(phi))#
#= bb(hnu - hnu_0)# where
#nu_0# is the threshold frequency.
Based on your question, all you need is the threshold frequency
#phi = hnu_0#
#color(blue)(nu_0) = phi/h#
#=# #[(201 cancel"kJ")/cancel"mol electrons" xx cancel"1 mol electrons"/(6.022xx10^(23)) xx (1000 cancel"J")/cancel"1 kJ"]/[6.626xx10^(-34) cancel("J")cdot"s"]#
#= color(blue)(5.04 xx 10^14# #color(blue)("Hz")# or#"s"^(-1)#