What is the threshold energy of zinc in joules? A photon of light, incident upon

Question

What is the threshold energy of zinc in joules? A photon of light, incident upon a clean, zinc surface ejects an electron with a kinetic energy of 2.1186 * 10-19 J; what are the energy (J), frequency (Hz) and wavelength (nm) of the photon? A common research laser is an AR-ion (argon-ion) laser, which emits a wavelength of 514.5nm. Would a photon from an Ar-ion laser be sufficiently energetic to kick an electron off a clean surface of zinc metal? If so, what kinetic energy would that electron possess?

Explanation / Answer

threshold energy of Zinc = 4.3 eV
   = (4.3)*(1.6*10^-19) J
   = 6.88*10^-19 J

Kinetic energy = 2.1186*10^-19 J

Energy of photon = 6.88*10^-19 + 2.1186*10^-19
    =8.9986*10^-19 J

use: E= h*f
frequancy, f = E/h
   = (8.9986*10^-19) / 6.626*10^-34
   = 1.36*10^15 Hz

wavelength = c/f
   = (3*10^8) / ( 1.36*10^15)
   =2.2*10^-7 m
   = 220 nm

Enrgy of photon in AR-ion = h*c/wavelength
   = (6.626*10^-34)*(3*10^8) / (514.5*10^-9)
   = 3.86*10^-19 J
Since energy is less than threshold energu of Zn , it can't eject electron

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