Question

Ultraviolet radiation of wavelength 176 nm is incident on the surface of a metal Electrons are released from the metal with a maximum kinetic energy of 4.52 eV (a) What is the maximum wavelength of the incident radiation that could cause electrons to be released from the metal? (b) If the wavelength of the incident radiation were changed to 288 nm, what would be the maximum kinetic energy of the emitted electrons?

Answer 1

Answer:a) 492 nm; b) 1.78 eV

Explanation: In order to solve this problem we have to use the photoelectric energy balance givenb by:

h*ν=Ek+W  where h is the Placnk constant, ν is the frequency of the radiation, Ek is the kinetic energy of the realised electrons and W is the work funcion of the incident metal.

Then we have:

W=h*ν-Ek= h*c/λ-Ek=1240 eV.nm/176 nm=2.52 eV

so the maximun wavelength to realese the electrons is when Ek=0 then

W=h*c/λmax so λmax= h*c/W= 1240/2.52=492.06 nm

Finally if we use 288 nm to realease the electrons, then Ek of the emitted electron from the metal is:

from  h*ν=Ek+W we have:

Ek=h*c/λ-W= (1240/288) eV*nm-2.52 eV=1.78 eV