Question

The work function of thallium is 6.82 X 10 -19 J. What is the maximum frequency of photon that will eject an electron from thallium metal?

Answer 1

`ν = 1.03 xx 10^15s^(-1)` ; `λ = 291nm`, in the ultraviolet region.

Explanation:

`ν = 1.03 xx 10^15s^(-1)`
That wasn’t entirely clear, but I am taking it to mean that the electron energy of the valence electron is the “work function” you state. In that case the energy of a photon must at least equal it in order to eject it from the orbital.
`E_("photon") = (hc)/lambda`
where:
`h = 6.63 xx 10^(-34) Js`
`c = 3.0 xx 10^8 m/s`
`lambda = m (or nm x 10^(-9))`
`ν = c/λ`
Calculate the wavelength required for the specified energy, then calculate the corresponding frequency.
`E_("photon") = (hc)/lambda = h xx ν = 6.82 xx 10^(-19) J`
`6.82 xx 10^(-19) J = 6.63 xx 10^(-34) Js xx ν`

`ν = (6.82 xx 10^(-19))/(6.63 xx 10^(-34) Js)`

`ν = 1.03 xx 10^15s^(-1)` ; `λ = 291nm`, in the ultraviolet region.