The work function of a metal is 2.56 x 10-19J. Calculate the frequency of a photon whose energy is required to eject from the metal an electron with kinetic...

Answer Details

The energy required to eject an electron from a metal is given by: Kinetic energy of ejected electron = Energy of photon – Work function We can rearrange this equation to find the energy of the photon: Energy of photon = Kinetic energy of ejected electron + Work function The kinetic energy of the ejected electron is given as 3.0 eV. We can convert this to joules using the conversion factor 1 eV = 1.6 x 10^-19 J: Kinetic energy of ejected electron = 3.0 eV x 1.6 x 10^-19 J/eV = 4.8 x 10^-19 J Substituting this value and the given work function into the equation for the energy of the photon: Energy of photon = 4.8 x 10^-19 J + 2.56 x 10^-19 J = 7.36 x 10^-19 J We can use the formula E = hf to relate the energy of the photon to its frequency f: E = hf where h is Planck's constant, h = 6.6 x 10^-34 J s. Rearranging the equation gives: f = E/h Substituting the values we obtained: f = (7.36 x 10^-19 J) / (6.6 x 10^-34 J s) ≈ 1.12 x 10¹⁵ Hz Therefore, the frequency of the photon required to eject an electron with a kinetic energy of 3.0 eV from a metal with a work function of 2.56 x 10^-19 J is approximately 1.12 x 10¹⁵ Hz.