Violet light of wavelength 405 nm ejects electrons with a maximum kinetic energy of 0.890 eV from a certain metal. What is the binding energy (in electronvolts) of electrons to this metal

  Ф = 2.179 eV

Explanation:

This exercise has electrons ejected from a metal, which is why it is an exercise on the photoelectric effect, which is explained assuming the existence of energy quanta called photons that behave like particles.

            E = K + Ф

the energy of the photons is given by the Planck relation

            E = h f

we substitute

           h f = K + Ф

           Ф= hf - K

the speed of light is related to wavelength and frequency

            c = λ f

            f = c /λ

            Φ =

let's reduce the energy to the SI system

            K = 0.890 eV (1.6 10⁻¹⁹ J / 1eV) = 1.424 10⁻¹⁹ J

calculate

           Ф = 6.63 10⁻³⁴ 3 10⁸/405 10⁻⁹  -1.424 10⁻¹⁹

           Ф = 4.911 10⁻¹⁹ - 1.424 10⁻¹⁹

           Ф = 3.4571 10⁻¹⁹ J

we reduce to eV

           Ф = 3.4871 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

           Ф = 2.179 eV

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