where ν is the frequency of light shining on the metal; W is the energy needed to remove an electron from the metal; and me and u are the mass and speed of the ejected electron, respectively. In an experiment, a student found that a maximum wavelength of 371 nm is needed to just dislodge electrons from a metal surface. Calculate the velocity (in m/s) of an ejected electron when the student employed light with a wavelength of 283 nm.

  v = 6.05 10⁵ m / s

Explanation:

This is an exercise of the photoelectric effect, which consists of the emission of electrons from a metal by the action of incident light, this phenomenon was explained by Einstein, assuming that the light rays are composed of particular called photons, for which the process is can explain by the collision of two particles,

         h f = K + Φ

where hv is the energy of the photons, K the kinetic energy of the electrons and fi the work function of the metal

speed, wavelength and frequency are related by

          c = λ f

we substitute

        h c /λ = K + Φ

let's apply this expression to our problem

λ = 371 nm = 371 10⁻⁹ m

the kinetic energy of zero electrons K = 0

          h  c /λ = Ф

         Ф = 6.63 10⁻³⁴  3 10⁸/371 10⁻⁹

         Ф = 5.36 10⁻¹⁹ J

this value is constant since the metal does not change

for λ = 283 nm = 283 10⁻⁹ m

          K = hc /λ - fi

          K = 6.63 10⁻³⁴  3 10⁸/283 10⁻⁹ - 5.36 10⁻¹⁹

          K = (7.028 - 5.36) 10⁻¹⁹

          K = 1,668 10⁻¹⁹ J

the expression of kinetic energy is

          K = ½ m v²

          v = √ (2K / m)

          v = √(2 1,668 10⁻¹⁹ / 9,1 10⁻³¹)

          v = RA (0.36659 10¹²)

          v = 0.605 10⁶ m / s

          v = 6.05 10⁵ m / s

a and b sometimes have a positive value