When light of a wavelength 307nm is shined on a uranium metal surface, electrons

Question

When light of a wavelength 307nm is shined on a uranium metal surface, electrons are ejected from the metal with velocity 5.4x10^5m/s. This phenomenon is called photoelectric effect.

a) calcualate the frequency, in Hertz (Hz), of the light shined on the metal surface?

b)In a seperate experiment the kinetic energy emitted electrons was observed to be 2.45x10^-19J. If the energy of the light shined on the uranium surface was 1.930x10^-18J/photon, what is the binding energy of uranium? give you answer in joules.

Explanation / Answer

a) Given that wavelength of light = 307 nm = 307 x 10-9 m ( 1 nm = 10-9 m )

    We know that

     c = v   where c = velocity of light = 3 x 108 m/s

                 v = frequency

     v = c/

       = 3 x 108 m/s / 307 x 10-9 m

      = 0.0098 x 1017 Hz

   v = 0.0098 x 1017 Hz

Therefore,

frequency of the light shined on the metal surface = 0.0098 x 1017 Hz

b)    We know that E = BE + KE     where BE = Binding energy

                              1.930 x10 -18 J = BE + 2.45 x 10-19 J

                               BE = 1.685 x 10-18 J

Therefore,

binding energy of uranium = 1.685 x 10-18 J

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