Page 23 - Topic 3
P. 23

CONCEPT CHECK – WAVE-PARTICLE                            high-intensity peaks at particular
        DUALITY                                                  frequencies (known as characteristic
                                                                 X-rays).
        DO YOU KNOW?
                                                                 The intensity of X-rays is decreased
                                                                 (i.e. attenuated) as they pass through
         Concept                          While   Before         matter by scattering and absorption.
                                          studying   the
                                                  test

         In interacting with matter, light                       Particles exhibit wave behaviour with
         behaves like particles (called                          a wavelength that depends on the
         ‘photons’), with energy given by                        momentum of the particle. This de
          E =  hf  and momentum given by                         Broglie wavelength can be
             h                                                   determined using the formula
          p =  ,  where h is Planck’s constant,
             λ                                                    λ =  h  ,  where h is Planck’s constant
         f  is the frequency of the light, and λ                     p
         is its wavelength.                                      and p  is the momentum of the
                                                                 particles.


         When light of sufficiently high
         frequency is incident on matter, it                     The wave behaviour of particles can
         may be absorbed by the matter,                          be demonstrated using a double-slit
         from which electrons are then                           experiment and the Davisson–
         emitted. This is called the                             Germer experiment.
         ‘photoelectric effect’.


                                                                CAN YOU?
         The intensity of the incident light
         affects the number, but not the
         energy, of emitted electrons.                           Application                     While    Before
                                                                                                 Studying   the test
                                                                   •   Describe an experimental
                                                                       method for investigating the
         The minimum frequency,  f ,  at                               relationship between the
                               0
         which electrons are emitted varies                            maximum kinetic energy of
         with the type of material and is called                       the emitted electrons,
         the ‘threshold frequency’.                                    calculated from the measured
                                                                       stopping voltage using

                                                                       E K max =  eV  and the
                                                                               s
         The work function, W , of a surface is                        frequency of the light incident
         the minimum energy required to                                on a metal surface.
         remove an electron from it.
                                                                   •   Describe how Einstein used
                                                                       the concept of photons and
                                                                       the conservation of energy to
         The work function is related to the
         threshold frequency by W =  hf .                              explain the experimental
                                  0
                                                                       observations of the
                                                                       photoelectric effect.

                                                                   •   Deduce the formula
         X-ray photons can be produced                                 E K  = hf − W  where  E K
         when electrons that have been                                   max                max
         accelerated to high speed interact                            is the maximum kinetic energy
         with a target. This is done in a simple                       of the emitted electrons.
         X-ray tube.                                               •   Plot experimental values of
                                                                       maximum kinetic energy vs
                                                                       frequency, and relate the
                                                                       slope and axes intercepts to
         The three main features of the
         spectrum of the X-rays produced in                            the formula:  E K max = hf − W .
         this way are:                                             •   Solve problems that require
           − a continuous range of                                     the use of  E  =  hf − W .
             frequencies (bremsstrahlung)                                        K max
           − a maximum frequency given by                          •   Describe the purpose of the
                   e V                                                 following features of a simple
                    ∆
              f max  =  h   where  V∆   is the                         X-ray tube: filament, target,
             potential difference across the X-                        high-voltage supply,
                                                                       evacuated tube, and a means
             ray tube
                                                                       of cooling the target.
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