Simple Nature - Light and Matter

constitute more detailed information than the over-all intensity ofa beam of light. Eyeball measurements can’t detect this type of information,since the eye is much bigger than a wavelength, but forexample an AM radio receiver can do it with radio waves, sincethe wavelength for a station at 1000 kHz is about 300 meters,which is much larger than the antenna. The correspondence principledemands that we be able to explain this in terms of the photontheory, and this requires not just that we have a large numberof photons emitted by the transmitter per second, as in example 7,but that even by the time they spread out and reach the receivingantenna, there should be many photons overlapping each otherwithin a space of one cubic wavelength. Problem 47 on p. 903verifies that the number is in fact extremely large.Momentum of a photon example 9⊲ According to the theory of relativity, the momentum of a beamof light is given by p = E/c. Apply this to find the momentumof a single photon in terms of its frequency, and in terms of itswavelength.⊲ Combining the equations p = E/c and E = hf , we findp = E/c= h c f .To reexpress this in terms of wavelength, we use c = f λ:p = h c · cλ= h λThe second form turns out to be simpler.Discussion QuestionsA The photoelectric effect only ever ejects a very tiny percentage ofthe electrons available near the surface of an object. How well does thisagree with the wave model of light, and how well with the particle model?Consider the two different distance scales involved: the wavelength of thelight, and the size of an atom, which is on the order of 10 −10 or 10 −9 m.B What is the significance of the fact that Planck’s constant is numericallyvery small? How would our everyday experience of light be differentif it was not so small?C How would the experiments described above be affected if a singleelectron was likely to get hit by more than one photon?D Draw some representative trajectories of electrons for ∆V = 0, ∆Vless than the maximum value, and ∆V greater than the maximum value.E Explain based on the photon theory of light why ultraviolet light wouldbe more likely than visible or infrared light to cause cancer by damagingDNA molecules. How does this relate to discussion question C?Section 13.2 Light As a Particle 843