Simple Nature - Light and Matter

equations of general validity are those that do not have c in them:E = hfp = h/λThis is essentially the reasoning that de Broglie went through,and experiments have confirmed these two equations for all the fundamentalbuilding blocks of light and matter, not just for photonsand electrons.The second equation, which I soft-pedaled in the previous chapter,takes on a greater important for electrons. This is first of allbecause the momentum of matter is more likely to be significantthan the momentum of light under ordinary conditions, and alsobecause force is the transfer of momentum, and electrons are affectedby electrical forces.The wavelength of an elephant example 12⊲ What is the wavelength of a trotting elephant?⊲ One may doubt whether the equation should be applied to anelephant, which is not just a single particle but a rather large collectionof them. Throwing caution to the wind, however, we estimatethe elephant’s mass at 10 3 kg and its trotting speed at 10m/s. Its wavelength is therefore roughlyλ = h p= hmv= 6.63 × 10−34 J·s(10 3 kg)(10 m/s)∼ 10 −37 (kg·m 2 /s 2)·skg·m/s= 10 −37 mThe wavelength found in this example is so fantastically smallthat we can be sure we will never observe any measurable wavephenomena with elephants or any other human-scale objects. Theresult is numerically small because Planck’s constant is so small,and as in some examples encountered previously, this smallness isin accord with the correspondence principle.Although a smaller mass in the equation λ = h/mv does resultin a longer wavelength, the wavelength is still quite short evenfor individual electrons under typical conditions, as shown in thefollowing example.The typical wavelength of an electron example 13⊲ Electrons in circuits and in atoms are typically moving through854 Chapter 13 Quantum Physics