Simple Nature - Light and Matter

How would you extract h from the graph in figure h? What if you didn’teven know E s in advance, and could only graph e∆V versus f ? ⊲Answer, p. 929Since the energy of a photon is hf, a beam of light can only haveenergies of hf, 2hf, 3hf, etc. Its energy is quantized — there is nosuch thing as a fraction of a photon. Quantum physics gets its namefrom the fact that it quantizes quantities like energy, momentum,and angular momentum that had previously been thought to besmooth, continuous and infinitely divisible.Number of photons emitted by a lightbulb per second example 7⊲ Roughly how many photons are emitted by a 100-W lightbulb in1 second?⊲ People tend to remember wavelengths rather than frequenciesfor visible light. The bulb emits photons with a range of frequenciesand wavelengths, but let’s take 600 nm as a typical wavelengthfor purposes of estimation. The energy of a single photonisE photon = hf= hc/λA power of 100 W means 100 joules per second, so the numberof photons is(100 J)/E photon = (100 J)/(hc/λ)≈ 3 × 10 20This hugeness of this number is consistent with the correspondenceprinciple. The experiments that established the classicaltheory of optics weren’t wrong. They were right, within their domainof applicability, in which the number of photons was so largeas to be indistinguishable from a continuous beam.Measuring the wave example 8When surfers are out on the water waiting for their chance tocatch a wave, they’re interested in both the height of the wavesand when the waves are going to arrive. In other words, they observeboth the amplitude and phase of the waves, and it doesn’tmatter to them that the water is granular at the molecular level.The correspondence principle requires that we be able to do thesame thing for electromagnetic waves, since the classical theoryof electricity and magnetism was all stated and verified experimentallyin terms of the fields E and B, which are the amplitudeof an electromagnetic wave. The phase is also necessary, sincethe induction effects predicted by Maxwell’s equation would fliptheir signs depending on whether an oscillating field is on its wayup or on its way back down.This is a more demanding application of the correspondence principlethan the one in example 7, since amplitudes and phases842 Chapter 13 Quantum Physics