Let’s do a back-of-the-envelope calculation of just how many photons are produced by a typical 60-W lightbulb: although we know that the filament acts as a blackbody, and thus produces a wide range of wavelengths, let’s take 600 nm as an average for our quick estimate. The energy of a photon is E = hf = hc/λ, so the energy (in Joules) of a single photon of 600-nm light is Eλ=600nm = 6.626 × 10−34 [J · s] × 2.998 × 108 [m/s]/600 × 10−9 m = 3.31 × 10−19 J.
A power of 60 W means 60 J/s, so the number of photons produced by a 60-W lightbulb is approximately 60 [J/s]/3.31 × 10−19 [J/photon] = 1.81 × 1020 photons per second. That is a huge number!
Only a small fraction of these reach our eyes, even if we look directly at the lightbulb. This is because the photons are spread over a sphere, and only a small fraction of the photons reach our eyes at a safe distance from the filament. Imagine that you are driving around at night, and you want to see if your friend is still awake. You look at the window from a block away (let’s assume 100 m) and see that the light is still on. How many photons reach your eye?
The photons can be assumed to be flying away from the lightbulb equally in all directions. Since you stand 100 m away, let’s place the lightbulb at the center of a sphere with a radius r = 100 m. The sphere has a surface area of 4πr2, so an r = 100 m sphere has a surface area of 125,664 m2. The pupil of the human eye has an effective diameter of 8 mm (r = 4 mm) in the dark, so its area r2 is around 50 × 10−6 m2. We need to scale down the total number of photons emitted by the lightbulb by 50 × 10−6 m2/125,664 m2 = 400 × 10−12. That means that 400 × 10−12 × 1.81 × 1020 = 72.4 × 109 photons from a 60-W lightbulb at a distance of 100 m reach your eye every second. That’s still a lot of photons from a relatively dim source!
A typical phototube barely gives a measurable current at that level, so how could we ever expect to detect a single photon? Fortunately, some very smart engineers at Westinghouse and RCA figured out that the single electron released from a photocathode by a single photon could be accelerated toward another electrode in order to produce secondary electrons. Two or more electrons are then released when the accelerated photoelectron slams into the electrode. As shown in Figure 28, the same process can be repeated over and over again with the secondary electrons used to successively multiply the number of electrons released in a cascade. A much larger number of electrons finally reach the anode as the result of a single photon hitting the photocathode. Commercially available photomultiplier tubes (PMTs) based on this principle produce as many as 106 to 107 secondary electrons at the anode for each photon that releases a photoelectron from the photocathode.
Figure 28 Photomultiplier tubes are the workhorse detector of experimental particle physics. (a) The photoelectrons released at the photocathode of a PMT are accelerated toward an electrode (first dynode), and cause the release of two or more secondary electrons. Each of these causes the release of two or more electrons from the second dynode. The cascade continues until a very large number of electrons are available for detection at the anode. (b) Technicians on a rubber boat inspect some of the 11,242 PMTs in the Super-Kamiokande neutrino detector in Japan.
Today, the PMT is the workhorse detector in experimental particle physics. One of the most extreme is the Super-Kamiokande detector used to hunt for elusive particles called neutrinos. This massive detector is buried deep within an abandoned zinc mine in Japan. It uses 11,242 PMTs to look at photons produced when the neutrinos decelerate as they hit 50,000 tons of pure water.
Let’s build the PMT probe (Figure 29) that we’ll use for many experiments. We chose the RCA 6655A PMT because it is affordable and widely available in the surplus market. This tube has ten dynodes that multiply a single photoelectron into 1.6 × 106 secondary electrons at the anode when operated at + 1,000 V. You can increase the voltage beyond + 1,000 V, and operate the PMT safely at +1,250 V, but be careful not to exceed its absolute maximum voltage of + 1,600 V.
Figure 29 This versatile photomultiplier probe is useful for many experiments described in this book. It is based on the RCA 6655A PMT, and features a gain of 1.6 million when operated at +1,000 V.
As shown in Figure 30, we enclosed our PMT probe in a die-cast aluminum box (Bud Industries model AN-1323). The PMT and its magnetic shield fit snugly within a 10-cm-long piece of aluminum optical instrument construction rail (66-mm profile, Thorlabs model XT66-100). A matching faceplate (Thorlabs model XT66SM2) screws to the 66-mm-profile rail from outside the aluminum box. It is used as a convenient, light-tight interface to other optical components. The plate is sealed against the metallic enclosure with black RTV silicone caulking, which can be purchased at any auto supply store. All other possible light leakage paths around the PMT are sealed with black electrician’s tape. There is enough room inside the box to accommodate the PMT’s tube socket, resistor divider, capacitors, potentiometers, and coaxial connectors. The bottom cover for the enclosure is not shown in the picture, but we drilled a blind hole in the center and tapped it to accept a 1/4″ 20 TPI machine screw, so that we may mount the probe on a standard camera tripod or on an optical table post.
Figure 30 Inside view of our PMT probe. The PMT and its magnetic shield fit snugly within a 10-cm-long piece of 66-mm aluminum optical instrument construction rail. A matching faceplate is used as an interface to other optical components. All possible light leakage paths around the PMT are sealed with black electrician’s tape. The resistive voltage divider and filter capacitors are assembled directly on the PMT’s tube socket.
A word of caution: never expose the PMT’s sensitive face to bright light! This will cause permanent damage to the tube, especially when the tube is powered. While not in use, our PMT is protected with a faceplate cap with an SM-2 series end-cap (Thorlabs model SM2CP2).
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