Cosmic rays and the cloud chamber The cloud chamber was the first tool physicists had that enabled them to see the elementary particles that resulted from radioactive decay. It is a fundamentally simple device containing vapor that is just ready to make a cloud, All it needs is something to condense on, and that may be the ions produced when an energetic charged particle zips through the gas. The resulting cloud, much like the contrail of a jet airplane at high altitude, is the track of the particle through the chamber. The first one was made by Charles Wilson in 1911. You can see it at the science museum at the Cavendish Laboratory. It makes a saturated vapor in water suddenly removing air from the chamber, so it cannot show tracks for a long period but it works very well for snapshots of the cosmic rays. It is the predecessor of the liquid bubble chamber that was the workhorse tool of high energy physics in the middle of the last century. At about the same time, Victor Hess carried electrometers, devices that measure the rate of ion production in a gas, on a ballon flight up to 5300 meters, and he found that there were more ions being made at higher altitude than down on Earth's surface. The source of the ionization must therefore be above Earth's atmosphere, and the term "cosmic ray" was adopted some years later. Hess received the Nobel Prize for his discovery. The primary cosmic ray is typically an energetic proton, or occasionally a heavy ion, from the Sun, a supernova, or some other distant source in the galaxy. When it strikes an atom in the atmosphere, among other products it produces u-mesons, and it is these muons that are responsible for the ionization and tracks we see in cloud chambers at lower altitude. in our study next week we will see that these particles are very similar to electrons, except more they are more massive and they are unstable. A muon will decay if left on its own primarily by this process p s e + Ve + Vii which is to say it turns into an electron and a pair of neutrinos. The lifetime of the muon before it does this is 22 us fa microsecond is 10'6 second, a millionth of a second), If a much goes through the chamber it ionizes the gas, but if it stops, about 2 microseconds later it produces an electron that also ionizes the gas. [The neutrinos hardly interact, so we do not see them at all.) The problem If muons only live for 2.2 microseconds, how is it they get down to Earth's surface? In that short a time, at the speed of light, the fastest speed they can go, they will travel I - (A! where A: is the elapsed time and c is the speed of light. That works out to / 3 x103 x 2.2 x10.6 = 660 meters or 0.66 kilometers, The upper part of Earth's atmosphere is of the order of 100 km away, and even at 10 km it is too far, How do Cosmic rays make it down to the surface? Observations There are several videos linked in this lab activity which will show you cosmic ray tracks in cloud chamber. One of the best is here recorded at the astronomical observatory at Pic du Mid' 'n France, 2.9 km above sea level. The chamber is 45x45 cm and about 5 cm high. Most of the tracks it detects are from horizontally traveling particles, other experiments have shown are only about 5% of the actual flux that is mostly vertical. This video is recorded in real time, so watch some of it and see if you can estimate how many new tracks there are per second. You may have to limit your attention to short interval and play it frame by frame to count the events. It is not an easy task. It won't matter if you miss a few. The best way is to examine the video for several seconds, then divide your count by the time. 1. Are all the tracks the same, or are some different? 2. How many did you count per second? 3. What is the volume of the chamber, in cm3 ? (Hint: simply multiply length by width by height in cm.) 4. How many were there per cm3 per 5? Estimate the error in your measurement by trying this in a few different time intervals and comparing your results. If you multiply by 20, that's the number of vertically traveling ones, so the total will be approximately 20x the number you actually count. Most (but not all) are muons. You can look at other videos too. The results depend on the altitude, because the particles are absorbed by air, and on the efficiency of the chambers that depends on their design and how saturated the vapor is. 5. In the same units of cm3 estimate your own volume Yes, that's hard to do accurately. One way is by displacement. if you put something into a liquid, the volume of the liquid displaced is the volume of the object submersed. We're talking about bathtubs here! Or, you can take your weight and divide by the average human density which is about 985 kg/m3, If you only know your weight in pounds, then use 1 kg = 2.2 lb. A cubic meter is 106 cubic centimeters. 6. If you were at Pic du Midi, how many cosmic ray muons would go through you, per second? Your exposure to cosmic rays, which cause mutations and possibly cancer, is higher the higher the altitude. Pilots and flight attendants may be classified as radiation workers for health purposes because of this risk, and they receive an average annual dose of about 3 miIIi-sieverts [mSv). The sievert (Svl is unit of ionizing radiation energy that is equivalent to 1 joule of energy absorbed per kilogram per meter2 per second. That is thought to convey a 5.5" risk of eventually developing cancer. Flying at cruise altitude delivers a dose of about 2.7 uSv/h, but this exposure is cumulative which is why there is a risk to high flyers. (A CT scan delivers a dose of around 30 mSv, and a banana which has naturally radioactive K (potassium) provides a does of around 0.1 uSv.) Time dilation So how is it that muons survive to reach us at sea level? Several of the video links in this activity will help to understand that the reason, as we see it, is time dilation The muons are traveling at nearly the speed of light. This Causes their "Clock", i.e. their lifetime or decay rate, to appear to us to run slowly, The detection of muons at sea level is a dramatic demonstration of special relativity, Let's do the math. The formula for time dilation is that an interval A 10 seen by the moving clock [the muon, in this case), is measured by a stationary observer ius, in this case) to be A1: A10/ t/l'l'uZiL-'Z 7. Assuming that the muons are traveling at 0.98 times the speed of light [something we can measure, but don't in this experiment), what would be the apparent lifetime of the muon to us? Now for the real challenge. To the muon, its lifetime is not altered by its speed. It sees the atmosphere of Earth going by, and still gets to the ground. 3. Why is that