Introduction To Nuclear Physics-Classical Physics-Handouts, Lecture notes of Classical Physics

Download Introduction To Nuclear Physics-Classical Physics-Handouts and more Lecture notes Classical Physics in PDF only on Docsity! PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 160 Summary of Lecture 44 – INTRODUCTION TO NUCLEAR PHYSICS Q.1 In the previous lecture you learned how it was discovered that the atom is mostly empty space with a cloud of electrons. At the centre is a small but very heavy nucleus that has protons and neutrons. The word "nucleon" refers to both of these. So you can think of the neutron or proton as being two different varieties of the nucleon. The masses of the two are very similar, and they are roughly 2000 times heavier than the electron. -27 -27 proton mass = 1.672 10 neutron mass = 1.675 10 electron p n M kg M kg = × = × -31 -19 -19 mass = 9.109 10 The neutron is neutral, of course, but the charge on the proton is 1.6 10 while the charge on the electron is the negative of this, 1.6 10 . 2. Using k eM kg C C = × × − × 2 2 ilograms is very awkward if you are dealing with such small particles. Instead we we use to write the mass of a particle in terms of its rest energy, / . So mass is measured in uni E mc m E c= = 2 2 2 ts of / . proton mass = 938 / neutron mass = 940 / p n MeV c M MeV c M MeV c = = 2 electron mass = 0.5 / 3. a) A hydrogen nucleus is just one proton. b) A deuteron has a proton plus one neutron. c) A triton (or tritium nucleus) has a proton plu eM MeV c= s two neutrons. All three atoms have one electron only, and thus completely identical chemical properties. 4. Hydrogen, deuterium, and tritium are called isotopes. If a nucleus with Z protons has N neutrons then its isotopes will have fewer, or more, neutrons. Since the number of electrons is also Z, the chemical properties of all isotopes are exactly the same. But for any given element, at most there is only one stable isotope. docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 161 1 3 6 4. A commonly used notation is where is the element, and . Of the elements that you see on the right, the most stable ones are H, He, and Li. Now consider oxygen. The most stab A Z X X A Z N= + 16 16 17 18 le isotope is O. When you breathe in oxygen from the atmosphere, 99.8% is O, 0.037% is O, and 0.163% is O. We shall see later what unstable means and how nuclei decay. 1/ 3 0 0 5. The diameter of the nucleus is about 10 million times smaller that the overall diameter of the atom. Nuclei follow an approximate rule for the radius, where 1.2 (remember, r r A r fm ≈ = -13 1/ 3 1/ 3 1/3 208 1 fermi 10 cm) and . Now, increases very slowly with . You can check that 16 2.52 while 208 5.93. This means that a very heavy lead nucleus is only about 2.4 t A Z N A A Pb = = + = = 16imes the size of the much lighter nucleus.O 6. To learn about how protons are distributed inside a nucleus, we send a beam of electrons at a nucleus and observe how they scatter in different directions. The negatively charged electrons interact with the positively charged protons, but they obviously will not see the neutrons. The scattered electrons are captured in a detector which can be moved around to different angles. In this way one can reconstruct the charge distribution which caused the electrons to be scattered in that particular way. 7. What energy should electrons have in order to see a nucleus? We know that electrons are waves with / (the De Broglie relation). To see something as small as 1 requires a wave with wave h p fmλ = 2 2 2 length at least 1 . A wave with longer wavelength would simply pass over the nucleus without being disturbed. So the minimum electron energy is, . Evaluation gives this to be a 2 2 fm p hE m m λ λ ≈ = = few MeV, requiring an electron accelerator of more than this minimum energy. docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 164 13. A few nuclei are stable, most decay. The decay law is simply derived: if the number of nuclei decreases by in time , then must be proportional to both the the number of nuclei dn dt dn n that are decaying and , so (minus sign for decrease). with the proportionality constant , we have , or . We have encountered the solution of this type of equatio dt dn ndt dndn ndt n dt λ λ λ ∝ − = − = − - 0 0 1 0 2 0 n before, . You can see that at 0, . Taking the log, we have ln . We define the half-life as the time it takes for half the original sample to decay. If / 2 then tn n e t n n n t T n n n λ λ = = = = − = 0 0 1 2 log , from which the half 2 log 2 0.693 life is related to by, . The larger , the more radioactively unstable a nucleus is. Some typical half-lives are: n t n T λ λ λ λ λ = − = = 214 -4 84 89 36 90 38 Polonium 1.64 10 Krypton K 3.16 minutes Strontium Sr 28.5 years P s× 226 88 14 6 Radium Ra 1600 years Carbon C 5730 years Uranium 23892 U 4.5 109 years You can see how hugely different the lifetimes of different nuclei are! 14. Here is a plot of the number of unstable nuclei left as a function of time. After each ha × lf-life, the number of nuclei decreases in number by half of the previous. Eventually there is only one nucleus left, and that too will eventually decay. So how can the derivation for the decay law be correct? Strictly speaking, we are not allowed to write down, or solve, a differential equation like because this assumes that ( ) is a continuous f dn n dt n t λ= − unction. But this is almost true because in real life we deal with very large numbers of nuclei and so it makes a lot of sense to think of ( ) as continuous.n t docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 165 222 86 218 4 84 2 15. Just to get an idea, consider the decay of Rn (Radon, a very dangerous gas that is found underground) into Po (Polonium, another terrible poison) and He (harmless, fortunate 22286 222 218 86 84 ly!). The half life is 3.8 days. So, if we started with 20,000 atoms of Rn, then in 3.8 days we would have 10,000 atoms of Rn and 10,000 atoms of Po In 7.6 days we would have 222 22286 865000 atoms of Rn, in 11.4 days, 2500 , Rn etc. 16. The decay law can be used to see how old things are. This is called radioactive dating. Carbon dating is widely used for living things 14 6 12 6 that died a few hundred or few thousand years ago. How does it work?This uses the decay of the unstable isotope, . Of course, the stable isotope of carbon is . When a living C C • 2 - organism dies, CO is no longer absorbed. Thus the ratio of carbon 14:12 decreases by half every 5730 years. We can measure the rate of decrease through or the "activity"toN N e λ= A with 0.23 / . (The becquerel Bq is the unit of radioactivity, defined as the activity of a quantity of radioactive material in which one nucleus decays per second t o oA e A Bq g λ−= = 14 6 7 . ) The amount of isotopes in the atmosphere is approximately constant, despite a half-life of 5730 y because there is a constant replenishment of through the reaction, C • 14 14 6 17. Let us use the above idea to find the time when this man died. His body was found a few years ago buried under deep snow in a mountain pass, so it it did not decay as usual N n C p+ → + 14 6 14 6 . By looking at the radioactivity in his body, it was found that that the activity of was 0.121 / of body tissue. This is less than the normal activity 0.23 / . because has C Bq g Bq g C 4 4 1 1 2 1.21 10 4 been decaying 0.693 0.693 away. First find , 1.21 10 5730 Then use, 0.121 0.23 which gives, 0.121 ln 1.21 10 and so 5300 years is 0.23 when this poor t y T e t t λ λ − − − − × × − = = = × = = − × × = 2 man was killed (or died somehow)! 18. The most famous formula of physics, , is the basis for nuclear energy. In 1935, it was discovered by two German physicists, Otto Robert Frisch and Lise E mc= Meitner, that a heavy nucleus can fission (or break up) into two or more smaller nuclei. The total energy is, of course, conserved but the mass is not. This is completely different from the docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 166 MA Mb Mc+ usual situation. In the picture below you see an example of fission. 2 The masses of the two nuclei add up to less than the mass of the parent nucleus, and the energy released is ( ) . This goes into kinetic energy and sends the two daughter nucl A b cQ M M M c= − − ei flying apart at a large velocity. There happen to be NO completely stable nuclei above 82, and no naturally occurring nuclei above 92. Above these limits the nuclei decay or fall apa Z Z= = rt in some fashion to get below these limits. 19. A very useful concept is "binding energy". Suppose you want to take a nucleon out of a nucleus. The binding energy is the amount of energy that you would have to provide to pull it on the average. Nuclei with the largest BE per nucleon are the most stable. As you 56 can see from the graph below, the most stable element is iron, with a BE per nucleon of about 8.6 MeV. This is why iron is the heavy element found in the largest quantity on ear Fe 4 235 th and inside stars. The curve is not smmoth and you see that a He nucleus (i.e. an parrticle, has a relatively high binding energy and so is relatively stable. In contrast, Uranium U α 2 or deuterium H are much less bound and they decay. 20. Nuclei can be unstable in different ways. A nucleus can emit , , and radiations. Usually a nucleus will emit one of these three, but α β γ it is possible to emit two, or even all three of these. (In addition, as we have discussed above, a nucleus can break up into docsity.com