1 00:00:00,000 --> 00:00:03,982 First question I'm going to answer is how old is the solar system? 2 00:00:03,982 --> 00:00:08,913 And the answer is it's rather old. it's easy to look at me and see that I'm 3 00:00:08,913 --> 00:00:11,568 old. But how do you look at a astronomical 4 00:00:11,568 --> 00:00:15,930 system and notice that it's old? Well, it turns out you date the rocks. 5 00:00:15,930 --> 00:00:20,840 We find on Earth some rocks that are as old as 4.4 billion years. 6 00:00:20,840 --> 00:00:25,523 We abbreviate that giga years such rocks are rare on Earth. 7 00:00:25,523 --> 00:00:30,924 Most of the rocks we find on Earth are tens or hundreds of millions of years 8 00:00:30,924 --> 00:00:33,765 old. But on the moon, rocks, old rocks are far 9 00:00:33,765 --> 00:00:39,061 more common and the oldest moon rocks are as old as four and a half billion years 10 00:00:39,061 --> 00:00:42,000 old. The meteorites meteors that fall onto 11 00:00:42,000 --> 00:00:47,502 Earth, we'll talk about that later on space rocks can be as old as a little 12 00:00:47,502 --> 00:00:51,311 older than that, 4.54 billion years, we sense a pattern. 13 00:00:51,311 --> 00:00:57,165 And indeed, our best estimate for the age of the solar system is about 4.56 billion 14 00:00:57,165 --> 00:01:00,269 years. So, 4.56 billion years ago is when the 15 00:01:00,269 --> 00:01:04,021 solar system formed. That's a pretty ambitious statement. 16 00:01:04,021 --> 00:01:07,467 How do you know how long ago the solar system formed? 17 00:01:07,467 --> 00:01:12,688 The answer, of course, is more physics. And the, technology that we use to figure 18 00:01:12,688 --> 00:01:17,121 out the age of a rock is called radioactive dating and to understand how 19 00:01:17,121 --> 00:01:21,671 we date rocks we're going to have to carry our understanding of the structure 20 00:01:21,671 --> 00:01:26,163 of the atom deeper in and we're going to have to look inside the atomic nucleus 21 00:01:26,163 --> 00:01:29,780 that rather for discovered, carries the entire mass of an atom. 22 00:01:29,780 --> 00:01:34,155 And remember, that a species of atom is identified by its atomic number, the 23 00:01:34,155 --> 00:01:38,938 positive charge in the nucleus and what rather for discovers is at that charge is 24 00:01:38,938 --> 00:01:43,717 carried basically by a number Z of positively charged massive particles we 25 00:01:43,717 --> 00:01:47,412 now called protons, we just call them hydrogen nuclei. 26 00:01:47,412 --> 00:01:51,860 a proton is nothing other than the nucleus of a hydrogen atom. 27 00:01:51,860 --> 00:01:55,214 And so, inside the nucleus are Z Hydrogen nuclei. 28 00:01:55,214 --> 00:01:58,490 This is a discovery by Rutherford in 1917. 29 00:01:58,490 --> 00:02:03,659 This accounts for approximately half of the mass of an average nucleus. 30 00:02:03,659 --> 00:02:07,445 What is the rest? Well, the rest is obviously neutral 31 00:02:07,445 --> 00:02:11,012 matter. Chadwick, in 1932, discovers the neutron. 32 00:02:11,012 --> 00:02:16,618 And it's realized that the rest of the mass of an atomic nucleus besides the 33 00:02:16,618 --> 00:02:22,082 protons is made up of A minus Z of these neutral particles called neutrons, that 34 00:02:22,082 --> 00:02:24,880 each have about the same mass as a proton. 35 00:02:24,880 --> 00:02:30,408 So helium nucleus, for example, contains two protons and two neutrons, for a total 36 00:02:30,408 --> 00:02:34,604 atomic mass of four. Now, if you look up the atomic mass of 37 00:02:34,604 --> 00:02:39,532 helium in the periodic table, you'll discover that it's slightly less than 38 00:02:39,532 --> 00:02:42,530 four. The reason for this is that the same 39 00:02:42,530 --> 00:02:46,805 combination of protons can appear with differing number of neutrons. 40 00:02:46,805 --> 00:02:50,830 Note that since the protons determine the charge of the nucleus, 41 00:02:50,830 --> 00:02:55,420 these, these will lead to two atoms, which have the same electron cloid and 42 00:02:55,420 --> 00:02:59,193 so, are chemically indistinguishable but have different mass. 43 00:02:59,193 --> 00:03:02,400 In fact, helium, for example, can appear in two forms. 44 00:03:02,400 --> 00:03:07,430 There are helium nuclei with two neutrons and two protons for an atomic mass of 45 00:03:07,430 --> 00:03:10,233 four. And there's a less stable isotope as it 46 00:03:10,233 --> 00:03:14,560 is called, of helium, helium three with two protons, so the same electron 47 00:03:14,560 --> 00:03:17,060 structure as helium, but only one neutron. 48 00:03:17,060 --> 00:03:21,754 And so, Z determines the chemistry, the number A minus Z of neutrons determines 49 00:03:21,754 --> 00:03:26,087 the mass, and in general, you can combine neutrons and protons in various 50 00:03:26,087 --> 00:03:29,158 combinations. This all brings up a great question, of 51 00:03:29,158 --> 00:03:32,150 course. Once you realize that the atomic nucleus 52 00:03:32,150 --> 00:03:36,786 is all, not all in one piece, it's made up of neutral and positive particles, you 53 00:03:36,786 --> 00:03:41,421 can ask, why doesn't that thing blow up? There is a whole lot of positive charge. 54 00:03:41,421 --> 00:03:45,528 There are these repellent Coulomb interactions between the protons. 55 00:03:45,528 --> 00:03:48,051 What is it that holds the nucleus together? 56 00:03:48,051 --> 00:03:52,452 We'll get to that later, but at the moment it suggests, and you are right 57 00:03:52,452 --> 00:03:57,231 that most combinations of neutrons and protons do not like to stay together and 58 00:03:57,231 --> 00:04:00,783 most nuclei, most assemblies you could put together 59 00:04:00,783 --> 00:04:04,703 decay and, in fact, many of those that we find in nature do decay. 60 00:04:04,703 --> 00:04:09,848 And they decay, it is discovered in the late 19th, early 20th century in one of 61 00:04:09,848 --> 00:04:12,911 three ways. One is a process called alpha decay. 62 00:04:12,911 --> 00:04:18,056 This is the emission of what is called an alpha particle that is soon discovered to 63 00:04:18,056 --> 00:04:22,160 be nothing other than a Helium nucleus. A nucleus of the stabilizer dopefolium) 64 00:04:22,160 --> 00:04:24,610 of helium with two protons and two neutrons. 65 00:04:24,610 --> 00:04:31,400 And so many nuclei decay by emitting, notice they emit a Helium nucleus, this 66 00:04:31,400 --> 00:04:37,363 means the remaining nucleus has a different nuclear charge so you've 67 00:04:37,363 --> 00:04:43,574 achieved chemical transmutation, one element is transmuted into another, the 68 00:04:43,574 --> 00:04:49,372 object of alchemy is achieved. sadly, lead is more often the product 69 00:04:49,372 --> 00:04:55,550 than the initial part of this and turning lead to gold is not yet a commercial 70 00:04:55,550 --> 00:04:59,366 enterprise. the other species of decay, continuing 71 00:04:59,366 --> 00:05:03,915 the order is beta decay. the beta rays that nuclei emit are 72 00:05:03,915 --> 00:05:09,199 discovered to be nothing other than electrons and a nucleus can emit an 73 00:05:09,199 --> 00:05:12,349 electron. I said that electric charge is conserved 74 00:05:12,349 --> 00:05:17,265 and indeed, the emission of an electron is found to be associated with the 75 00:05:17,265 --> 00:05:21,990 conversion of a neutron to a proton. So, in a sense a neutron decays into a 76 00:05:21,990 --> 00:05:25,437 proton and electron, the proton remains in the nucleus, 77 00:05:25,437 --> 00:05:29,332 the electron escapes. The net result is that the total number 78 00:05:29,332 --> 00:05:34,886 of nucleons in the nucleus is unchanged, A is unchanged, but Z increases by one so 79 00:05:34,886 --> 00:05:39,355 again, you've changed the element. There is also positive beta decay in 80 00:05:39,355 --> 00:05:42,155 which the, the particle emitted has the same 81 00:05:42,155 --> 00:05:46,782 mass as the electron but positive charge as opposed to the electron's negative 82 00:05:46,782 --> 00:05:51,292 charge and this is accompanied by the conversion of a proton to a neutron, so 83 00:05:51,292 --> 00:05:55,744 again, A is unchanged in beta decay but in this kind of beta decay, Z in fact 84 00:05:55,744 --> 00:05:59,404 decreases by one. many heavy elements also spontaneously 85 00:05:59,404 --> 00:06:02,893 undergo fission, which is a more dramatic thing where a 86 00:06:02,893 --> 00:06:07,905 heavy nucleus basically splits up into two smaller nuclei, often throwing off a 87 00:06:07,905 --> 00:06:12,599 couple of alpha particles as well. And this is a process in which, again, 88 00:06:12,599 --> 00:06:16,786 you start with a heavy nucleus and end with two smaller ones. 89 00:06:16,786 --> 00:06:21,100 And all of these are, in general, accompanied by the emission of high 90 00:06:21,100 --> 00:06:26,156 energy photons gamma rays. So, this process go on, what is all that 91 00:06:26,156 --> 00:06:30,841 got to do with dating the solar system? Well, we'll see that in a minute and 92 00:06:30,841 --> 00:06:34,831 radioactivity however, has lots of applications and it contributes much to 93 00:06:34,831 --> 00:06:37,204 our life, let's start with something we know. 94 00:06:37,204 --> 00:06:40,925 And remember, helium, we said. was a rare element on Earth, it was first 95 00:06:40,925 --> 00:06:44,376 discovered on the sun. if you did your homework last week you 96 00:06:44,376 --> 00:06:48,096 might understand what's going on. At the temperatures in the Earth, so, so, 97 00:06:48,096 --> 00:06:51,950 helium is lighter than air. Helium, if we pop a helium balloon, then 98 00:06:51,950 --> 00:06:57,317 the helium without the balloon will float in the Earth's atmosphere up to the top, 99 00:06:57,317 --> 00:07:00,980 to the outer atmosphere, to something called the exosphere. 100 00:07:00,980 --> 00:07:06,031 And at the temperatures of about 1,000 or 1,500 degree Kelvin that obtain there, 101 00:07:06,031 --> 00:07:11,030 the kinetic energy of helium atom with its small mass, means that its velocity 102 00:07:11,030 --> 00:07:15,393 is about a sixth, if you computed last week, of the escape velocity at that 103 00:07:15,393 --> 00:07:17,678 altitude. That means the hotter, faster. 104 00:07:17,678 --> 00:07:20,228 And remember, there's a statistical distribution. 105 00:07:20,228 --> 00:07:24,769 This is only an average kinetic energy. The faster helium atoms evaporate and 106 00:07:24,769 --> 00:07:27,776 escape Earth, [COUGH] and so, in fact, Earth does not 107 00:07:27,776 --> 00:07:31,020 have the mass needed to retain an atmosphere of helium. 108 00:07:31,020 --> 00:07:35,660 This explains why despite the fact that hydrogen and helium are the most common 109 00:07:35,660 --> 00:07:40,358 species of atoms in the solar system, our atmosphere is not comprised of hydrogen 110 00:07:40,358 --> 00:07:43,258 and helium. Hydrogen and helium, hydrogen molecules 111 00:07:43,258 --> 00:07:47,724 with an atomic mass of two and helium atoms with an atomic mass of four move 112 00:07:47,724 --> 00:07:50,160 fast enough to escape the Earth's gravity. 113 00:07:50,160 --> 00:07:55,185 we still have lots of hydrogen on earth because hydrogen binds and is found in 114 00:07:55,185 --> 00:07:58,863 things like water. Helium, being a noble gas, does not bind 115 00:07:58,863 --> 00:08:02,357 anything, so any atom of helium will eventually evaporate. 116 00:08:02,357 --> 00:08:06,770 In fact, earth loses large quantities of helium to space all the time. 117 00:08:06,770 --> 00:08:10,466 So, where, you ask, do we find helium to fill our helium balloons? 118 00:08:10,466 --> 00:08:14,666 Earth having been around, they claim for four billion years, would have been 119 00:08:14,666 --> 00:08:19,202 completely free of helium were it not for the fact that helium is being produced 120 00:08:19,202 --> 00:08:23,962 inside the Earth, and escaping out to the atmosphere at a constant rate, and helium 121 00:08:23,962 --> 00:08:28,274 is being produced as alpha decay, so every bit of helium, every atom of helium 122 00:08:28,274 --> 00:08:32,754 you've ever put in a birthday balloon is the result of radioactive decay inside 123 00:08:32,754 --> 00:08:35,050 the Earth, primordial helium is long gone. 124 00:08:35,050 --> 00:08:41,415 In addition, this process both the helium nuclei, the alpha particles, the beta 125 00:08:41,415 --> 00:08:46,400 particles, the gamma rays, escape from the nucleus with lots of energy. 126 00:08:46,400 --> 00:08:50,895 They plow into the surrounding medium distribute this energy. 127 00:08:50,895 --> 00:08:54,754 What this ends up doing is dumping energy in the surroundings. 128 00:08:54,754 --> 00:08:59,734 This is bad if the surroundings are your lungs but in the inside the Earth, this 129 00:08:59,734 --> 00:09:02,348 turns out to be a source of internal heat. 130 00:09:02,348 --> 00:09:07,265 So, there is, at the inside the Earth, an ongoing process of radioactive decay. 131 00:09:07,265 --> 00:09:12,369 We see it's mostly happening in the core and mantel and this heats the inside of 132 00:09:12,369 --> 00:09:16,190 the earth. That's something that radioactivity can 133 00:09:16,190 --> 00:09:19,909 do. but for our purposes, what do you want to 134 00:09:19,909 --> 00:09:23,604 understand is how we use radioactivity to date a rock. 135 00:09:23,604 --> 00:09:27,574 So, the idea is that radioactive decay is a random process. 136 00:09:27,574 --> 00:09:33,118 Any given atom is independently, or any given nucleus will decay independently 137 00:09:33,118 --> 00:09:36,540 with a probability per unit time that is constant. 138 00:09:36,540 --> 00:09:41,662 What this amounts to is that if you have a sample within some prescribed time 139 00:09:41,662 --> 00:09:47,290 dependent on the species of nucleus that you are studying half of all the atoms 140 00:09:47,290 --> 00:09:50,832 will have decayed. And then, within that same period, half 141 00:09:50,832 --> 00:09:55,069 of the remaining atoms will have decayed, the process has no memory. 142 00:09:55,069 --> 00:09:59,306 Once a nucleus has not decayed for some time, the clock starts over. 143 00:09:59,306 --> 00:10:04,112 It's as likely to decay in the next second as it was in the previous second 144 00:10:04,112 --> 00:10:08,658 given that it didn't decay. This leads to a mathematical expression 145 00:10:08,658 --> 00:10:13,411 for the time dependence of the number of nuclei of a given species, 146 00:10:13,411 --> 00:10:19,655 which says, that in a given time, called the half-life, t1/2, a half of the sample 147 00:10:19,655 --> 00:10:23,841 will have decayed. So, if you start with some number at time 148 00:10:23,841 --> 00:10:29,028 zero, when t is equal to t and to the, to t1/2, the half-life, you will have half 149 00:10:29,028 --> 00:10:33,739 of the sample left, another half-life later, you will have a quarter, and so on 150 00:10:33,739 --> 00:10:36,798 exponentially. And what that means is, on the other 151 00:10:36,798 --> 00:10:41,508 hand, this decay say, if the predominant mode of decay is alpha decay, then you 152 00:10:41,508 --> 00:10:46,219 have one nucleus that when it decays will produce another species of nucleus. 153 00:10:46,219 --> 00:10:50,991 So, with time, the concentration of what is called the daughter nucleus will 154 00:10:50,991 --> 00:10:54,050 increase while the parent concentration decreases. 155 00:10:54,050 --> 00:10:58,244 Now, if you knew the initial concentrations of 156 00:10:58,244 --> 00:11:03,092 daughter and parent, if you could, and for some reason know what you started 157 00:11:03,092 --> 00:11:07,552 with, then you could compare the initial concentration to the current 158 00:11:07,552 --> 00:11:10,966 concentration and extract from that, the amount of time 159 00:11:10,966 --> 00:11:14,079 that has passed. The best way to do this in dating rocks 160 00:11:14,079 --> 00:11:17,859 though there are other forms, carbon dating, where you make a different 161 00:11:17,859 --> 00:11:20,972 comparison. But imagine that you have a process where 162 00:11:20,972 --> 00:11:23,725 the daughter nucleus is a chemical element. 163 00:11:23,725 --> 00:11:29,379 Remember, these are different chemical elements whose chemistry is such that it 164 00:11:29,379 --> 00:11:34,618 escapes, it boils out of liquid rock, and therefore, is not contained within a 165 00:11:34,618 --> 00:11:38,686 freshly solidified rock. So, when a piece of rock solidifies, 166 00:11:38,686 --> 00:11:43,030 there are no daughter nuclei, but the parent nucleus is trapped, 167 00:11:43,030 --> 00:11:46,201 is bound, can be bound within the crystal. 168 00:11:46,201 --> 00:11:52,358 Then, once the rock is solid the parent nuclei start to decay and they produce 169 00:11:52,358 --> 00:11:57,419 concentrations of the daughter, the ratio of concentrations is then 170 00:11:57,419 --> 00:12:02,315 dependent on time like this. If you can measure both of these, you can 171 00:12:02,315 --> 00:12:08,018 and you know the half-life, then you can extract the length of time that has 172 00:12:08,018 --> 00:12:10,666 passed. can we find such candidates? 173 00:12:10,666 --> 00:12:16,909 Surely the beautiful thing is that the degree of instability of various nuclear 174 00:12:16,909 --> 00:12:22,776 species varies wildly from fractions of a second to billions of years for the 175 00:12:22,776 --> 00:12:26,387 half-life. In particular, many of the isotopes of 176 00:12:26,387 --> 00:12:30,449 uranium decay. They decay by various processes but the 177 00:12:30,449 --> 00:12:33,834 end product of many of the processes is lead. 178 00:12:33,834 --> 00:12:39,959 And it turns out that a mineral called zircon binds uranium when it forms, but 179 00:12:39,959 --> 00:12:45,533 not lead, so when a zircon rock forms it will contain essentially no lead but it 180 00:12:45,533 --> 00:12:51,039 might contain trace amounts of uranium, that uranium will decay with half-lives 181 00:12:51,039 --> 00:12:55,817 of the order of a few billion years. And so, if you find lead in a chunk of 182 00:12:55,817 --> 00:12:58,516 zircon, it was produced there by radioactivity. 183 00:12:58,516 --> 00:13:03,267 If you compare the concentration of lead to the concentration of uranium, you can 184 00:13:03,267 --> 00:13:06,376 figure out how long that rock has been sitting there. 185 00:13:06,376 --> 00:13:09,133 This is tricky because lead can in fact escape. 186 00:13:09,133 --> 00:13:13,709 Lead is not completely trapped and so, you might find less lead than should be 187 00:13:13,709 --> 00:13:16,290 there. In the case of lead and uranium, we're 188 00:13:16,290 --> 00:13:20,162 fortunate there are two different isotopes of uranium produced two 189 00:13:20,162 --> 00:13:24,200 different isoptoes of lead as their final 190 00:13:24,200 --> 00:13:29,252 product. And with slightly different half-lives, and so, you can compare the 191 00:13:29,252 --> 00:13:34,372 relative concentration of the two isotopes of lead and the two isotopes of 192 00:13:34,372 --> 00:13:37,512 uranium. And in this beautiful diagram, you see 193 00:13:37,512 --> 00:13:42,086 sort of the plots by age of the predicted ratios of concentrations. 194 00:13:42,086 --> 00:13:45,363 You see that the samples have lost some lead. 195 00:13:45,363 --> 00:13:50,690 Their lead concentration is lower. then the uranium concentration you would 196 00:13:50,690 --> 00:13:56,080 predict but they lie along this line and the intersection of the two lines gives 197 00:13:56,080 --> 00:13:58,250 you the age these rocks. And 198 00:13:58,250 --> 00:14:01,513 this is the way that we date the solar system. 199 00:14:01,513 --> 00:14:07,374 This is how we know that the oldest rocks we find in the solar system are four and 200 00:14:07,374 --> 00:14:09,040 a half billion years old.