CLASS 28. THE DISCOVERY OF THE NUCLEUS 28.1. INTRODUCTION The beta particle had been determined to be the electron, but the identity of the alpha particle was not as straight forward. While this may not seem relevant to the discovery of the nucleus, the study of alpha particles led to a very important discovery that showed Thomson s model of the atom to be incorrect. Although Thomson s model of the atom was the dominant model, it was not the only model being considered. In 1901, Jean Perrin suggested a purely speculative model based on the analogy with the solar system: Each atom will be constituted, on the one hand, by one of several masses very strongly charged with positive electricity, in the manner of positive suns whose charge will be very superior to that of a corpuscle, and, on the other hand, by a multitude of corpuscles, in the manner of small negative planets, the ensemble of their masses gravitating under the action of electrical forces, and the total negative charge exactly equivalent to the total positive charge, in such a way that the atom is neutral. 4 The Japanese physicist Hantaro Nagaoka proposed in 1904 a model in which electrons revolve in rings around a positively charged body. Nagaoka's model had a fault, which was that the negatively charged electrons orbiting around the positively charged nucleus didn t seem to take into consideration that the electrons should repel each other, and that the positive nucleus would attract the electrons. 28.2. GOALS Explain how the alpha particle was identified to be a helium nucleus; Explain Rutherford s scattering experiments and how his results showed the Thomson model of the atom to be incorrect; Describe how a Geiger counter works; Explain the model developed by Rutherford to explain his results, including the strengths and weaknesses of the model. 28.3. UNDERSTANDING ALPHA PARTICLES 28.3.1. Candidates. Scientists knew that alpha particles have positive charge, and that their chargeto-mass ratio (4.8 10 7 C kg )is one half that of a hydrogen ion. The charge-to-mass ratio of an alpha particle is thus about 4000 times smaller than the charge-to-mass ratio of a beta particle. This means that the alpha particle either has a very small charge or a very large mass compared to the beta particle. Two possibilities were considered (see Figure 28.1): the alpha particle could be a hydrogen molecule missing one electron (H 2 + ) or a helium atom missing two electrons (He ++ ). 4 Dahl, Flash of the Cathode Rays, p 322. H + H+ = hydrogen ion mass = 1 charge = +1 q 7 C = 9.6 10 H H + mass = 2 H + 2 = H molecule ion He ++ m kg charge = +1 q 1 7 = 9.6 10 m 2 C ( kg) He++ = He ion mass = 4 charge = +2 q 1 7 C = 9.6 10 m 2 ( kg) Figure 28.1: Possible explanations for the particle. The top shows the hydrogen ion for reference. The bottom two diagrams show possible identities of the particle.
28.3.2. Experimental Data. In 1901, Rutherford and Frederick Soddy found that thorium can change into another element. In 1902, they identify this element as a new element in the noble gas family, radon (which had been discovered in 1900 and also is radioactive). In 1903, William Ramsey and Frederick Soddy discovered that the compound radium bromide gives off helium gas. Other researchers found that helium also was emitted by a number of other radioactive compounds. In 1903, Rutherford and Soddy publish a paper suggesting that it might be possible for atom to split and form other atoms, and that radioactivity is a consequence of atoms breaking apart. The data available at this point is not completely convincing, so more experiments were necessary. 28.3.3. Rutherford s Mousetrap. In 1906, Rutherford improved the experiment to measure the charge-to-mass ratio of the alpha particle. His results suggested that the more likely identity of the alpha particle is a helium nucleus. Between 1906 and 1907, Rutherford and T.D. Royds at McGill University in Canada ran the following experiment. They started with a tube that had glass walls thin enough that alpha particles could escape, but radon gas could not. They placed a small amount of radon gas in the tube, and then sealed the thin-walled tube into a larger container. They evacuated the outer container and waited. After a few weeks, they found that helium gas had collected in the space between the two tubes, as shown in Figure 28.2. Since only particles could escape from the inner tube, this meant that particles must be helium nuclei. Why helium nuclei and not helium atoms? Remember that the charge-to-mass ratio had been measured and it required two electrons to be missing from a He atom if the alpha particle was to have the correct charge-to-mass ratio. 28.3.4. Radioactive Transmutation. In addition to determining that the particle was a He nucleus, Rutherford and Royd had made another very important discovery: it was possible for one element to emit a fragment that is itself the nucleus of another element. Rutherford and Soddy had predicted this in their 1903 paper and these experiments strongly supported their idea. Their experiment suggested that the original element (radon) must have changed identity if part of it had been emitted as an particle. This challenged a basic tenet of the time, which was that elements are immutable: they cannot change. Alchemists throughout history had tried to initiate transmutation turning one element into another to turn base metals such as lead into noble metals such as gold. Such ideas had been thought to be absurd by this time, but Rutherford s observation suggested that maybe this idea should be reconsidered. Transmutation had developed such a bad name that Rutherford pleaded with people not to use the term transmutation. The term was used widely; however, we now refer to the process of one element turning into another via the emission of a particle (such as an alpha or beta particle) radioactive decay. 28.4. RUTHERFORD S SCATTERING EXPERIMENTS 28.4.1. The Experiment. Rutherford was continuing his study of the alpha particle Radon He A few weeks later Radon Figure 28.2: Rutherford s determination of the identity of particles. Radon is a gas, but is shown here as a dot for clarity. Ernest Rutherford (1871-1937) was born in New Zealand, although most of his work was done in England (with J.J. Thomson) and in Canada (at McGill University). Rutherford was awarded the 1908 Nobel Prize in chemistry for his work with radioactivity. He was unhappy that the prize was in chemistry rather than physics, and his acceptance speech made a remark to the effect that he had seen many transformations in his studies, but never one more rapid than his own from physicist to chemist. Rutherford is a rare example of someone who made his most important contribution to science after winning the Nobel Prize.
Figure 28.3: a) What you might expect if you pass particles (denoted by the yellow beam) through mica b) What Rutherford actually saw. by examining how alpha particles interacted with matter. Rutherford sent a beam of -particles through a sheet of mica and noticed that the width of the beam recorded on a photographic plate was wider than the width of the beam before it entered the mica, as shown in Figure 28.3. Figure 28.3a shows what Rutherford expected to see. Figure 28.3b shows an exaggerated version of what Rutherford actually saw. The angle of deviation was only a few degrees it is shown larger here so that you can see the difference more easily. This suggested to him that something inside the mica was causing the particles to bounce around ( scatter ), with the result that the alpha particles ended up going in slightly different directions due to the scattering. You can think of scattering of particles as being similar to, for example, billiard balls colliding; however, you have to keep the masses of the particles in mind. Rutherford knew that alpha particles wouldn't be deflected much by electrons in the atom, since the alpha particles weighed 8,000 times as much as the electrons and the alphas were moving very quickly. This surprising result prompted him to continue the experiments to gain insight into Thomson s plum pudding model. Rutherford suggested that perhaps the rays were scattering off of something inside the atoms of the mica. Alpha particles are positive, the electrons are negative and the yellow material surrounding the electrons also is also positive (as shown in Figure 28.4). Like charges repel and unlike charges attract, but the alpha particles are going through the gold at very high speed, so there isn t much time for them to interact with the gold atoms. Rutherford calculated that a very large field was required to bend the particles through an angle just 2 away from the path they would follow if they passed undisturbed through the mica. The majority of the particles were coming through the mica undisturbed, so it seemed more likely that the alpha particles were bouncing off something smaller than they are, as shown in Figure 28.4. Since many of the alpha particles go straight through, the density of whatever is scattering the alpha particles must be relatively low. These first experiments were consistent with what was expected from Thomson s model. 28.4.2. Improving Accuracy: The Geiger Counter. Rutherford s assistant, Ernst Geiger, and his undergraduate student Ernest Marsden performed most of the experiments. The alpha particles were detected when they hit a scintillation screen which made a flash on the + + + + 2 degrees Figure 28.4: A possible explanation for the diverging beam using the plum pudding model. The pink box shows where you would expect the beam to be if there were no interactions.
screen where a particle hit. To ensure accuracy, the person watching the screen had to sit in the dark for an hour to get his eyes used to the dark. Geiger invented the Geiger counter in 1906 so he wouldn t have to sit around in the dark watching flashing screens. The Geiger counter works by taking advantage of the fact that radioactive particles ionize the air around them. The Geiger counter has a positively charged central wire and a negatively charged outer conductor, as shown in Figure 28.5. An incoming radioactive particle entering the Geiger counter ionizes some of the gas in the counter. The ionized gas molecules (which are positively charged) move toward the outer conductor. The freed electron can ionize other gas molecules, which multiplies the signal. Between 1909 and 1910, Geiger and Marsden (with Rutherford s input) repeated Rutherford s scattering experiment using gold foils instead of mica. They chose gold because one can make very thin foils (so more alpha particles can get through), and because gold is a large atom, with an atomic radius of about 1.6 x 10-10 m and an atomic mass of 197 u. Alpha particles are much smaller, with a mass of about 4 u. Rutherford and his collaborators expected the same results with gold as they found with mica, but hoped that the larger atoms might give them more understanding of what exactly was happening in the atom. They expected that most of the alpha particles would go through, with some alpha particles being scattered by maybe a few degrees. Gas Molecules Gas Molecules Positive Positive Negative ionizes gas molecule, freeing electron(s) Positive Negative freed electron can ionize other gas molecules as it moves toward the positive wire Gas Molecules Negative Figure 28.5: How the Geiger counter works.
28.4.3. Scattering Alpha Particles from Gold. If we draw a circle around the gold foil and make a line where Rutherford and Marsden expected to see scattering, it would look like Figure 28.6a. What they actually saw can be seen in Figure 28.6b. 5 The results were very surprising. Although the vast majority of the alpha particles went through the gold foil as expected, some alpha particles were deflected through a larger angle and a very small fraction of the alpha particles (about 1 in 20,000) came directly back toward the alpha particle source. The proposed explanation of the scattering using the Thomson plum pudding model had been that the alpha particles were much larger than either the electrons or the positive material. Although the particles interacted with both positive and negative charges, the interactions were weak and should deflect the path only a little. Although one might explain the smaller angle deviations by considering that the particle might scatter more than one, there was not way within the Thomson plum pudding model to explain the backscattering (the particle coming back toward the beam) observed from the gold experiment. This was a major problem for Thomson s model of the atom. 28.5. RUTHERFORD S MODEL By 1911, Rutherford developed a model for the atom that was more consistent with these data. His idea was Alpha particle beam Gold Foil Figure 28.6a: What Rutherford and collaborators expected to see Alpha particle beam Gold Foil Figure 28.6b: What Rutherford and collaborators actually saw. that the positive charge in an atom was centralized in a small, dense region of the atom, in contrast to the plum pudding model, which had it spread throughout the atom. Rutherford s paper explaining this idea initially didn t make much impact. Thomson never accepted Rutherford s model and referred to it only to explain why it was wrong; however, Thomson s model could not explain Rutherford s results as well as the model Rutherford developed. 28.5.1. The Rutherford Model of the Atom. Rutherford suggested that the atom was composed of a positively charged nucleus surrounded by electrons. Rutherford never actually used the word "nucleus" in his paper he used charge concentration". This large positively charged mass explained the backscattering Rutherford had observed. If an alpha particle hit the nucleus head on, it could bounce right back, just as a ball you threw at the wall bounces back to you. The elements of the Rutherford model are: 1. Every atom consists of small central core (the nucleus) in which most of the mass of the atom is concentrated. 2. The nucleus contains all the positive charge in the atom. For an atom with atomic number Z, the charge of the nucleus is +Ze where e is the fundamental charge 1.602 10-19 C. 3. Electrons revolve around the nucleus. The total atom is neutral, so the magnitude of positive charge is equal to the magnitude of negative charge. Rutherford s calculations suggested that 5 An animation is available at http://micro.magnet.fsu.edu/electromag/java/rutherford/
the total charge of all the electrons had to be Ze, since the atom is electrically neutral. An atom with atomic number Z thus has Z electrons. 4. The electrostatic force of attraction between the positively charged nucleus and negatively charged electrons provides the necessary centripetal force to the electron to move in the circular path. An analogy can help explain this: you can whirl a ball on a string around in a horizontal plane above your head. If you cut the string, the ball flies off. The force between the positive charge of the nucleus and the negative charges of the electrons plays the same role as the string. 5. The size of nucleus is of the order of 10-13 cm and the size of the atom is of the order of 10-8 cm. This means that the electrons must be about 100,000 times the radius of the nucleus away from the nucleus. If our classroom were the nucleus, the electrons would be about 380 miles away from us. The majority of the atom thus is made up of empty space. 28.5.2. How the Rutherford Model Accounts for the Data. The nucleus is so small that the odds overwhelmingly are in favor of an alpha particle going right through the gold foil as if nothing were there. Because most of the Rutherford atom is empty space, most alpha particles encounter no scattering as they pass through the gold foil. This explains why most of the particles are not deflected. Some particles, by chance, will pass near gold nuclei. Since the gold nucleus and the alpha particle both are positively charged, they repel each other and the alpha particle will be slightly deflected. Some or all of the small deflections will add up and the particle will deviate from a straight-line path by a few degrees. A very few alphas will hit a gold nucleus almost head-on. The alpha particle gets very close to the nucleus, is repelled by the positive charge of the nucleus, and travels back. This can result in the alpha particle being deflected by 90 or more. 28.5.3. Impact on the Periodic Table. The Dutch physicist A. Van den Broek was the first to suggest that the charge on the nucleus is the atomic number. The unit of charge is e. An alpha particle has charge +2e, the hydrogen nucleus should have a charge of +e and the nucleus of gold would have charge +79e. This gives us a physical meaning for the atomic number Z. The periodic table now becomes a list of atoms in order of the number of electrons (or the amount of positive charge) they contain. The charge of the nucleus increases with increasing atomic number. 28.5.4. The Problem with Rutherford s Model. There is a problem with Rutherford s model. Scientists had learned that a charged particle moving in a circular orbit radiates (loses) energy. Since energy must be conserved, the orbiting electron will have less energy and the radius of the orbit will decrease. The electron eventually should spiral into the nucleus. If this were true, no atom would be stable. This suggested that there might be some details missing in the Rutherford model; however, it does not invalidate the model. 28.6. HISTORY INTERVENES When World War I broke out, most scientists dropped what they were doing to focus on war-related research. Rutherford researched how he could make submarines less detectable. 28.7. SUMMARIZE 28.7.1. Definitions: Define the following in your own words. Write the symbol used to represent the quantity where appropriate. 1. Backscattering 2. Nucleus 28.7.2. Equations: No equations
28.7.3. Concepts: Answer the following briefly in your own words. 1. According to Rutherford s model, what makes up most of an atom? 2. What is the physical meaning of the atomic number in the Rutherford model of the atom? 3. According to Rutherford s model, the volume of an atom is mostly a) occupied by protons and neutrons; b) filled with electrons; c) occupied by tightly bound protons, neutrons and electrons; d) empty space. 4. Explain why Thomson s plum pudding model was replaced by Rutherford s model. What data could not be explained by Thomson s model? 5. Describe Rutherford/Soddy s idea of radioactive transmutation. Why was it controversial? What experiment provided convincing evidence that they were correct? 6. Describe Rutherford and Royd s experiment. How did their experiment tell them that the particle was a He nucleus and not something else? 7. Was there any data that the Rutherford model of the atom couldn t explain? 8. For each, select the most appropriate radiation:, β, γ a) most penetrating; b) most easily absorbed by Al foil; c) most strongly ionizing; d) may require very thick shields for protection; e) cannot be deflected by a magnet; f) large q/m value; g) discovered via the Rutherford-Royd experiment; h) involved in transmutating radium to radon 28.7.4. Your Understanding 1. What are the three most important points in this chapter? 2. Write three questions you have about the material in this chapter. 28.7.5. Questions to Think About 1. Can radioactive transmutation be used to turn lead into gold? Why or why not? 2. Why don t you ever see pictures of the atom drawn to scale? 3. What was the motivation behind Rutherford s scattering experiments? Was he trying to disprove Thomson s model?
PHYS 261 Spring 2007 HW 29 HW Covers Class 28 and is due March 23 th, 2007 1. Can radioactive transmutation be used to turn lead into gold? Why or why not? 2. Explain why Thomson s plum pudding model was replaced by Rutherford s model. What data could not be explained by Thomson s model? Was there any data that the Rutherford model of the atom couldn t explain? 3. Describe Rutherford/Soddy s idea of radioactive transmutation. Why was it controversial? Describe the experiment that provided convincing evidence that they were correct.