At the time of the gold foil experiment, scientists knew a little about the element radium. I’m sure you’ve heard of radium. It probably makes you think about radioactivity, and then you probably think of the Earth science lesson you had involving half-life. Radium is an element that naturally emits alpha particles (or helium ions). So radium “puts off” or emits streams of helium atoms. Geiger and Marsden pointed the radium in the direction of the gold foil, much like you would point a gun, and waited for the radium to naturally emit the alpha particles.
Question 9: What really is radioactivity? Why do some elements emit or “put off” streams of alpha particles? Do any elements emit particles other than alpha particles?
Radioactivity occurs naturally, but can also be triggered. Radium, for example, naturally radiates alpha particles, which is why it was a good element to use for the gold foil experiment.
Recall how the electromagnetic force causes protons to repel one another. Also recall that there are three quarks in each proton and neutron that exert forces on each other by way of the gluon, called the strong force. The more protons there are, the bigger the strong force has to be in order to cancel out the electromagnetic force repelling the protons away from each other. This occurs by way of the neutron, because it adds no extra repulsion force, but does contribute to the strong force holding the quarks of the protons and neutrons together. This means that the more protons there are, the more neutrons are needed in the nucleus in order to balance out the repulsion force between the protons.
Moreover, when you group more than about protons together, no matter how many neutrons are included, the nucleus becomes unstable. This is where we get nuclear decay, which causes radioactivity. Instability of the nucleus can also occur if the nucleus has too many neutrons. We call nuclei that have lots of protons and neutrons heavy nuclei, and heavy nuclei are not stable. The atom tries to gain stability through various means.
The three most common means for an atom to gain stability are as follows. The first way is by ejecting alpha particles. The second way is by converting a proton to a neutron or a neutron to a proton (whichever is needed) by ejecting a beta particle. A beta particle is another name for an electron or a positron. A positron is a positively charged particle that has the same mass as an electron, but is positively charged. We have not talked about it yet, but neutrons themselves can convert to protons by releasing an electron (and a tiny particle called an anti-neutrino). When we say that the neutron releases an electron, we don’t mean that the electron is somewhere inside the neutron and the neutron lets it out. Rather, the electron and antineutrino are essentially essentially created out of ``nothing," as strange as this may sound. The third way a nucleus gains stability is by releasing energy via a gamma ray or gamma emission. A gamma ray is just a photon or a bit of light. Sometimes we call this electromagnetic radiation. Gamma rays are on the high-energy, and therefore high-frequency and short wavelength side of the electromagnetic spectrum.
Question 10: What is quantum mechanics and why did it develop? What part of physics was not complete?
“The more success the quantum theory has, the sillier it looks.” (Einstein, “Zangger”)
Quantum mechanics is the study of subatomic particles (particles smaller than the atom), like electrons, protons, neutrons, and light (photons), and how they interact. Anything you see now in the news about nanoscience deals with quantum mechanics. It may help you to know that about carbon atoms lined up gives you the size of one nanometer. Nanotechnology is just the manipulation of atoms on the nanoscale.
You may have seen atoms pictured like solar systems. The nucleus is like the Sun and the electrons orbit around the nucleus like the planets orbit our Sun. This is not quite what happens and scientists who study subatomic particles have found some very interesting results in experimentation and philosophical thinking, using logic (Einstein called these logic experiments “thought” experiments, or gedanken experiments).
So what led scientists to think that the atom was like a solar system? And now what leads them to think that the atom is not exactly like a solar system?
Let’s explore the first question by studying Ernest Rutherford who was a scientist around the early 1900s (just after J. J. Thomson discovered clear evidence of the negatively charged electron in the cathode tube). Recall the Geiger-Marsden experiment from earlier. Geiger and Marsden sent alpha particles (created by the natural radioactivity of radium) toward gold foil and they found that a small percentage of the alpha particles bounced back. This caused Rutherford to believe that a dense mass is located in the center of an atom, albeit small. In 1911 Rutherford theoretically placed the electrons zipping around the nucleus for his model of the atom. It was known that the overall charge of the atom was zero and if the electrons were around the outside of the dense center, then the center had to be positively charged to keep the whole atom neutrally charged.
Rutherford explored this scenario and did some calculations, which produced some confusion. According to classical physics, the electron should release electromagnetic radiation while it orbits. In accordance with classical physics, all accelerated charged particles produce radiation, or in other words, release waves of light. The key word here is accelerated. Note that here we are referencing the familiar centripetal (circular) motion.
Recall that any object moving in a circle is constantly changing direction, and for an object to change direction, there must be a force acting on it causing it to change direction. According to Newton’s second law, if there is a force, there is an acceleration . The laws of electricity and magnetism then show that the electron must be releasing radiation because it is constantly accelerating (orbiting). As it releases the radiation, it will lose energy, and therefore it should spiral inwards toward the nucleus. According to this theory, all matter is unstable, and the amount of time it would take the electrons to collapse into the nucleus is only ! There has to be a better theory for the structure of an atom, as this one does not work for two reasons. The first is that the electrons would collapse into the nucleus. The second is that scientists would be able to detect a continuous (smooth) spectrum of radiation emitted by the spiraling electron, and they do not. The reason that the radiation from the electron is continuous is that the radiation emitted by the orbiting electron depends on the radius at which the electron is orbiting, and if the radius of the electron continuously decreases (toward the nucleus), then the frequency of the radiation produced by the orbiting electron must also change continuously, and in fact would increase (Weidner ).
What scientists do detect is radiation of discrete frequencies, meaning that there are no in-between frequencies emitted. Think of it this way: Electrons may emit a frequency of a or a frequency of , but no frequencies in between. Therefore, the electron can’t be spiraling inward, as it would have to emit each frequency associated with each radial distance from the nucleus. (A thorough analysis of the mathematics that govern this logic can be studied in a modern physics course, usually the course taken right after a general physics class in college.)
Niels Bohr came next with an improvement on the picture of the atom around 1913 (he was a student of Rutherford and Thomson). Bohr suggested that the atom had a nucleus of positive charge like before and that the electrons orbit around the nucleus at specific radii, like our solar system (like Rutherford’s model), with some modification. It does not describe the atom quite as accurately as Louis de Broglie does in the 1920s, but it does make some good leaps forward. He involves Einstein’s idea of the photon, which we will discuss later.
What Bohr did was discard the very idea that the orbiting electron would spiral inward (as predicted by classical mechanics), and proceeded from there. He considered the idea that the electron orbited at discrete radii instead. What is meant by this is that the electron can be at a distance of or from the nucleus, but nowhere in between. This would mean that the electron would not spiral inward and would have a certain amount of energy, the amount associated with
that radius of orbit. For an electron to increase or decrease its distance from the nucleus, it would have to obtain or release a discrete amount of energy that would place it at the next orbit. In other words, if you don’t give the electron enough extra energy, it won’t jump to the next orbit, and it won’t orbit in between. Perhaps thinking of orbits like a flight of stairs would help. You may stand on the first step or the second step, but you can’t stand in between. You have to use the exact amount of energy needed to get to the next step. Using enough energy to get halfway to the next step will not result in you floating in-between the second step and the first step; that is preposterous! It’s the same, according to Bohr, for the electron. This solves the problems Rutherford’s model had. This means that no energy is lost by orbiting, and therefore the electron does not spiral to the nucleus, and does not emit a continuous spectrum of light as it spirals inward. Bohr doesn’t explain how the light (photon) is created, rather he just makes the connection that as the electron makes a quantum jump to a lower orbit (closer to the nucleus), it emits a photon whose frequency corresponds to the amount of energy lost in moving closer to the nucleus.
So what are the shortcomings of Bohr’s model of the atom? It does not account for the wave-mechanical nature of matter and light (it’s okay if you don’t understand that phrase), nor can it account for atoms with more than one electron, and also it doesn’t really explain why certain radii are allowed. We need a new scientist to take us a little further into understanding the internal structure of an atom.
The next person to make a conjecture for the structure of an atom is the French scientist Louise de Broglie. First, let’s discuss light for a moment. Sometimes we think of light as little traveling packets, called photons. Sometimes we think of light as waves, with a frequency and a wavelength. It turns out that both seem to be good descriptions of light depending on the nature of the experiment we want to understand. We’ll discuss this in a moment using Einstein’s Nobel-winning experiment called the photoelectric effect. Louise de Broglie initially just made the assumption that matter had wave-like properties, and then followed the logic to its end by using mathematics. The idea is strange, but the mathematics produces an accurate model for physics, and corroborates with experimentation results well.
The more we peer into the internal structure of atoms, the stranger things seem to be, and because we can’t see inside directly, we rely on mathematics and indirect methods of analyzing the particles. Sometimes physics is stranger than science fiction! Please note, though, that physics is always logical, just not always intuitive. The natural language of physics is mathematics, and mathematics by its very nature follows logical reasoning. However, its solutions are not always what we expect!
Question 11: What is the photoelectric effect? What does it mean to say that matter has wave-like properties?
Einstein was awarded the Nobel Prize in physics for interpreting the results of this ingenious experiment, first performed by Heinrich Hertz in the late 1800s. The photoelectric effect explores the energy of electrons and the energy carried by light. What Hertz did was shine ultraviolet light on zinc and he found that it became positively charged, which could not be explained at the time. The striking finding is that electrons are observed as soon the light is turned on, rather than the several minutes predicted from classical theory (electricity and magnetism). What Einstein figured out was that electrons can be “knocked” from the metal through the energy from the light shined on the metal, with a few important reservations. First, it depends on the frequency of light that is used. If you use a frequency that is not high enough, the electron will not be affected. The frequency necessary depends on the amount of energy binding the electron to the metal, called the work function. Of course, all light has energy. Prior to the results of this experiment, scientists believed that if you shone light on an object long enough, the energy possessed by the light would build up in that object. What Einstein showed is that energy does not “build up” in the electron. One has to use a frequency of light that has enough energy to provide one swift “kick” (the energy of the light is proportional to its frequency, as predicted by de Broglie) to cause the electron to jump from its orbit.
What are the ramifications of this experiment? For one, we learn that light can be described as a little chunk of energy. For example, suppose your friend is standing on the edge of the deep end of a pool and you want to push him in. Suppose you use a tiny push and he doesn’t fall in, so you push him again with a tiny push. Will he fall in this time? No. It doesn’t matter how many tiny pushes you give him in a row, if the push isn’t large enough, it won’t overcome the friction he has between his feet and the ground and therefore he won’t fall in. It only takes one push that is “just large enough” to make him fall in. It’s the same with an electron. You can “push” on an electron with a bit of light as long as you want, but it won’t be knocked out of its orbit unless the push you give it is sufficiently large. This led Einstein to see light as little particles instead of waves. If light were a wave, one would surmise that the energy would build up over time, but if you think of light as a little packet or ball of energy, you can then see that if the packet doesn’t contain enough energy, it will never cause a change in the electron. You can also think of the light hitting the electron as a collision like you studied in your momentum chapter. The energy from the light-packet (photon) is given to the electron, and if it’s not enough, the electron will not have enough energy to escape its orbit and eject from the atom (any extra energy will go into kinetic energy of the electron). This was a breakthrough for physics.
But physicists have sufficient evidence of the properties of light to also see it as a wave (the way it interferes with other light), so we say that light has wave-particle duality. It is neither an ordinary classical particle, nor an ordinary wave; instead it has properties that are similar to both a particle and a wave at the same time.
The same can actually be said for all matter. The difficulty in seeing evidence of the wavelength of matter results from how very tiny its wavelength is. Light has a long wavelength relative to the wavelength of matter. (Please note that light is not made of matter, rather it’s just a bit of wiggling energy made of electricity and magnetism. It’s a strange concept.)
So what evidence do we have that matter itself is also a wave? If we look at “stuff,” we don’t see it “waving.” Of course, earlier we said that de Broglie just made the assumption mathematically and the theory followed from there to produce accurate mathematical relationships. Experimentally we now have evidence as well (so we don’t have to just rely on an assumption that de Broglie used), and the wavelength for matter is called its de Broglie wavelength.
Now you might ask: How in the world could one test to see if matter, such as an electron, has a wavelength? Let’s consider how we know that light has wave-like properties. We know that light waves interact, or interfere. We know that if two beams of light overlap, i.e., when two crests or two troughs overlap, we get constructive interference (the amplitudes add together) and when a crest and a trough overlap, we get destructive interference (they cancel out for that position). You should recall this from your lessons on light and sound. If we could cause two electrons to interfere like that, we would know that electrons, and therefore matter, behave like waves.
Physicists have been able to do this. (If you would like to view some great pictures or diagrams of this, visit http://en.wikipedia.org/wiki/Double-slit_experiment. Picture two little slits parallel to one another (like two cuts in a thick sheet of paper). Now picture shining a beam of light through these slits. The light would pass through the two slits and form two beams on the other side, but they wouldn’t just be two columns of light. Think about how light shines through a keyhole. On the other side of the keyhole the light spreads out. This result is called diffraction. The light shining through the two slits will diffract and form two beams of light that spread out. Because they spread out, they will overlap and interfere,
and if you place a screen for the beams to shine on, you should see the pattern of interference. Where the two beams’ crests overlap, you have a bright place on the screen, and the same for two troughs. Where you have a crest interfering with a trough, the two beams will cancel out, and you will have a dark spot. (You can show this by using a simple, handheld laser pointer and a piece of hair. Simply tape a piece of paper on the wall where the beam will shine and hold a piece of hair in the path of the beam. You will see a series of bright and dark spots formed by the interfering beams. The piece of hair serves as an obstacle around which the laser has to diffract on either side.) Scientists have done the same experiment with electrons, called the double-slit xperiment. They shot electrons through two slits and used a detecting screen to show the pattern they made. If the electrons behave like little balls (picture baseballs being thrown through two slits) one should see two bright spots across from the slits where the electrons hit. If the electrons behave like waves, one should see an interference pattern just like that of the beams of light. What scientists found is that an interference pattern emerged when releasing many electrons one particle at a time. It’s as if each electron “interfered with itself” and formed the pattern, one hit at a time on the screen. It doesn’t make intuitive sense, and wrapping your mind around such a foreign and abstract concept is difficult, however, the mathematics that predicted this behavior for the electron (and all matter) is now supported by this experimental evidence. C. Davisson and L. H. Germer were the first scientists to confirm the wave-nature of electrons in 1927, followed by scientist G. P. Thomson.
Question 12: What is special relativity and why did it develop? What part of physics was not complete?
If you were to ride on a beam of light, what would light look like? This is the question that Einstein asked himself while he was just a teenager. We already discussed that light is a bit of electricity and a bit of magnetism oscillating, or waving, so what would this look like if we could travel with it?
CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies Page 14
