Includes student results for determining the electron's charge/mass ratio
The electron was first discovered in 1898 by Sir John Joseph Thomson. Almost 100 years ago J.J. Thomson was at Cavendish Laboratory at Cambridge University. Thomson was investigating 'Cathode Rays' which had been a puzzle for a long time. Through his experiments Thomson put forward a then controversial theory in which the 'Cathode Rays' were made up of streams of particles much smaller than atoms, Thomson called these particles 'corpuscles'. Thomson mistakenly believed that these 'corpuscles' made up the entire atom. This idea was controversial as most people at this time thought that the atom was the smallest particle in matter and was divisible.
Thomson's theory was not explicitly supported by his experiments. It took more experimental work by Thomson and others to conclusively prove the theory. The atom is now known to contain other particles as well. Yet Thomson's bold suggestion that 'Cathode Rays' were material constituents of atoms turned out to be correct. The rays are made up of electrons: very small, negatively charged particles.
Science lecturers who traveled from town to town in the mid nineteenth century delighted audiences by showing them the ancestor of the neon sign. They took a glass tube with wires embedded in opposite ends. They then applied a high voltage across the tube. When the air was pumped out of the tube the interior of the tube would glow. In 1859 a German physicist sucked out still more air with an improved pump and saw that where this light from the cathode reached the glass it produced a fluorescent glow. Evidently some kind of ray was emitted by the cathode and lighting up the glass. One theory was that the rays were waves traveling in an invisible fluid called the "ether." At that time, many physicists thought that this ether was needed to carry light waves through apparently empty space. Another possibility was that cathode rays were some kind of material particle. Yet many physicists, including J.J. Thomson, thought that all material particles themselves might be some kind of structures built out of ether, so these views were not so far apart Experiments were needed to resolve the uncertainties. When physicists moved a magnet near the glass, they found they could push the rays about. But when the German physicist Heinrich Hertz passed the rays through an electric field created by metal plates inside a cathode ray tube, the rays were not deflected in the way that would be expected of electrically charged particles. Hertz and his student Philipp Lenard also placed a thin metal foil in the path of the rays and saw that the glass still glowed, as though the rays slipped through the foil. Didn't that prove that cathode rays were some kind of waves? In 1897, drawing on work by his colleagues, J.J. Thomson set out to prove his theory by performing three experiments.
The 1897 Experiments
The First Experiment
In a variation of an 1895 experiment by Jean Perrin, Thomson built a cathode ray tube ending in a pair of metal cylinders with a slit in them. These cylinders were in turn connected to an electrometer, a device for catching and measuring electrical charge. Perrin had found that cathode rays deposited an electric charge. Thomson wanted to see if, by bending the rays with a magnet, he could separate the charge from the rays. He found that when the rays entered the slit in the cylinders, the electrometer measured a large amount of negative charge. The electrometer did not register much electric charge if the rays were bent so they would not enter the slit. As Thomson saw it, the negative charge and the cathode rays must somehow be joined together.
The Second Experiment
All attempts had failed when physicists tried to bend cathode rays with an electric field. Now Thomson thought of a new approach. A charged particle will normally curve as it moves through an electric field, but not if it is surrounded by a conductor (a sheath of copper, for example). Thomson suspected that traces of gas remaining in the tube were being turned into an electrical conductor by the cathode rays themselves. To test this idea, he took great pains to extract nearly all of the gas from a tube, and found that now the cathode rays did bend in an electric field after all. J.J. Thomson concluded from these two experiments, "I can see no escape from the conclusion that cathode ray] are charges of negative electricity carried by particles of matter." But, he continued, "What are these particles? Are they atoms, or molecules, matter in a still finer state of subdivision?"
The Third Experiment
Thomson's third experiment sought to determine the basic properties of the particles. Although he couldn't measure directly the mass or electric charge of such a particle, he could measure how much the rays were bent by a magnetic field, and how much energy they carried. From this data he could calculate the ratio of the electric charge of a particle to its mass (e/m). He collected data using a variety of tubes and using different gases.
The results of Thomson's were astounding. Just as Emil Wiechert had reported earlier that year, the mass-to-charge ratio for cathode rays turned out to be over one thousand times smaller than that of a charged hydrogen atom. Either the cathode rays carried an enormous charge (as compared with a charged atom), or else they were amazingly light relative to their charge.
Philipp Lenard settled the choice between these possibilities. Experimenting on how cathode rays penetrate gases, he showed that if cathode rays were particles they had to have a very small mass-far smaller than the mass of any atom. The proof was far from conclusive. But experiments by others in the next two years yielded an independent measurement of the value of the charge (e) and confirmed this remarkable conclusion
Thomson announced the hypothesis that "we have in the cathode rays matter in a new state, a state in which the subdivision of matter is very much further than in the ordinary gaseous state: a state in which all matter... is of one and the same kind; this matter being the substance from which all the chemical elements are built up."
From his three experiments in 1897 Thomson presented three hypotheses about cathode rays
Cathode rays are charged particles (which he called 'corpuscles').
- These corpuscles are constituents of the atom.
- These corpuscles are the only constituents of the atom.
Thomson's hypotheses met with some skepticism. The second and third hypotheses were especially controversial. Years later he recalled "At first there were very few who believed in the existence of these bodies smaller than atoms. I was even told long afterwards by a distinguished physicist who had been present at my lecture at the Royal Institution that he thought I had been 'pulling their legs.'
The word 'electron' first used by G. Johnstone Stoney in 1891 had been used to denote the unit of charge found in experiments that passed electric current through chemicals. In this sense Joseph Larmor, J.J. Thomson's Cambridge classmate, used the term. Larmor devised a theory of the electron that described it as a structure in the ether. But Larmor's theory did not describe the electron as a part of the atom. When the Irish physicist George Francis FitzGerald suggested in 1897 that Thomson's corpuscles were really 'free electrons' he was actually disagreeing with Thomson's hypotheses. FitzGerald had in mind the kind of 'electron' described by Larmor's theory.
Gradually scientists accepted Thomson's first and second hypotheses, although with some subtle changes in their meaning. Experiments by Thomson, Lenard, and others through the crucial year of 1897 were not enough to settle the uncertainties. Real understanding required many more experiments over later years.
Theories about the atom proliferated following Thomson's 1897 work. Thomson proposed a model, sometimes called the 'plum pudding' model, in which thousands of tiny, negatively charged 'corpuscles' swarm inside a sort of cloud of mass less positive charge. This theory was disproved by Thomson's former student, Ernest Rutherford. Using a different kind of particle beam, Rutherford found evidence that the atom has a small core, a nucleus. Rutherford suggested that the atom might resemble a tiny solar system, with a massive, positively charged centre circled by only a few electrons. Later this nucleus was found to be made up of new kinds of particles (protons and neutrons), much heavier than electrons.
In 1911 Robert Milikan set out to try and determine the charge of an electron. He did this by balancing charged oil droplets in an electric field, using the equipment shown below.
Milikan used a microscope to observe the oil droplets between the plates. When there is no P.D. between the plates the droplets fall at a steady speed. However when a P.D. is applied between the plates the oil droplets do one of three things
- Droplets with an overall negative charge fall more slowly or even stop moving.
- Droplets with an overall positive charge fall more quickly
- Droplets with no charge are not affected.
These droplets are charged as they are forced out of the nozzle. As the plate voltage increases some of the drops fall more and more slowly until the drops stop moving, at this point the electric fore is equal to the weight of the oil droplet. The electric force on the droplet is given by the charge (q) multiplied by the electric field strength (V/d).
q=Droplet Charge V= Holding Voltage d= Distance between plates m=droplet mass g= Acceleration due to gravity.
From his experiments Milikan determined that the charge on an electron was 1.6×10-19 C.
In order for Milikan to determine the mass of an oil droplet accurately he found that when the P.D. across the plate was off, the speed that oil droplets fell at was determined only by the mass of the oil droplets. So by timing how long it takes for a droplet to fall with the plates off he could calculate the mass of the droplet.
Milikan noticed that the droplets fell at a constant speed, which meant that the weight of the droplet was balanced by the viscous force of the droplet falling through the air. The viscous force on an object is given by the formula.
F= Viscous force h= Viscosity of fluid R= Sphere radius v= Sphere speed
This gives the formula
However the mass of an object is also given by the density of the object multiplied by the volume of the object. Therefore
What follows is our attempt to measure e/m at Egglescliffe School:
Another way of determining e/m is to use the fine beam tube method. In this method electrons are produced by thermionic emission, and then accelerated inside a sphere containing nitrogen gas at a low pressure. When the electrons strike a nitrogen molecule they cause it to emit green light. Either side of the sphere there are a pair of magnetic coils, placed to provide a uniform magnetic filed inside the sphere. The magnetic field causes the electrons to be deflected, if the field is strong enough then the electrons will orbit in a circle. The gas is at low pressure so as not to scatter the electrons so they will not form a beam
The electrons inside the tube are accelerated by a potential difference V (supplied by the h.t. unit) between the cathode and the conical anode. The kinetic energy gained by the electrons when they are accelerated is given by the formula
The electrons are in circular motion so by Newton's Second Law applied radially
The only source of the force on the electrons is the magnetic force caused by the interaction of the electrons with the magnetic field, this force can be given by the formula
By combining these two we come up with the formula
This can be rearranged to give
Then substitute this into the formula giving the kinetic energy of the electrons. After rearranging :
The strength of the magnetic field (B) can be calculated by the formula
µ0 =4p×10-7 Hm-1 N = Number of coils
I = Current through coil R = radius of coil
See Appendix A for experimental results
The magnifying power of an optical microscope is limited by the wavelength of visible light. An electron microscope uses electrons to "illuminate" an object; since electrons have a much smaller wavelength than light, they can resolve much smaller structures than light can. The smallest wavelength of visible light is about 4,000 angstroms (1 angstrom is 1×10-10 meters) the wavelength of electrons used in electron microscopes is usually about .5 angstrom.
All electron microscopes comprise several basic elements. They have an electron gun emitting electrons that strike the specimen and create a magnified image. Magnetic 'lenses' that create magnetic fields are used to direct and focus the electrons, because the conventional lenses used in optical microscopes to focus visible light do not work with electrons. A vacuum system is an important part of any electron microscope. Electrons are easily scattered by air molecules, so the interior of an electron microscope must be at a very high vacuum. Finally, electron microscopes also have a system that records or displays the image produced by the electrons.
There are two basic types of electron microscopes: the transmission electron microscope (TEM), and the scanning electron microscope (SEM). In a TEM the electron beam is directed on to the object to be magnified. Some of the electrons are absorbed or bounce off the specimen others pass through and form a magnified image of the specimen.
The sample must be cut very thin to be used in a TEM usually the sample is no more than a few thousand angstroms thick. A photographic plate or fluorescent screen is placed beyond the sample to record the magnified image. Transmission electron microscopes are capable of magnifying an object up to 1 million times.
A scanning electron microscope creates a magnified image of the surface of an object. When using an SEM, the object to be magnified does not need to be thinly sliced; the sample can be placed in the microscope with little, if any, preparation. An SEM scans the surface of the sample bit by bit, in contrast to the TEM, which looks at a relatively large part of the object all at once. In an SEM, a tightly focused electron beam moves over the entire sample, much the way an electron beam scans an image on to the screen of a television.
Electrons in the tightly focused beam might scatter directly off the sample, or cause secondary electrons to be emitted from the surface of the sample, these scattered or secondary electrons are collected and counted by an electronic device located to the side of the sample. Each scanned point on the sample corresponds to a pixel on a television monitor; the more electrons the counting device detects, the brighter the pixel on the monitor is. As the electron beam scans over the entire sample, a complete image of the sample is displayed on the monitor. Scanning electron microscopes can magnify objects 100,000 times or more. SEMs are particularly useful because, unlike TEMs and powerful optical microscopes, SEMs produce detailed pictures of the surface of objects, providing a realistic three-dimensional image.
Various other electron microscopes have been developed. A scanning transmission electron microscope (STEM) combines elements of an SEM and a TEM, and can resolve single atoms in a sample. An electron probe microanalyser, which is an electron microscope fitted with an X-ray spectrum analyzer, can examine the high-energy X-rays that are emitted by the sample when it is bombarded with electrons. Because the identity of different atoms or molecules can be determined by examining their X-ray emissions, electron probe analyzers not only provide a magnified image of the sample as a conventional electron microscope does, but also information about the sample's chemical composition.
Appendix A - Results from e/m experiment
|Va (Volts)||r (m)||I (A)||B (T) ×10-4||e/m (CKg-1) ×1011|
The accepted value of e/m is 1.76×1011 CKg-1.
It is hard to get accurate results from this method as it is difficult to accurately measure the radius of the circle of electrons, and also the fine beam tube that I was using had lost some of it's hydrogen making it hard to see the cathode rays.
Page contributed by Peter Richards (Yr 13 student 1999-2000)