The implications of E=mc² in practice
Reminder: have you read the preceding page on E=mc2?
* Header source: historyonthenet.com
What are the practical applications of all this, and where did all this inherent energy and power come from? This requires a consideration of the major historical developments in scientific discovery since Einstein’s theoretical formulation of the relevant principles.
The atom’s nucleus was discovered in 1911, but this did little at the time to open any doors to testing the mass-energy concept, and matters remained unchanged for over two decades, but during the 1930s, two key developments took place. The first was the discovery of the neutron by British physicist James Chadwick in 1932, and in the same year scientists were able to use the first particle accelerator or atom smasher to take a peek inside the world of the atom. In so doing they came to realise that an atom was not like some monolithic billiard ball, but instead an elegant mechanism with several moving parts: a nucleus consisting of protons and neutrons orbited by a swarm of electrons – “not unlike a hive with its restless swarm of bees”[1].
The strong and weak nuclear forces illustrated
Neutrons are electrically neutral. They do not repel each other and remain tightly huddled within the atom’s nucleus making no attempt to escape. Not so protons whose positive charge is naturally repulsive, confined only by the strong nuclear force, “a kind of invisible nuclear glue”, but even that did not always work and some individual protons still managed to break free. This leakage is what constitutes radioactivity, and the larger the nucleus, the greater the potential for instability. When scientists weighed the nucleus before and after such a leakage and compared it with the mass of the escaping proton, they found it always weighed less by an amount greater than the mass of the escaped proton, which had taken with it some of the ponderous pent-up tension hitherto existing within the nucleus, entirely in accordance with Einstein’s equation. It was “as if protons were like siblings whose revulsion was so intense it was palpable ..(and) after a sibling fled, the remaining family weighed less by an amount equal to the runaway’s mass plus his share of the material tension”[2]. Considered this way, radioactivity was “a heavy functional nucleus’s way of relieving stress”.
Different forms of the same element with the same number of protons, but differing numbers of neutrons in their nuclei are referred to as isotopes. Thus C 12 and C 14 are both isotopes of carbon one with 6 neutrons and one with 8 neutrons, both with 6 protons. The stability of any atom's nucleus depends on the ratio of protons to neutrons. Many isotopes have a ratio of protons to neutrons that renders them unstable, and when the protons break away, they also give off ionizing radiation, known as radioactivity.
Scientists then turned their collective minds to seeing if they could make a dysfunctional nucleus fall apart completely and with this in mind turned their attention to uranium, the largest atom found in nature and mined from pitchblende, whose nucleus consisted of “92 irascible protons just bursting to get out”. Compared to the hydrogen atom (1 proton, 1 electron), the uranium atom is "a monster, the heaviest atom in nature, bulked out with 92 protons and 140 odd neutrons, so scarce in the cosmos that hydrogen atoms outnumber it by 17 trillion to one, and unstable, given to decaying at quantum mechanically unpredictable moments down a chain of lighter elements. [3].
The scientists originally tried bombarding this bloated specimen with electrons, but that didn’t work because the electron was too small. They tried it with protons, but the repulsive force of the neutrons own protons never let them get close enough. Finally in 1934, using a neutron, the nucleus disintegrated releasing a hundred billion times more energy that one could ever get from old fashion combustion.
A convenient way of visualising the uranium nucleus is something akin to a bunch of grapes squeezed together by nuclear rubber bands, or as a liquid drop – "a shimmering, jostling, oscillating globule that pinches into an hourglass and then fissures at its new waist” – a poor approximation, perhaps, “for the lumpy, raisin-studded complex at the heart of a heavy atom, with each of 200-odd particles bound to each of the others by a strong close-range nuclear force”, but as Gleick, goes on to point out, it was this enticing image would eventually lead to the use of the word “fission” to describe the splitting process prompted by neutron bombardment, even if only for want of a better alternative [4].
Uranium's (U's) two most common isotopes are U 238 (92 protons, 146 neutrons; natural abundance 99.274) and uranium 235 (92 protons 143 neutrons; NA =.720). Uranium decays slowly by emitting an alpha particle (two protons and two neutrons bound together into a particle identical to a helium nucleus), but where the atoms are present in sufficient concentrations (a critical mass), and fission occurs and the uranium nucleus is split, one uranium nucleus - splitting into odd pairs of smaller atoms, barium and krypton or tellurium and zirconium, plus a bonus of new neutrons and free energy and releasing neutrons able to split more nuclei - brings about a spontaneous and sustained nuclear chain reaction with not only massive numbers of nuclei splitting and releasing energy all at once, but at the speed of light – squared! ”Where this occurs, a massive explosion or bomb is the result. Uranium-238 has a small probability for spontaneous fission; uranium-235 has a much higher likelihood of interaction between an incident neutron and a target nucleus with slow neutrons. [5]
The significance of E=mc² in this context is that the mass of a body is a measure of its energy content. So, whenever mass converts to pure energy, the resultant energy is by definition moving at the speed of light. Pure energy consists of electromagnetic radiation in its various forms and electromagnetic radiation travels at a constant 300,000 kms or 186,000 miles per second. The speed of light squared is the conversion ratio that determines just how much energy is inherent in the mass being converted. It is ‘squared’ because when something is moving say four times as fast as something else, it doesn’t just have four times the energy, but 16 times the energy. So the speed factor is squared. The most dramatic consequences of this law are observed in nature: for example in nuclear fission and fusion processes where stars like the sun emit energy and lose mass, and the same law also applies to the forces set free in the detonation of an atomic bomb.
When you take into consideration the fact that the speed of light squared equals 90,000,000,000 kms per second, it is obvious that the amount of energy bound up in even the smallest mass is huge. The first nuclear bomb exploded on 16 July 1945, was the product of converting .9 of a gram of uranium into a correspondingly huge amount of energy (the equivalent of 20,000 tons of TNT) and the atomic bomb dropped on Hiroshima in 1945 was the product of the conversion of less than .6 of a gram of uranium into energy[6]. It has been estimated that if you were to convert every one of the atoms in a paper clip into pure energy, leaving no mass whatsoever, the paper clip would yield 28 kilotons of TNT, roughly the size of the Hiroshima bomb [7]. At the moment, such an exercise remains academic on our planet, since it would require temperatures and pressures greater than those at the core of our sun [8].
Nor should the more peaceful consequences of E=mc² be overlooked. As Michael Guillen points out, burning fossil fuels such as wood, oil and coal is incredibly inefficient. A modern power plant burning a lump of high grade coal produces enough energy to keep one light bulb shining for only about four hours, but if that same lump of coal were transformed completely into energy, it would keep the same light bulb burning for 1,680 billion hours [9]. Such is the power lurking behind the deceptive simplicity of E=mc². [10]
[1] Michael Guillen, Five Equations that changed the world – The power and poetry of Mathematics, 256; Robert P. Crease, The Great Equations – Breakthroughs in Science from Pythagoras to Heisenberg, Norton, New York,Crease, 172. For more detail, see /particles-and-forces.html
[2] Guillen, 257.
[3] James Gleick, Richard Feynman and modern physics, Little Brown, London, 1992, 94-5.
[4] Ibid, 95.
[5] The process of a sustained nuclear chain reaction is deftly illustrated with the assistance of floating snooker balls in Derek Muller’s television documentary Uranium – Twisting the Dragon’s tail, Part 1 at http://www.dailymotion.com/video/x37o8t7 commencing about 20 minutes in. The tale is also told in Guillen, op cit, 258-259; and Crease, op cit, 172-177.
[6] Greene (2000), 51. Einstein and Hawking, Masters of the Universe, (Part 2), BBC 2019, precis at https://in.mashable.com/science/10936/einstein-and-hawking-masters-of-our-universe-tells-a-brief-history-of-relativity
[7] The “Little Boy” bomb detonated over Hiroshima, containing about 140 lb (64 kg) of enriched uranium, has also been equated with the mass of one BB pellet: “One BB pellet was enough to destroy an entire modern city”: Dana Mackenzie, The Universe in Zero Words – The story of Mathematics, Elwin Street Productions, Sydney, 2012, 158.
[8] Nova Science Programming On Air and Online website: http://www.pbs.org/wgbh/nova/einstein/lrk-hand-emc2expl.html
[9] Guillen, 254-5.
[10] For the implications of E=mc² in the context of terrestrial fusion, see Terrestrial Fusion
* Header source: historyonthenet.com
What are the practical applications of all this, and where did all this inherent energy and power come from? This requires a consideration of the major historical developments in scientific discovery since Einstein’s theoretical formulation of the relevant principles.
The atom’s nucleus was discovered in 1911, but this did little at the time to open any doors to testing the mass-energy concept, and matters remained unchanged for over two decades, but during the 1930s, two key developments took place. The first was the discovery of the neutron by British physicist James Chadwick in 1932, and in the same year scientists were able to use the first particle accelerator or atom smasher to take a peek inside the world of the atom. In so doing they came to realise that an atom was not like some monolithic billiard ball, but instead an elegant mechanism with several moving parts: a nucleus consisting of protons and neutrons orbited by a swarm of electrons – “not unlike a hive with its restless swarm of bees”[1].
The strong and weak nuclear forces illustrated
Neutrons are electrically neutral. They do not repel each other and remain tightly huddled within the atom’s nucleus making no attempt to escape. Not so protons whose positive charge is naturally repulsive, confined only by the strong nuclear force, “a kind of invisible nuclear glue”, but even that did not always work and some individual protons still managed to break free. This leakage is what constitutes radioactivity, and the larger the nucleus, the greater the potential for instability. When scientists weighed the nucleus before and after such a leakage and compared it with the mass of the escaping proton, they found it always weighed less by an amount greater than the mass of the escaped proton, which had taken with it some of the ponderous pent-up tension hitherto existing within the nucleus, entirely in accordance with Einstein’s equation. It was “as if protons were like siblings whose revulsion was so intense it was palpable ..(and) after a sibling fled, the remaining family weighed less by an amount equal to the runaway’s mass plus his share of the material tension”[2]. Considered this way, radioactivity was “a heavy functional nucleus’s way of relieving stress”.
Different forms of the same element with the same number of protons, but differing numbers of neutrons in their nuclei are referred to as isotopes. Thus C 12 and C 14 are both isotopes of carbon one with 6 neutrons and one with 8 neutrons, both with 6 protons. The stability of any atom's nucleus depends on the ratio of protons to neutrons. Many isotopes have a ratio of protons to neutrons that renders them unstable, and when the protons break away, they also give off ionizing radiation, known as radioactivity.
Scientists then turned their collective minds to seeing if they could make a dysfunctional nucleus fall apart completely and with this in mind turned their attention to uranium, the largest atom found in nature and mined from pitchblende, whose nucleus consisted of “92 irascible protons just bursting to get out”. Compared to the hydrogen atom (1 proton, 1 electron), the uranium atom is "a monster, the heaviest atom in nature, bulked out with 92 protons and 140 odd neutrons, so scarce in the cosmos that hydrogen atoms outnumber it by 17 trillion to one, and unstable, given to decaying at quantum mechanically unpredictable moments down a chain of lighter elements. [3].
The scientists originally tried bombarding this bloated specimen with electrons, but that didn’t work because the electron was too small. They tried it with protons, but the repulsive force of the neutrons own protons never let them get close enough. Finally in 1934, using a neutron, the nucleus disintegrated releasing a hundred billion times more energy that one could ever get from old fashion combustion.
A convenient way of visualising the uranium nucleus is something akin to a bunch of grapes squeezed together by nuclear rubber bands, or as a liquid drop – "a shimmering, jostling, oscillating globule that pinches into an hourglass and then fissures at its new waist” – a poor approximation, perhaps, “for the lumpy, raisin-studded complex at the heart of a heavy atom, with each of 200-odd particles bound to each of the others by a strong close-range nuclear force”, but as Gleick, goes on to point out, it was this enticing image would eventually lead to the use of the word “fission” to describe the splitting process prompted by neutron bombardment, even if only for want of a better alternative [4].
Uranium's (U's) two most common isotopes are U 238 (92 protons, 146 neutrons; natural abundance 99.274) and uranium 235 (92 protons 143 neutrons; NA =.720). Uranium decays slowly by emitting an alpha particle (two protons and two neutrons bound together into a particle identical to a helium nucleus), but where the atoms are present in sufficient concentrations (a critical mass), and fission occurs and the uranium nucleus is split, one uranium nucleus - splitting into odd pairs of smaller atoms, barium and krypton or tellurium and zirconium, plus a bonus of new neutrons and free energy and releasing neutrons able to split more nuclei - brings about a spontaneous and sustained nuclear chain reaction with not only massive numbers of nuclei splitting and releasing energy all at once, but at the speed of light – squared! ”Where this occurs, a massive explosion or bomb is the result. Uranium-238 has a small probability for spontaneous fission; uranium-235 has a much higher likelihood of interaction between an incident neutron and a target nucleus with slow neutrons. [5]
The significance of E=mc² in this context is that the mass of a body is a measure of its energy content. So, whenever mass converts to pure energy, the resultant energy is by definition moving at the speed of light. Pure energy consists of electromagnetic radiation in its various forms and electromagnetic radiation travels at a constant 300,000 kms or 186,000 miles per second. The speed of light squared is the conversion ratio that determines just how much energy is inherent in the mass being converted. It is ‘squared’ because when something is moving say four times as fast as something else, it doesn’t just have four times the energy, but 16 times the energy. So the speed factor is squared. The most dramatic consequences of this law are observed in nature: for example in nuclear fission and fusion processes where stars like the sun emit energy and lose mass, and the same law also applies to the forces set free in the detonation of an atomic bomb.
When you take into consideration the fact that the speed of light squared equals 90,000,000,000 kms per second, it is obvious that the amount of energy bound up in even the smallest mass is huge. The first nuclear bomb exploded on 16 July 1945, was the product of converting .9 of a gram of uranium into a correspondingly huge amount of energy (the equivalent of 20,000 tons of TNT) and the atomic bomb dropped on Hiroshima in 1945 was the product of the conversion of less than .6 of a gram of uranium into energy[6]. It has been estimated that if you were to convert every one of the atoms in a paper clip into pure energy, leaving no mass whatsoever, the paper clip would yield 28 kilotons of TNT, roughly the size of the Hiroshima bomb [7]. At the moment, such an exercise remains academic on our planet, since it would require temperatures and pressures greater than those at the core of our sun [8].
Nor should the more peaceful consequences of E=mc² be overlooked. As Michael Guillen points out, burning fossil fuels such as wood, oil and coal is incredibly inefficient. A modern power plant burning a lump of high grade coal produces enough energy to keep one light bulb shining for only about four hours, but if that same lump of coal were transformed completely into energy, it would keep the same light bulb burning for 1,680 billion hours [9]. Such is the power lurking behind the deceptive simplicity of E=mc². [10]
[1] Michael Guillen, Five Equations that changed the world – The power and poetry of Mathematics, 256; Robert P. Crease, The Great Equations – Breakthroughs in Science from Pythagoras to Heisenberg, Norton, New York,Crease, 172. For more detail, see /particles-and-forces.html
[2] Guillen, 257.
[3] James Gleick, Richard Feynman and modern physics, Little Brown, London, 1992, 94-5.
[4] Ibid, 95.
[5] The process of a sustained nuclear chain reaction is deftly illustrated with the assistance of floating snooker balls in Derek Muller’s television documentary Uranium – Twisting the Dragon’s tail, Part 1 at http://www.dailymotion.com/video/x37o8t7 commencing about 20 minutes in. The tale is also told in Guillen, op cit, 258-259; and Crease, op cit, 172-177.
[6] Greene (2000), 51. Einstein and Hawking, Masters of the Universe, (Part 2), BBC 2019, precis at https://in.mashable.com/science/10936/einstein-and-hawking-masters-of-our-universe-tells-a-brief-history-of-relativity
[7] The “Little Boy” bomb detonated over Hiroshima, containing about 140 lb (64 kg) of enriched uranium, has also been equated with the mass of one BB pellet: “One BB pellet was enough to destroy an entire modern city”: Dana Mackenzie, The Universe in Zero Words – The story of Mathematics, Elwin Street Productions, Sydney, 2012, 158.
[8] Nova Science Programming On Air and Online website: http://www.pbs.org/wgbh/nova/einstein/lrk-hand-emc2expl.html
[9] Guillen, 254-5.
[10] For the implications of E=mc² in the context of terrestrial fusion, see Terrestrial Fusion