{"id":5373,"date":"2011-01-27T14:48:49","date_gmt":"2011-01-27T14:48:49","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2011\/01\/27\/energy-from-mass-mass-from-ene\/"},"modified":"2011-01-27T14:48:49","modified_gmt":"2011-01-27T14:48:49","slug":"energy-from-mass-mass-from-ene","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2011\/01\/27\/energy-from-mass-mass-from-ene\/","title":{"rendered":"Energy from Mass, Mass from Energy"},"content":{"rendered":"

I probably ought to get a start on the big pile of grading I have waiting for me, but I just finished a draft of the problematic Chapter 7, on E=mc<\/i>2<\/sup>, so I’m going to celebrate a little by blogging about that.<\/p>\n

One thing that caught my eye in the not-entirely-successful chapter on momentum and energy in An Illustrated Guide to Relativity<\/cite><\/a> was a slightly rant-y paragraph on how it’s misleading to talk about the energy released in nuclear reactions as being the conversion of mass into energy, because what’s really involved is just the release of energy due to the strong force. It struck me as oddly hostile, but on reflection, there’s a sense in which it’s absolutely right.<\/p>\n

When you say that a nuclear reactor or a nuclear explosion works by converting mass into energy, that creates the impression that some of the stuff you had before the reaction has vanished, turned into energy. If you count up the total number of quarks and leptons, though, that’s not true– you still have exactly as many quarks as you did at the start. Depending on what process you’re talking about, some of them may have changed from one type to another (the chain to fuse hydrogen into helium involves converting a couple of protons into neutrons by changing up quarks to down quarks), but the total number of material particles does not change as you go through the reaction.<\/p>\n

Where does the energy come from, then? Well, you’ve got the same number of particles, but they’re in a different arrangement at the end of the reaction than when they started. The new configuration has a different energy than the old, which means some energy has been freed up to become kinetic energy of the reaction products. In that sense, the reaction isn’t really any different than the emission of light by an atom when one of its electrons drops from a higher energy state to a lower energy one– the interaction giving rise to the energy is different, but the fundamental process is just a re-arrangement of stuff that was already there.<\/p>\n

<\/p>\n

Why do we talk about mass changes in the nuclear case and not the atomic one? Well, because the energy scales are very different. An ordinary electronic transition in an atom changes the energy of the atom by at most something like 10 eV, while the mass of an atom is several times the mass of a proton, which is 938,000,000 eV. Even for a really light atom like hydrogen, that’s a change in the mass of less than one part in 108<\/sup>, which is completely insignificant.<\/p>\n

The energy released in fission or fusion reactions, on the other hand, is on the MeV scale, which is a few tenths of a percent of the mass of the reactants. Which isn’t terribly large, but is significant enough to be worth noting.<\/p>\n

So, does that means that it’s illegitimate to talk about nuclear reactions as examples of converting mass to energy? That’s going too far in the other direction. While it’s true that the processes people talk about when discussing nuclear energy are only releasing energy by reconfiguring the particles that are already there, the whole point of the equivalence of mass and energy is that it’s every bit as valid to call the interaction energy “mass” as it is to call individual particles “mass.” And, in fact, 99% of the mass associated with everyday objects comes from exactly the same source as the energy released in nuclear reactions.<\/p>\n

If you look up information on the proton<\/a>, you’ll find that it’s made of two up quarks and a down quark. Looking up information on quarks<\/a> will tell you that the up quark has a mass of 2.4 MeV\/c2<\/sup>, while the down quark has a mass of 4.8 MeV\/c2<\/sup>, for a total quark mass of 9.6 MeV\/c2<\/sup>. Which is fine, but the first link in this paragraph will also tell you that the mass of a proton is 938 MeV\/c2<\/sup>.<\/p>\n

Where does the rest of that energy come from? It comes from the strong nuclear interaction, which binds the quarks together into the proton, and also binds protons and neutrons into the nucleus. There’s energy associated with the strong force, and that energy accounts for 99% of the mass of the proton. You can find that energy described as a couple of different particle types– sometimes pions, sometimes gluons– but whatever name you give to it, the energy comes from the strong interaction.<\/p>\n

So, while it’s true that the energy released in nuclear reactions is freed up just by changing from one configuration of quarks and leptons to a different configuration of quarks and leptons, the vast majority of the energy associated with the reacting particles is also due to the strong nuclear interaction acting on a particular configuration of quarks.<\/p>\n

So, as is usual when I run across a source taking some very strong position, my take on swung from “That’s weirdly hostile” to “That’s a good point,” and ended up somewhere in the wishy-washy middle. It’s certainly true that the creation of particles in high-energy collisions is a cleaner example of conversion between energy and mass than nuclear power is, so as much as I’m tired of hearing about particle physics, I still spent more time on that than on nuclear power in the E = mc<\/i>2<\/sup>. Given that 99% of the mass of everything has its origin in strong interactions, though, I can’t get all that worked up over the distinction. It’s a decent enough hook for a blog post, though…<\/p>\n","protected":false},"excerpt":{"rendered":"

I probably ought to get a start on the big pile of grading I have waiting for me, but I just finished a draft of the problematic Chapter 7, on E=mc2, so I’m going to celebrate a little by blogging about that. One thing that caught my eye in the not-entirely-successful chapter on momentum and… Continue reading Energy from Mass, Mass from Energy<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[146,7,141,11],"tags":[],"class_list":["post-5373","post","type-post","status-publish","format-standard","hentry","category-atoms_and_molecules","category-physics","category-relativity","category-science","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/5373","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=5373"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/5373\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=5373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=5373"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=5373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}