If you’re like most people, you grew up around the equation E=mc2. You generally learn it in cartoons before you ever even see it in school. Any time Hollywood wants to make someone look smart, they surround them with a bunch of formulas, most of them fake, and always, without fail, one of them is E=mc2. You see it on everything from posters to ties, and if you look hard enough, you could probably even find some Rule-34 stuff. And of course, always associated with and usually accommodating this formula is none other than a certain personality who has permeated every aspect of culture and become a pop icon in and of themselves. Few others of their field have ever been a part of so many movies, TV shows, books, and even various lines of toys and bagels. You know exactly who I'm talking about already. Your grandkids will know, and their grandkids will know, because both are so intertwined with one another and global culture, forever.
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| No! |
Yet, have you ever really given some thought as to why the formula is special? "Well, it has something to do with nuclear explosions, right?" Well, yes, in roughly the same way that rain has something to do with rainbows. Or that the clowns have something to do with creepy. Or maybe both.
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| Your welcome. |
A few of you most likely even know the meaning of the letters by rote: "energy equals mass times the speed of light...squared." Maybe you've even got this idea that if you threw a ball at high enough speed, "...like the speed of light times itself, it'd, like, turn into pure energy or something, man." Chances are, if you're reading this article, you're either unaware of the actual true meaning of this formula, or you were bored enough to read an article about something you already knew about. Regardless, at some point in your life, did you ever stop to wonder, however briefly, why the hell even your cat seems to know this formula by heart, even if they have no idea what it means.
Why is E=mc2 so special? Well, it all comes down to something called "Mass Defect." Chances are, you've never heard of it, and if you have, it's because you're taking (or already took) a class that required you to learn about it. So what is Mass Defect?
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| Really? |
In layman's terms, Mass Defect is the observation that any given atom has less mass than the sum of its parts. In simplest terms, it means that 1+1=3. Only not really. It's more like 250 + 250 + 250 + 250 + 8 = 1000. In other words, there is a mathematical defect between the two observed masses.
As Antoine Lavoisier was kind enough to point out to us about 250 years ago, mass doesn't just magically appear or go away, it merely changes its form or composition. As this changed the presumably previously held view that matter pops into existence at the whims of elves and fairy magic, this is kind of set the whole foundation of modern chemistry as we know it. It is also the reason why you had to learn how to balance all those annoying chemical equations.
As Antoine Lavoisier was kind enough to point out to us about 250 years ago, mass doesn't just magically appear or go away, it merely changes its form or composition. As this changed the presumably previously held view that matter pops into existence at the whims of elves and fairy magic, this is kind of set the whole foundation of modern chemistry as we know it. It is also the reason why you had to learn how to balance all those annoying chemical equations.
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| "Let's see, how best can I piss off students 200 years from now?" |
To illustrate the Mass Defect principle, let's consider the humble Helium-2 atom. It is composed of 2 protons, 2 neutrons, and 2 electrons. If you don't yet have some idea of what a proton, neutron, or an electron is, the rest of this article will be completely lost on you, and here's a lovely article on the subject you can read before continuing. Otherwise, let's assume you're familiar with those and continue, representing the parts of Helium-2 like so:
42He = 2 11p+ + 2 10n + 2 00e-
On the left-hand side of the equation, the 4 equals the total number of neutrons and protons, the 2 equals the number of protons only, the He, of course, means, Helium, and the lack of any positive or negative sign to the right of He means it has a neutral charge, which means there are exactly as many electrons as there are protons. Two protons (+), two electrons (-), two neutrons (0). Neutral charge. So we have a perfectly normal, happy little atom in very stable condition.
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| "...a happy little atom..." |
First we need the observed weight of the Helium-2 atom. It is generally agreed upon that the atomic mass is 4.002602 g/mol.Normally we'd just round it off because, really, who needs 7 significant figures? Well, in this case, WE do. This also means the lazy version of Avogadro's number isn't going to fly. We need more sig figs, so instead of 6.02 x 10^23, we're going to use 6.022142 × 10^23. Also, since it's a real pain to type "x 10^##" we're just going to shorten that to "E". So if you see E23, that means "x 10^23" and if you see E-23 that means "x 10^-23" Because that's how roll. How do you know what to divide by what? Well, set it up so your units cancel out. And because Mass Effect is measured in kilograms, we want to convert the result into kg as early as possible, so once again, to avoid mistakes, set up the problem so your units cancel out.
Therefore, the weight of one Helium-2 atom is 6.646476E-27 kg.
Now, let's take the component parts of the atoms and compare the combined mass.
Mass of a Proton = 1.672622E-27 kg
Mass of a Neutron = 1.674927E-27 kg
Mass of an electron = 9.109382E-31 kg
And, remember, we have 2 of each, so at this point, so we have to add up twice of each of those amounts. If the universe works the way we think it should, then aswer should be 6.646476E-27 kg.
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| The universe is a lie! |
6.696920E-27 kg is obviously more than 6.646476E-27 kg. This presents a real problem. If the law of conservation of mass tells us that mass is neither created nor destroyed, then the law obviously has a defect in it somewhere. A mass defect.
In this case, the Mass Defect of Helium-2 is 5.044388E-29. The two sums are off by 0.753240%
Now to most of us, 0.75% is negligable. If you buy a box of 100 toothpicks, do you really care if you got 99, 100, or 101? No. But if you are carrying an 80-lb backpack on a camping trip in the mountains, though, that extra 3/5ths of a pound is enough to start a serious argument.
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| "What do you mean, 'the toilet paper weighed too much,' where is it?" |
207.976652 grams/mole. It has 82 protons, 126 neutrons, and 82 electrons. Now, do the math using the same steps we used to find the Mass Defect of He-2.
1 atom of Pb-208 = 3.453533e-25 kg.
82p + 126n + 82e = 3.482705e-25 kg.
Mass Defect = 2.917203E-27 kg.
Percent Difference = 0.837626%
So what have we learned? That the Mass Defect is the difference in kilograms between the complete atom (also called a nucleon), and its separate component parts (particles). We have also learned that it doesn't appear to be an immediately obvious relation between elements and the amount of mass lost in forming (He-2 was off by 0.75% vs. Pb-208 which was off by 0.84%).
So why the hell do atoms get more massive after they've been split apart? Ah, but remember, mass is neither created, nor destroyed, it merely changes form. The particles didn't get more massive upon breaking apart, they merely returned to their truer mass state. A better question to ask is "What the hell happened to that all that mass when the element formed in the first place?" Where did it go?
It converted into energy. Atoms are bound together by incredibly strong forces with immense amounts of energy required to break those forces. It's called "binding energy." A portion of the mass of each of the particles is converted into the binding energy that holds the atom together in such an incredibly strong fashion. How much energy? A lot. A hell of a lot, as
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| When he wasn't busy scratching out some sick beats. |
∆E = ∆m * (c2)
Where:
∆E = The change in energy in Joules.
∆m = The change in mass in kilograms (aka, The Mass Defect)
c2 = the speed of light, squared.
So, when we observe that our happy little Helium atom earlier lost 2.917203E-27 kg as a result of its mass defect, we can then predict how much energy this was converted to:
∆E = (2.917203E-27) * (2.997925E8)2
We get ∆E = 2.621852E-10 Joules
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| ...hooray? |
At this point you may be feeling a tad underwhelmed. That's less than 3 billionths of a Joule. That's nothing! Did you forget we're talking about one atom? And that a mole has roughly 6.02 x 10^23 atoms in it? Let's do a little corrective math to put it in perspective.
(6.022142E23 atoms/mol) * (621852E-10 Joules/atom) = 1.578917E14 Joules
(1.578917E14 Joules) / 1000 = 1.578917E11 kJ.
At this point, let's just round it to 1.58 x 10^11 kJ.
Just for perspective, the chemical reaction that results from the burning of one gram of Hydrogen (which is also equal to one mole of Hydrogen), which produces is 120 kJ, which beats the hell out of fossil fuels in terms of energy from combustion.
Let's compare again: Burning Hydrogen
120 kJ/mol
...to the binding energy of one mole of Helium...
15800000000 kJ/mo
This is what makes E = mc2 so special. It revealed to us the enormous untapped power of the atom, and the capacity for mass to convert to energy, and vice versa. It provided both the explanation for the mass defect, as well as a source of power in magnitudes no one had ever thought possible before. That power gave us the nuclear bomb, nuclear power plants, and eventually will give us power from fusion.
When a clean, inexpensive way to harness it is discovered, the energy worries of mankind will cease to exist for many, many generations. When we figure out out a way to cleanly, and inexpensively convert the two back and forth, we will quite literally have the capacity to make and remake the universe around us. It is, in every sense of the word, a formula the describes the power of a G-d. Who wouldn't find it fascinating? Who wouldn't want to tap into that kind of potential?
This is the reason E = mc2 captured the attention of the entire world even to the point where people with no inkling of what it means celebrate its very existence in every way conceivable. If Science were a religion, E = mc2 would be its Cross, its Star of David, its Crescent. And Albert Eintstein would be its most revered prophet.
And that is what makes E = mc2 so special.
fuck this. we should all just keep watching cartoons. And keep being spoonfed propoganda about the russians in Boston.
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