Nuclear Energy: Energy and Mass

Alright people, Physics Unit 5 is a fair ways off but not so far as we can ignore it. This time I come to talk to you about, well, I've already said in the title.

This is the part that really centres around the part of physics everyone knows, and that many I wager look forward to when they start doing physics, E = mc². It feels like the opening gate to the really intense stuff that physics can be about, and the stuff that when you go deeper into it, you will be hard pressed not to bring up at bars, boring everyone else even though you know just how interesting it all is and if only you can explain it the right way they'll understand too.

"No, look, it's not that difficult. Once an object's mass is compressed within a sphere of radius r_s, then it's escape velocity is equal to the speed of light, and it becomes a black hole. Now just let me explain the Chandrasekhar limit..."

If for some reason you haven't grown up in a society where every generic science class in your childhood cartoons had a blackboard plastered with Pythag and E = mc² then what you need to know is that over a century ago a guy called Albert Einstein published his theory of special relativity in which he showed, among many other significantly more complicated things, that mass and energy are connected, specifically that Energy E is equal to the mass m of an object, multiplied by the speed of light (in a vacuum) c squared. So, when an object loses gains energy, say, kinetic, by speeding up, it gains more mass. Now, normally this is fairly indistinguishable from normal. For example, imagine an 650 kg object like, say, this flying car.

Let's say it accelerates from rest until it's casually moving along at a breezy 40 m/s. Good old Newtonian physics tells us that gives it a kinetic energy of 520kJ. Now we just need to divide that by c² to find that at such a velocity the car/plane has an measly extra 5.78x10^-12kg.  Now it clearly this is nothing compared to the 650 kg we started with, so doesn't really bear thinking about. Indeed, in order to gain a single kilogram the car would have to be moving at 1.66x10⁸ m/s which you may notice is somewhat faster than we are currently able to get cars moving these days.

This equation follows us right down to the nuclear scale, where it can be used to find the energy released from particles during radioactive decay. So long as we know the difference in mass before and after decay, we can plug this into the equation and find the energy given out.

Moving on, some definitions for you to remember!

Binding energy: This is the work that must be done to separate a nucleus into it's constituent protons and neutrons.

Mass defect: The difference between the mass of the nucleus and that of the separated nucleons. Interestingly enough there is a difference, as well shall go into.

See? It's funny because defect sounds like effect. Only the most original comedy here, folks.

The binding energy of a nucleus can be thought of as a measure of a nucleus' stability, that is, how readily it will break down after a few glasses of gin. Apply enough Long Island Ice Teas, or work, and you can overcome the nuclear strong force, remove a nucleon from a nucleus, thus increasing the potential energy of that nucleon. Do this lots, and the total energy released is equal to the nucleus' binding energy.

The mass defect is more or less as simple as the definition. The accumulated mass of the separate nucleons is greater than that of the nucleus they were once part of. The difference in this mass is the mass defect. What this means is that when a nucleon is worked off a nucleus it somehow gains mass. If you are keeping up, it may not surprise you to learn that this extra mass comes from the potential energy gained by the work done on the nucleon to separate it from it's nucleus. Specifically, the binding energy of a nucleus is equal to the mass defect multiplied by the speed of light squared, or:

E=Δmc²

Looks familiar, huh?

Now, a century on, we still don't really know exactly why mass and energy have this relationship, because this whole mass thing is a bit of a bitch. I'm sure we'll come to that another time. For now just understand that energy and mass are essentially one and the same. If you don't believe me, consider this explanation I nicked from a recent Ask A Physicist.

 "Protons are made of quarks, but if you add up the masses of the individual quarks, they only add up to a per cent or so of the total proton mass. The rest is interaction energy. From the outside, you cannot tell the difference between "real mass" and mass with is really energy. There is no difference." 

So, physics continues to push us over that sketchy line between understanding and Shermer's last law. Bring on the magic.

Join me after the break, when I delve into the world of nuclear power.