# E=MC^2 - easy explanation for kids

1. Jan 14, 2016

### Tom Minogue Hastings

Been lurking on these threads looking for easy explanations of E=mc2 as it relates to nuclear fission weapons. Shame, SHAME, to yall advanced physicists who dismiss and disrespect and flame amateurs on other threads asking for easy examples for kids. I'm a humanities teacher teaching Astrophysics. I hate math and so do my kids.

1. Do you know of a kids science website that best explains E=MC2?

2. How can you easily explain E=MC2 without using math, so that a 10-year-old girl easily understands? All explanations I've seen merely review each factor without APPLYING real world examples like atomic bombs.

3. How does C2 apply to Hiroshima? "C2 refers to the tremendous amount of potential energy E hiding in every object." So Mass can be converted to Energy, in case of Fatman and Littleboy, by imploding TNT against Uranium to release an atomic chain reaction. How do nuclear bombs relate to lightspeed?

4. What is difference between 1kg of my body, 1kg baseball, 1kg uranium, 1kg plutonium? Does 1kg yield exact same amount of Energy whether it is a baseball or fistful of plutonium?

5. What am I missing? I can only think of Hiroshima for nuclear fission and our sun for nuclear fusion of hydrogen into helium. I cannot picture how nuclear power plants control rate of chain reactions. Nor can I picture how a rock can remain radioactive for thousands of years.

6. How does light APPLY to explosive release of potential energy? How do light photons produced by stars relate to C2 created by a nuclear power plant? Would E=MC2 be impossible if you remove photons from equation, or is C2 not sunlight but merely a proxy for potential energy and has nothing to do with light photons?

7. If C2 means the Potential Velocity of an object is lightspeed squared, how do you explain that to a kid? Velocity of a baseball or just one atom inside baseball? Why is velocity lightspeed? What if velocity is less than lightspeed? How can you apply such a crazy concept using examples, or explain C2 as it relates to Star Trek Warp Speed?

8. What are other easy examples a kid could picture? Can you explain using real applied examples instead of math?

2. Jan 14, 2016

### axmls

I can answer a few of these questions.

I think as an equation, a 10-year-old girl would be able to understand the energy-mass equivalency. That is, by knowing that $c$ is constant, certainly they could see that for larger masses, you get larger energies. That's one point of understanding right there.

In special relativity, all objects have some amount of "rest energy" given by $E = m c^2$. That is, an object that is just sitting there, floating in space still has some energy associated with it.

All that appears in the formula is a mass term, thus equal rest masses are associated with equal energies.

Special relativity says nothing about the existence of photons. All $c$ is is the speed that light travels in a vacuum, and it happens to be squared in this equation. Nothing is traveling here; i.e. there are no atoms traveling the speed of light here. The speed of light appears in this equation simply because it's a very important constant in relativity (and it's harder to explain that without going into a derivation of $E=m c^2$.)

$E = m c^2$ is nothing but the statement that all mass has an associated energy with it whether it's moving or not, and that mass and energy are related to each other by a factor of the square of the speed of light.

Fun fact: the real equation is $E^2 = p^2 c^2 + m^2 c^4$. If the momentum of the object is zero (i.e. the object is not moving--$p = 0$), then it becomes $E^2 = m^2 c^4 \implies E = m c^2$.

3. Jan 14, 2016

### Tom Minogue Hastings

Thanks for explaining C has nothing to do with light or photons. Scary thing about Google omnipotence: Google read your post to me so when I opened youtube, it offered a video called "speed of light is not
about light." Google knows all. It then offered this useful video on Sun energy even I can understand:

As a teacher and fan of Carl Sagan and Neil Degrasse Tyson, I only now just learned that C stands for Constant, nothing to do with light. What does that tell you about Science Education in America!

Search "E=MC2 for kids" on youtube and you get mostly inscrutable whiteboard equations way too complex for kids. Americans are behind in science because scientists are horrible teachers. School teachers like me don't even understand what we are teaching. Americans have no patience for whiteboard equations. We need props, toys, simple pictures and music videos!

Still looking for kid-friendly science sites and videos without the boring whiteboard math. Know any?

4. Jan 14, 2016

### axmls

No, don't get me wrong. C in this case certainly does stand for the speed of light. It's just not the case that anything in particular is traveling at the speed of light. The object is at rest and it has a certain energy, and they're related by the speed of light squared.

Like I said, it's difficult to grasp why the speed of light is relevant without getting into the math.

5. Jan 14, 2016

### Ibix

Could you provide a link to that happening on physics forums?

It might be worth pointing out that they are going to need maths to study astrophysics properly. I feel I ought to point out that most of the rest of your questions don't seem to be directly related to astrophysics so much as nuclear physics.

E is energy, m is mass, c is the speed of light (incidentally, case can be important in maths - you should write E=mc2, or else it means something else). Einstein showed that things that there is some energy in objects just because they have mass, in addition to energy that they have because they are moving. The amount of energy is its mass times the square of the speed of light.

The speed of light is just a conversion factor here. Similar to the way you get ounces from pounds is to multiply by sixteen, to get the energy content of a mass you multiply by the speed of light squared. It's not related to anything moving at the speed of light. It is no coincidence that the speed of light pops up here, but rather the fact that it's the conversion factor and it is the speed of light is a consequence of something else.

In nuclear fission, a heavy atom splits in to a couple of lighter atoms and three(ish) neutrons. But if you add up the masses of the lighter atoms ("daughter nuclides") and the neutrons, they come to a bit less than the mass of the heavy atom. The difference has been converted to energy. The neutrons collide with other heavy atoms and cause them to fission, emitting more neutrons and more energy. The consequence, in a large enough chunk of fissile material, is a very big bang.

The speed of light is just a conversion factor here, as above.

If 1kg of mass is converted to energy, the amount of energy released is the same whatever the source of mass. There's no easy way to convert your body or a baseball to energy, however. Plutonium can (relatively) easily be persuaded to convert a small fraction of its mass to energy, which is why it's used in fission and your body or a baseball is not.

Note that only a small fraction of the fissile material in a bomb or power plant is converted to energy. A total conversion of a 65kg warhead (the minimum size of a Uranium weapon, if memory serves) would have a yield in the gigaton range - twenty-odd times more powerful than the biggest bomb we've ever built.

All stars run off nuclear fusion, not just our sun. We continue to experiment with fusion power (look up tokamaks and laser initiated fusion, for example), and most modern nuclear weapons are fusion weapons. You've mentioned all the applications of fission of which I am aware. However there were naturally occurring fission reactors in the Gabon around 1.7bn years ago: https://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor.

Controlling a nuclear fission reaction is simple in principle. You recall I said each fission event releases three neutrons. Each neutron can start another fission event - so one gets you three, which get you nine, which get you twenty seven. That's a runaway chain reaction that makes a very large bang. However, if you find a material that absorbs neutrons with no ill effect (e.g. boron) you could soak up two of the neutrons. In that case, one gets you one gets you one. That's a stable chain reaction. Reactors have some mechanism to insert neutron absorbing material between the uranium ("control rods", typically), and simply keep adjusting them to keep the reaction going, but not too fast.

The radioactivity of rocks is not the same as fission or fusion, although it is a related process. Some kinds of atoms decay slowly, some fast. The ones that decay slowly can take millenia to decay; that's all the explanation there is for that (at least at the level I think you're willing to accept).

Forget about light in this context. The speed of light squared is merely a conversion factor. Photons have nothing to do with it.

It doesn't mean anything about "potential velocity", whatever that might be.

Not sure there are any applications outside of radioactivity, fission and fusion.

6. Jan 14, 2016

### Janus

Staff Emeritus
There are a couple of differences between an atomic bomb and a nuclear reactor. One is the "grade" of fuel they use. Only one isotope of Uranium,for example, undergoes fission (Isotopes are chemically identical but differ in the number of neutrons in the atom). The isotope of Uranium that is fissionable(U325), only represents a small fraction of any sample of naturally occurring Uranium. In order for Uranium to be usable for a reactor or a bomb, it must be "enriched", or have the fraction of U325 increased. For nuclear reactors, it is increased to about 5%. Weapons grade Uranium is better than 90% U235. (so even if a nuclear power plant lost all control over the reactor, it could not blow up like a bomb, as the fuel is not enriched enough for the reaction to run that fast. Nuclear power plants also have "control rods" which absorb neutrons emitted by fissioning atoms. by absorbing some of the neutrons before they interact with another atom and cause it to fission, you can slow the reaction or stop it completely. One reason for control rods is that as the reactor runs, it uses up its U235 and the fuel becomes less and less enriched and the reaction would slow down. By partially removing the control rods which damp the reaction, you can maintain the same reaction rate as this happens by letting some neutrons that would be absorbed by the rods to participate in the reaction.

Radioactive materials can remain so for so long just because the ratio of mass to energy is so small. The amount of energy they lose to radiation results in a very very small loss of mass, and as long as they don't radiate too strongly, it can take a long long time without any appreciable loss in mass. The more radioactive a substance is the faster it will do this and the shorter it will last. Substances that can radiate for thousands or millions or years can do so because they don't radiate as strongly.

There is something special about the speed c. It is a fundamental constant which determines how the universe "works". Because it is "built in" to the universe, it tends to pop up a lot in equations that try how to describe how the universe works (much like pi pops up when working with anything dealing with circles). One of the things it determines is how fast light travels in a vacuum. Now other things can travel at c, but light is the only one that we can easily work with and measure, so we tend to call c "the speed of light". But you don't need light to have c. c is in mc^2, but mc^2 has nothing to do with light. In mc^2, c determines the relationship between mass and energy, and with light, it determines its speed. It is the same constant being used for two different things.

That is not to say that some of the energy released in a nuclear reaction by cannot be in the form of photons, as gamma rays, which is why nuclear plants are shielded, But this doesn't have anything to do with c. Even the light we get from the Sun isn't directly produced from the fusion at its core. Much of the energy of that fusion is carried away by the kinetic energy of the resulting atoms, which in turn bump into other atoms, and all this bumping together of atoms is what in turn, produces the photons at the surface. (Just like rubbing to pieces of metal together. After a while, they get hot and if you can get them hot enough, they will glow).[/QUOTE]

7. Jan 14, 2016

### Drakkith

Staff Emeritus
Umm, okay.

I'm not even sure why you're trying to teach this concept to a 10-year old, but I'll give it a whirl.

It turns out that mass and energy are intimately related. When you add or remove a quantity of energy from an object, you also remove a quantity of mass from that same object. In other words, if you remove energy from an object, the object gets lighter, or less massive. Conversely, adding energy to an object increases that object's mass. The ratio between the energy and the mass added or removed is determined by the equation E=MC2.

As an example: Stick a metal bar into a fire until it is cherry red. Since energy was added to the bar to heat it up, that bar is now heavier (more massive) than it was previously. Now stick that bar into a bucket of water and cool it down. It's mass has returned to what it was before sticking it in the fire.

In a nuclear fission weapon, atoms of uranium or plutonium are split into smaller pieces in a chain reaction, each of which releases energy. Each individual split releases only a small amount of energy, but since there are many, MANY atoms undergoing fission, a great deal of energy is released in total. The energy released by the fission of a single atom is MUCH more than the amount of energy released by any single chemical reaction (such as burning gasoline in an engine). In fact, the amount of energy released is so great that if we were able to gather all of the material of the bomb after the explosion we would be able to measure the actual mass loss (about 1 gram for the Little Boy weapon dropped on Hiroshima).

As you can see, the concept does not apply solely to things like nuclear reactions and radioactivity, but to ALL objects at ALL times. Mass-energy equivalence is NOT about mass turning into energy or energy turning into mass, but about the fact that energy has mass (or, as most people like to say, mass has energy). At no point does any energy or mass disappear and turn into the other. Even a massless photon, radiated away from an object and taking energy with it, is hiding the fact that the system containing the photon and the object has not lost any mass. For example, let's say that we have a sealed container of low-pressure gas. Inside this container two atoms of gas collide and their collision releases a single photon. That photon then traverses the length of the container until it is absorbed by the wall. If we measure the mass of the container before the collision, after the collision while the photon is in flight, and after the photon is absorbed by the container wall, we will find that the mass of the container is the same in all three cases. (The container is just in the example to make it easier to understand. The system could simply be the two gas atoms and the photon, with no container present.)

I also feel it's important for you to understand that the equation you've been using is actually a special case of a more general equation. The full form of Einstein's equation is: E2=M2C4+P2C2, where P stands for the object's momentum. In my example in the above paragraph, the mass of the two individual gas atoms doesn't change, but their momentum does, which is where the energy to create the photon comes from. Also note that the energy and momentum of a photon are related by this same equation. Setting M equal to zero gives us: E2=P2C2. Simplifying results in E=PC, which is the exact relation between the energy and momentum of a photon (or any massless object).

8. Jan 14, 2016

### sandy stone

A quick Google search yielded the assertion that just over 1/2 gram of mass was converted to energy in the Hiroshima bomb. In other words, if you could weigh the fission products of the bomb and compare that to the original weight of the fissionable material, you would be 1/2 gram short. So, not much mass for a lot of energy. However, to be accurate, you would have to say that 1/2 gram is really the mass equivalent of the binding energy of the original nuclei, that goes away when the nuclei are rearranged in the chain reaction/explosion. Don't know if the 10-year-olds need that level of detail.

9. Jan 14, 2016

### Staff: Mentor

Easy enough to check this.... The Hiroshima bomb was about 10 kilotons, which is $5\times{10}^{13}$ Joules in mks units. $c^2$ is about $10^{17}$ using the same mks units, plugging those numbers into $E=mc^2$ we get $m=5\times{10}^{-4}$ kilograms which is 1/2 gram. That's not much out of the 100-odd kilograms of uranium that went into that bomb.

Uranium fission converts a few percent of the mass of the fissioned uranium atoms to energy, and the gunbarrel design of that bomb fissions only a few percent of the uranium atoms in the bomb. A few percent of a few percent is a small number, but $c^2$ is big enough that we still talking about a lot of energy.

10. Jan 14, 2016

### Staff: Mentor

Actually it's less than one-tenth of one percent. The difference in binding energy between uranium and the fission products is about 0.9 MeV per nucleon, and the nucleon mass is about 940 MeV, more than 1000 times that.

11. Jan 14, 2016

### Staff: Mentor

Ah - right.

12. Jan 15, 2016

### mpresic

When I was about 10, I read "Our Friend the Atom" It is a very good book from Walt Disney (I believe). It discusses atomic energy , which is probably what you want anyway.
In short: I know of no kid's website that discusses E=MC^2.. (I do not know why anyone would want to explain E=MC^2, to a 10 year old, unless the kid asked). Then I would discuss it in a manner that gauged the child's interest and understanding. A 10-year old math or physics prodigy might understand it at an undergraduate level, but most intellectually curious kids with less focused gifts, I would not go in depth.

Lay off the bomb stuff, unless you want to give the kids bad dreams at night.

Really, I have not read the book in years but "Our Friend the Atom" is very good. I think this is where I got my start and I have advanced degrees in physics. The Children section in most libraries may also have some good sources, including a good kid's encyclopedia.

I taught college Freshman physics for nine-years, I never thought less of any > 18 year old students if they did not know what E=MC squared means.

13. Jan 16, 2016

### Staff: Mentor

Before you worry about "how" it is important to decide "why". What do you hope to accomplish and how will your teaching improve the student's scientific knowledge. In my opinion, you shouldn't teach something that the student is not already prepared to understand and you shouldn't teach science as a collection of random facts.

14. Jan 16, 2016

### Staff: Mentor

That would not be the proper response. The proper response if you think someone is being dismissive, disrespectful, or "flaming" is to use the "Report" function. We don't want to clutter up this thread with arguments over who should or shouldn't have said what in some other thread.

15. Jan 16, 2016

### Staff: Mentor

The rate of fission reactions depends on the flux of neutrons through the fuel. Fission power plants control the reaction rate using "control rods" made of a material that absorbs neutrons readily (cadmium is a common one), that can be lowered into or raised out of the reactor core. When the rods are lowered in, more neutrons are absorbed by the rods and the reaction rate goes down; when the rods are raised, fewer neutrons are absorbed by the rods and the reaction rate goes up.

We don't have working fusion power plants yet, but in experiments that have been done with fusion in plasmas, the reaction rate is controlled by the rate at which fuel, in the form of plasma, is inserted into the reactor.

16. Jan 16, 2016

### Staff: Mentor

If you're trying to teach actual physics, Star Trek is not a good source. There is no such thing as "warp speed" in actual physics.

17. Jan 17, 2016

### m4r35n357

Sounds like you are in the wrong job. How can you hope to teach something you cannot understand yourself? Ah OK, you can ask here for someone to do your job for you . . .

Do your students (I don't think you mean they are 10, and what has gender got to do with it?) know about Galilean relativity and optics (without maths)? Because SR will make absolutely no sense without knowing what went before.

Big numbers and wizzy videos are no substitute for teaching, and maths is not optional.

I am a student, not a teacher BTW.

18. Jan 17, 2016

### Ibix

Point taken.

19. Jan 17, 2016

### Staff: Mentor

I can pretty much guarantee you that if you have a class of more than just a few kids, at least some of them do not hate math. If you want to understand Tolstoy, you will need to learn a little Russian. If you want to understand Nietzsche, you will need to learn a little German. If you want to understand nature, you will need to learn a little math.

My recommendation if you are a humanities teacher you should teach to your strengths. Don't focus on a collection of facts, focus on the scientific process. Teach about the history of how the scientific method was used over centuries to refine and overthrow the different models. What models did people use, what assumptions did they make, how did they test their models, what were the data, why were new models proposed? The goal should be to help them understand the scientific method and be critical thinkers. Without math you won't be able to teach them how to do astrophysics, but you can use astrophysics to teach them how to think scientifically. In my opinion.

20. Jan 17, 2016

### Drakkith

Staff Emeritus
Given that the OP isn't teaching an actual science/physics class (as far as I know at least), I think it's perfectly fine to leave out essentially all the math. I attended a small lecture a year or two ago by an astronomy professor from the University of Arizona. It was a lecture for the general public, geared towards anyone who had seen the signs posted around campus and decided that they wanted to go. Part of this lecture was about different ways to detect exoplanets. The professor explained all of these methods without using any math at all, and everyone seemed to understand it just fine. They certainly didn't know the underlying mathematical relationship between the radial velocity of a star and the doppler shift of the emitted light, but they understood that when a star is moving away from us its light is redshifted a bit and when it is moving towards us its light is blueshifted a bit, much like how a horn or siren changes pitch at the source moves by you. Or that as a planet moves around its star, if the orientation is just right, it blocks out a small portion of the star's light, which we can detect.

That being said, there are some concepts that work well when explained this way. Something involving simple motion and colors is inherently easy to visualize since most people experience these things every day and have little problem understanding them. Other concepts... not so much. Mass-energy equivalence is one of those concepts in my opinion. The average person has utterly no idea what energy is (or even what mass is usually), how it works, and, perhaps most importantly, what it isn't. It's too abstract and without getting into the math, which they aren't going to do, they will never understand what it is. You can, of course, simply tell them the facts, but this isn't really something that's going to keep people interested, especially kids.