Einstein's equation E= mc^2?

Question

In Einstein's equation E= mc^2,

What does m stand for? If it's the mass, then what mass? Could it possibly the mass defect which is the difference between the mass of an atom and the sum of its protons, neutrons, and electrons?

Also, if c is the speed of light, which equals 3.0x10^8 then does c^2 equal (3.0x10^8)^2? or no?

And the E is the energy in joules, right?

Thank you!

When you guys say that m is the mass of the matter, I am asking if it is about mass defect possibly. Becuase I am taking chemistry and am learning about this in chemistry and is included by the section where mass defect is explained.

If not, then what matter is the m when I am learning about atoms in chemistry?

Answer 1

m is mass, any mass, if could be your mass if you turned into complete energy.

c is 3.0x10^8 if you use meters per second and c^2 is (3.0x10^8)^2.

E is energy and could be joules depending on the other units you use. For meters and seconds and kilograms it would be joules.

Answer 2

What does m stand for? If it's the mass, then what mass? Could it possibly the mass defect which is the difference between the mass of an atom and the sum of its protons, neutrons, and electrons?

m is inertial mass. In relativity, there is inertial rest mass and inertial mass. The rest mass is frequently shown as m0. It's the mass we see when it is at rest relative to an outside observer. You have rest mass m0 for example. Your car has rest mass m0 and so on.

m, the inertial mass, is the apparent mass we see when the object is traveling faster than v = 0 relative to an outside observer. As v --> c, the speed of light, inertial mass m --> infinity. We call it inertial mass because inertia is a major characteristic of any mass; while energy E has no inertia.

The size of the mass m is the same as the size of mass m0. What makes m >= m0 is its inertia, its resistance to change in velocity. Since F = ma and a = F/m, we see that as m --> infinity, it takes more and more force F to maintain an acceleration a. Eventually m gets so large that there is not enough force in the entire universe to accelerate that m any more. Which is why mass cannot go faster than light speed.

Since m >= m0, we have delE = E - E0 = mc^2 - m0c^2 = (m - m0)c^2 and delE is the relativistic kinetic energy. That is, it represents the amount of energy put into the rest mass to get it up to whatever velocity v yields the inertial mass m.

delE = (M0 - m0)c^2 as well; where M is, for example, the mass of an atom (protons, neutrons, electrons) and m is the sum of masses of its children after it splits. When an atom splits M0 > m0 always. That is, the sum of the resulting children masses is always less than the parent mass. That mass difference results in delE being released. And when billions and billions of atoms go off nearly simultaneously, we have an atomic explosion. Kaboom.

Also, if c is the speed of light, which equals 3.0x10^8 then does c^2 equal (3.0x10^8)^2? or no?

Yep if c = 3 X 10^6, the c^2 = 9 X 10^12; that's basic math.

And the E is the energy in joules, right?

Depends on the units of m and c doesn't it? The energy would be kg-(m/sec)^2 if m is in kg and c is in m/sec. The arcane definition for kg-(m/sec)^2 is joules. What would it be for slug-(ft/sec)^2 which are the English units?

Answer 3

1+1=2

Answer 4

It is the equation to calculate the energy equivalent of matter.
E = m x c² , where E is the enrgy produced, "m" is the mass of the matter (nuclear fuel), and "c" is the velocity of light.
If one kilogram of matter is converted into energy, that will be equal to [mxc²] joules. It is tremendous amount of energy.
E = 1 Kg x {3 x 10^8}² = 9 x 10^16 joules. This much of energy is more than sufficient for a city like New York (where almost everything is done on electricity) for more than five years. It is only an approximate idea.

Answer 5

It sometimes helps to look at Einstein's equation the other way round: rather than thinking of converting mass into energy, see it rather as the observed change in mass when there is an energy change. The equation then becomes Change in mass = (Change in energy)/c^2.

So when (say) 1 g of hydrogen combines with 8 g of oxygen [yes I know it isn't precisely 1:8, but let's assume it is for the purpose of the illustration] it converts it into 9 g of (water + energy). The energy is fairly small in this case, so when one works out (energy/9x10^16) it is a very very small mass indeed. So although it is technically incorrect to say that 1 g of H and 8 g of O make 9 g of water plus some heat, the difference is so small that there is no possible way to detect it. Although we cannot verify it by measurement, the amount of water produced is actually very slightly less than 9 g.

When we come to nuclear reactions, the energy changes are so large that it IS possible to detect the mass of the energy produced.

So your question can be answered not in terms of rest mass etc:, but in terms of the mass of the energy changes.

If ever you get to do particle physics, you will find that energy and mass are used quite interchangeably. For instance the electron has a mass of 0.51 MeV - where the MeV (mega electron-volt) is a unit of ENERGY.

Answer 6

1. Mass of an object. The equation states that if a mass m were converted to energy (at the root of it, mass and energy are really teh same thing), it'd be mc^2 worth of energy.

2. Yes that is how you do c^2.

3. Energy is in joules if you used SI units for m and c, that is, kg and m/s. You did for c, since 3E8 is the speed of light in meters / second, so just make sure you use kg for mass and you're good.

Answer 7

The mass in the equation can be the mass defect or the mass difference between bound protons and unbound protons. Then you apply E=mc^2 to get the energy released in a reation such as fission or fusion.

Answer 8

You pretty much got it. m is mass, the mass of the matter (kg). C is the speed of light. c^2 = 9*10^16.

It's the matter energy equivilence equation. And yes, 5 kg of mass does contain 4.5*10^17 joules of energy. that's 125 billion killowatt hours. or enough energy to drive a car at 80 mph for about 35000 years.

One little nuclear reaction can produce a big boom.

Answer 9

m is the mass as measured in the rest frame. Mass is not a frame invariant quantity.

The mass deficit arises because protons and neutrons are bound in the nucleus. The binding energy has a mass equivalance, which is given by E = mc^2. In other words, given a binding energy of E the increase in mass of the bound nucleus as measured from outside is m = E/c^2.

Answer 10

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