Mass Energy Equivalence

This equivalence of mass and energy is a consequence of Einstein’s theory of special relativity. Which simply means that mass can be converted into energy and visa-versa.

According to this equivalence, mass and energy are inter convertible. so whenever you have mass, it means you’ve got lots of energy just sitting inside. How much energy? It’s given by Einstein’s famous relation

E=mc2

Where,

  • m is the mass in kilograms
  • c is the velocity of light in a vacuum c ≅3×108 m/s
  • Which is 300 million in SI units. On squaring it, this number is huge. No wonder in saying that mass is concentrated energy.

    For example, consider a little marble of 20-gram marble. Converting this 20g completely into energy contains we get the same amount of energy as is released in the explosion of a 500,000-ton hydrogen bomb. So why aren’t we afraid of marbles?

    Matter-Antimatter Annihilation

    This energy is really difficult to release. So if you’ve got a marble, there’s almost no way that you could release all that energy. The only way to convert all of that mass into energy is through matter-antimatter annihilation.

    What Is Annihilation?

    Annihilation is a process that is mostly observed in the collision of subatomic particles. That is when a subatomic particle collides with its antiparticle. The matter and antimatter collide and all the energy is released from both in the form of electromagnetic waves.

    This is a very uncommon process as there is not much antimatter around. Matter and antimatter both have mass but there’s not a lot of antimatter around.

    Example:

    If we consider electron, we do have antielectrons. If we look at this process. A positron, which is an antielectron and an electron, come together and annihilate and just produce energy in the form of a gamma photon. This gamma means photons, which basically just means energy for our purposes. So how much energy is released?

    Well, the mass of an electron or a positron is 9.11 × 10-31kg.

    So the energy that’s released will be E= mc2 from electron + mc2 from positron = 2mc2

    And that turns out to be 1.64 × 10-13joules. It’s not very much, but that was an electron and a positron. But instead of one electron-positron pair, a mol of them are annihilated, we get 1010 joules. that’s a lot of energy.

    It turns out that almost every single release of energy actually can be understood in terms of this energy mass equivalence.

    Chemical Energy

    Water is a molecule formed by taking two hydrogen atoms and an oxygen atom thus making two bonds. The bond between oxygen and hydrogen, the bond between oxygen and the other hydrogen. These bonds cost energy, how much energy? 918 kilojoules per mol. Which implies that there are about 1.5× 10-18 joules of bond energy per molecule.

    Here we can observe that the mass of a water molecule is slightly less than the mass of hydrogen times 2, plus the mass of oxygen. This difference in mass is called mass defect and it is associated with the mass of the binding energy. The change in mass is the energy, is given by

    E=Δmc2

    Where,

  • Δm is the change in mass
  • c is the velocity of light
  • This mass defect is or the order 1010, very minor number. Thus, not very considerate situation

    Nuclear Energy

    It’s a bit of a larger situation. For example, consider the alpha decay of uranium 238.

    So uranium 238 goes to thorium 234 and helium 4. Now if you add up the mass of this helium nucleus and this thorium nucleus, you get a smaller mass than the mass of this uranium nucleus. Smaller by how much? Well again, it’s not by a lot.

    Relative mass, \(m_{r}=\frac{\Delta m}{m}\)

    This relative mass turns out to be about 2 × 10-5 it’s still small but it’s 5 orders of magnitude bigger than the chemical energy released. Hence we can clearly understand nuclear reactions release so much more energy than chemical reactions because the fraction of the mass that’s released in terms of energy is 100,000 times greater.

    Neutron Star

    What about other processes that we could use to release all of this untouched energy? Well, neutron stars and black holes are probably our best bet for releasing the largest amount of this mass-energy other than matter-antimatter annihilation. It turns out that with a neutron star you can get relative releases of the energy of order 7 percent(7× 10-2). So that’s 0.07 versus 0.00002, this is a huge amount of energy and with some types of rotating black holes, you can get it up to almost half, 42 percent.

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