*protium*. It contains just one proton and one electron. Let’s determine the total energy of one protium atom. Its mass is 1.007822 atomic mass units. So what is the total energy one hydrogen atom produces if obliterated?

By obliterated, we mean 100% conversion from matter to energy, not the mere energy of separation of particles, as in fission.

## Einstein’s Mass-to-Energy Equation

In our calculating, it is important we stick to proper units. If we were cooking and the recipe called for a cup of flour, would we substitute a tablespoon? Our equation is Einstein’s mass to energy expression,E = mc²

If the mass is in atomic mass units, then energy must be in joules and the velocity of light meters per second.## Preparing for the Math

We gave, by definition,1 a.m.u. = 1.66 x 10⁻^{27} kilograms.

1.0078 x 1.66 x 10⁻^{27} = 1.673 x 10⁻^{27} kilograms

^{8}.

## Calculations – Total Energy One Hydrogen Atom

We are ready for our calculation. We write,E = 1.673 x 10⁻^{27} x (2.998 x 10^{8})^{2} = 1.504 x 10⁻^{10} joules

The energy for the complete conversion of one hydrogen atom is

E = 1.504 x 10⁻^{10} joules

## Realizing the Enormity of It All

If the obliteration of a single atom of hydrogen doesn’t sound like it results in much energy, consider how much one single mole of hydrogen atoms contains. Each mole contains 6.023 x 10^{23}molecules (Avogadro’s number). Then,

6.023 x 10^{23} x 1.504 x 10⁻^{10} = 9.059 x 10^{13} joules

**Note:**You may also enjoy reading Calculate Atom Weight Two Ways**References:**

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Thank you. Thank you very much. I always wondered how much energy there is (under hypothetical 100% conversion) in a cubic inch of earth soil (dirt), but I guess that would be too undefined. Thank you for the 100% conversion of a gram of protium. Everyone says it can’t be done, and I suppose they are right, but you did it anyway. Thank you.

Thanks for the article. The amount of energy in a small bit of matter is amazing to me. However, there is actually more in one mole than you figured. The calculation should be 9.059 x 10^13.

Thanks for spotting the error… I added when I should have multiplied!