Hydrogen is the lightest of the elements. However, there are three isotopes of hydrogen. The lightest of these is 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.
But the hydrogen atom has a mass of 1.0078 a.m.u. Therefore one protium atom has a mass in kilograms of,
1.0078 x 1.66 x 10⁻27 = 1.673 x 10⁻27 kilograms
The velocity or speed of light in meters per second = 2.998 x 108.
Calculations – Total Energy One Hydrogen Atom
We are ready for our calculation. We write,
E = 1.673 x 10⁻27 x (2.998 x 108)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 1023 molecules (Avogadro’s number). Then,
6.023 x 1023 x 1.504 x 10⁻10 = 9.059 x 1013 joules
That is, 90,590,000,000,000 joules or approximately 91 trillion joules! That is about 25 billion kilowatt-hours. And the numbers would be two to three times as great for deuterium or tritium, respectively. Still saying “So what?” One mole of protium hydrogen atoms (not the bi-molecular gas) is 1 gram.
Note: You may also enjoy reading Calculate Atom Weight Two Ways
References:
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