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 EquationIn 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 = mc²If the mass is in atomic mass units, then energy must be in joules and the velocity of light meters per second.
Preparing for the MathWe 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 kilogramsThe velocity or speed of light in meters per second = 2.998 x 108.
Calculations – Total Energy One Hydrogen AtomWe 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 AllIf 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 joulesThat 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
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