The relationship between energy (E) and frequency ( ) for ...
• The relationship between energy (E) and frequency (() for electromagnetic radiation (Planck's quantum of energy)
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• The relationship between wavelength (() and frequency (() for electromagnetic radiation
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From these relationships, we can determine the relationship between energy and wavelength:
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or, rearranging:
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• The relationship between wavelength (() and momentum (m*v) for DeBroglie's "particle wave"
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From the above relationships, we can calculate the relationship between energy (E) and momentum (m*v)
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Simplify, and solve for E:
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The highest velocity (v) attainable by matter is the speed of light (c), therefore, the maximum energy would seem to be:
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or
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Why do nuclear bombs make such a loud "pop"?
• The Fuel value of hydrogen is 142 x 103 J g-1
• If all matter were converted into energy
E = 1x10-3kg * (3x108m/s)2
E = 9x1013 kg m2 s-2
E = 9x1013 J
In other words, we can get out about 9 orders of magnitude greater energy if the hydrogen is converted directly into energy, rather than combusting it.
Nuclear fission and fusion reactions convert a fraction of their matter into energy. The bomb that was dropped on Hiroshima contained about 15 kg of the 235Uranium isotope, a fissionable material. The actual amount of mass that was converted into energy is estimated at about 1 kg (releasing around 1 x 1017 J of energy in a split second). The estimated temperature at the moment of detonation is estimated to have been around 5 million degrees. In addition to the sun-like heat, much of the damage was due to the pressure wave that was produced.
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