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Mitchtwitchita
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Homework Statement
Nuclear energy changes are significantly greater than chemical changes. The detonation of 1.00 g of the explosive trinitrotoluene (TNT) releases 2.760 kJ. How many grams of TNT would be needed to match the energy released by one gram of U-235?
Homework Equations
Delta E = delta m * c^2
The Attempt at a Solution
Mass U = 234.993 u
Mass e- = 92(0.000549 u)
Mass nucleus = 234.993 u - 92(0.000549 u)
=234.942492 u
92 protons: 92(1.007276 u) = 92.669392 u
143 neutrons: 143(1.008665 u) = 144.239095 u
Total = 236.908487 u
Delta m = 236.908487 - 234.942492
=1.965995 u
Energy released:
Delta m = (1.965995 u)(1.6605 x 10^-27 kg/u)
=3.2645347 x 10^-27 kg
Delta E = delta m * c^2
Therefore, (3.2645347 x 10^-27 kg)(2.998 x 10^8 m/s)^2
=2.934 x 10^-10 J
Therefore, the difference in mass between 1 U-235 nucleus and its constituent nucleons is converted into 2.934 x 10^-10 J of energy.
Since 1.00 g of U-235 = 2.56 x 10^21 nuclei,
(2.934 x 10^-10 J)(2.56 x 10^21 nuclei)
=7.51 x 10^11 J
=7.51 x 10^8 kJ
Therefore, 7.51 x 10^8 kJ/2.760 kJ
=2.72 x 10^8
Therefore, 2.72 x 10^8 g of TNT would be needed to match the energy released by one gram of U-235.
I HAVE NO IDEA IF THIS IS RIGHT OR IF I'M ON THE RIGHT TRACK, COULD SOMEBODY PLEASE LET ME KNOW!