(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Delta E = delta m * c^2

3. 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!

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# Homework Help: Nuclear Physics

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