How Is Energy Calculated in Uranium 235 Fission?

[dav1d]

Homework Statement

Another mode in which uranium 235 can undergo fission is U + n -> Te + Zr +n. Calculate the energy change when 1g of uranium 235 undergoes fission in this way. The masses are U=235.04u. n=1.0087u. Te=134.92u. Zr=99.92u.

Homework Equations

The Attempt at a Solution

The mass of the left side is 236.0487u
The mass of the right side is 235.8487u

delta M=-0.2u

E=mc^2
=-0.2u x 9x106 J/kg x(1.66x10^-27kg/u)
=-.2.988x10^-21J/u ? (Please help me with units here!)

E1g=-2.988x10^-21J/u x 1g
(Units have failed me here, please tell me where I went wrong...)

 

[Delphi51]

E=mc^2
=-0.2u(1.66x10^-27kg/u)*(3x10^8m/s)²
= 2.99 x 10^-10 Joules per Uranium nucleus.
How many Uranium nucleii fission?

 

[dav1d]

For the speed of light, I used 9 x 10^16 J/kg. Can you show the unit analysis for just squaring 3x10^8 m/s ?

To answer your question

1 gram of U-235, the mass of 1 U-235 nucleus is 235.04u given, so 1gram/235.04u=2.5621772x10^21. Then2.99 x 10^-10 x 2.5621772x10^21 = 7.66091009 × 1011 Joules?

 

[Delphi51]

Pick any energy formula, say E = mgh. So Joule = kg*m/s²*m.
and Joule/kg = m/s²*m = m²/s²

In my calc, I have
E=mc^2
=-0.2u(1.66x10^-27kg/u)*(3x10^8m/s)²
The u's cancel out and the answer is in kg*m²/s²
which is Joules as seen in E = ½mv² or E = mc².
Your answer looks good now. You just wrote the exponent 16 as 6 in the first calc and there is some confusion about where the decimal place is.

 

[asteriatic]

Your calculations are correct, but the units need to be converted to joules (J) per gram (g). The final answer for the energy released would be -2.988x10^-18 J/g. This represents the amount of energy released per gram of uranium 235 undergoing fission in this way. It is important to note that this is a very small amount of energy, but when multiplied by the large amount of uranium 235 used in nuclear reactions, it can be a significant source of energy. Additionally, this calculation does not take into account any additional energy released from the decay of the daughter nuclei (Te and Zr) or the kinetic energy of the neutrons released. Overall, this is a simplified calculation and the actual energy released may vary depending on the specific conditions of the fission reaction.