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.