Question 25.10: Fission Energy Big Time! Estimate the energy released if all...
Fission Energy Big Time!
Estimate the energy released if all the nuclei in 1 kg of uranium undergo fission.
ORGANIZE AND PLAN About 200 MeV are released with each uranium nucleus that fissions. We need the number of nuclei in 1 kg of uranium, which we ll then multiply by 200 MeV.
\text { Known: Molar mass of }{ }^{235} U \text { is } 235 g / mol \text {; energy released per } fission = 200 MeV.
The number of uranium nuclei is
\text { number of nuclei }=1000 g \times \frac{1 mol }{235 g } \times \frac{6.022 \times 10^{23} \text { nuclei }}{1 mol }=2.56 \times 10^{24} \text { nuclei }.
Therefore, the energy released is
E=200 MeV \left(2.56 \times 10^{24}\right)=5.12 \times 10^{26} MeV.
That’s a big number, so we convert to joules:
E=5.12 \times 10^{26} MeV \times \frac{1.60 \times 10^{-13} J }{1 MeV }=8 \times 10^{13} J.
REFLECT That’s still a big number and it’s about what we d get from chemical reactions involving 20,000 tonnes (20 million kg) of chemical reactants. Release it all at once, and you’ve got a bomb. In fact, 1 kg is just about the amount of uranium that fissioned in the bomb that destroyed Hiroshima.