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maceng7
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Homework Statement
A nuclear power station reactor using 235 U (Uranium) as fuel has an output of 107 W. How much uranium is consumed per hour if the overall efficiency is 10%. The 235 U decays by the following reaction:
n + 235 U → 144 Nd + 89 Y + (3)(n) + (7)(e-)
Homework Equations
P = E / time
E = mc2
The Attempt at a Solution
I started out by finding the change in mass in the reactants and products:
mass of reactants = 236.05258 amu
mass of products = 235.845131 amu
Δ mass = 0.207449 amu
I then used E = mc2 to find the energy released from one uranium nuclei:
E = (0.207449amu)(1.66054 x 10^-27 kg)(2.9979 x 10^8 m/s)^2
E = 3.096 x 10^-11 J/atom
I then found the efficiency of the reactor:
efficiency = output/input x 100%
0.10 = output / input
input = 10^8 Joules
P = E/t
E = (10^8 W)(3600s)
E = 3.60 x 10^11 J
I now know how much energy is inputed into the generator each hour and I know how much energy is released per atom of Uranium. I can find the total number of atoms that undergo this reaction in one hour:
3.60 x 10^11 J / 3.096 x 10^-11 J/atom = 1.16x10^22 atoms
I used avogadro's number to find the number of moles
(1.16x10^22 atoms) * (1 mol / 6.022x10^23 atoms) = 0.0193 moles
I use n = m / M to find the mass in grams:
0.0193 mol * 235.043915 amu = 4.54g
It would be great if anyone could check my steps in my solution. The answer is 4.54 g but I just want to make sure my process is correct and maybe if there is another way to get to the same answer. Thanks, I appreciate it!
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