# Nuclear Reactions, Can anyone check my solution?

1. Mar 30, 2013

### maceng7

1. The problem statement, all variables and given/known data
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-)

2. Relevant equations
P = E / time
E = mc2

3. 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!

Last edited: Mar 30, 2013
2. Mar 31, 2013

### Staff: Mentor

I would directly divide the released energy per reaction by the mass of an uranium atom to get J/kg, but your method is fine, too.