Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).

Question

Accepted Answer

Welcome back, everyone determine the energy produced per mole of uranium 235 in the following fission reaction, we're given our reaction in the atomic masses of each species involved. Let's recall that our first step in a problem of that kind is to find the mass defect. And we're going to call that mass defect as delta M delta M is essentially found by taking the sum of masses of reactants and subtracting the sum of masses of products. So let's go ahead and apply this formula. First of all, we want to sum the masses of our two reactants and those are a neutron and uranium 235. So we are given the mass of a neutron in atomic mass units. That would be 1.00866 atomic mass units. And we want to add the mass of uranium 235 which is 235.04 392. Now, we want to subtract the sum of masses of the products and we can begin with xenon. Now, Xan has an atomic mass of 139 point 92164 atomic mass units were specifically referring to its isotope Zen on 140. Now, we want to also subtract the mass of strontium 94 which has an atomic mass of 93.91 535 and also subtract the mass of two neutrons. So we can essentially say two multiplied by the mass of one neutron. So that's 1.00866 atomic mass units. If we perform the calculation, we get a mass defect of zero point 198, 27 atomic mass units. Now essentially to calculate the energy produced, we want to recall the formula delta E, the change in energy is equal to delta M, the mass defect multiplied by C squared which is the speed of light squared. It is really important to understand that in this formula, we want to use SI units and it allows us to calculate the energy produced per one nucleus, right. So what we're going to do is take the previously obtained number that would be 0.198 27 atomic mass units. And we want to convert that into SI units of mass. Now, the si units of mass are kilograms. So we're going to use dimensional analysis and relate kilograms to atomic mass units. We know that one atomic mass unit equals 1.66054 multiplied by send to the power of negative 27 kg. So this allows us to convert the mass defect into kilograms. And now we want to multiply that by the speed of light squared, the speed of light would be three point 00, multiplied by sense, the power of eight meters per second. And we essentially want to square that. Now this will give us the amount of energy produced per nucleus. And since we want to get the energy per mole, we simply want to multiply our answer by Avogadro's number, which is 6.022 multiplied by sends the power of 23rd moles to the power of negative first, right? Because if we have our energy change per nucleus and one mole contains avocado's number of nuclei, then we simply want to get the total energy multiplying by avocado's number. And now we can easily get our result which is 1.7818 multiplied by, since the power of 13th jules per mole of uranium 235 that would be our final answer. And thank you for watching.

Calculate the quantity of energy produced per mole of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass = 136.9253 amu) and Zr-97 (atomic mass = 96.910950 amu) (discussed in Problem 58).

Verified Solution

Key Concepts

Nuclear Fission

Mass-Energy Equivalence

Binding Energy