If ^235U (235.043930 u) is struck by a neutron it undergoes fission producing ^144 Ba (143.922953 u), ^89 Kr (88.917630 u) and three neutrons (1.0086649 u).
(a) Calculate the energy in MeV released by each fission reaction.
(b) Calculate the energy released per gram of ^235U in MeV/g.
I will be happy to critique your thinking. Find the change of mass from the reactants to products.
To determine the energy released by each fission reaction, we can use the concept of mass-energy equivalence from Einstein's famous equation, E = mc^2, where E represents energy, m is the mass change, and c is the speed of light.
(a) Energy released by each fission reaction:
To calculate the energy released by each reaction, we need to find the mass change (∆m) in atomic mass units (u) and then convert it to energy using the conversion factor 1 u = 931.5 MeV.
∆m = (mass of products) - (mass of initial uranium isotope)
∆m = (mass of ^144Ba + mass of ^89Kr + 3 * mass of neutron) - (mass of ^235U)
Let's substitute the respective masses provided:
∆m = (143.922953 u + 88.917630 u + 3 * 1.0086649 u) - 235.043930 u
Now we can calculate the energy released using the formula:
Energy released (E) = ∆m * 931.5 MeV
(b) Energy released per gram of ^235U:
To calculate the energy released per gram of ^235U, we need to divide the energy released by the mass of ^235U, keeping in mind that 1 gram is equivalent to 6.022 × 10^23 amu (atomic mass units).
Energy released per gram of ^235U = Energy released / mass of ^235U * (1 gram / (6.022 × 10^23 amu)) * (1 amu / 1.66053906660 × 10^-24 gram)
By substituting the values, we can calculate the energy released per gram of ^235U in MeV/g.
Please note that to obtain precise values, it is necessary to use a calculator or a scientific computing tool.