Calculate the energy change when one ²³⁵U nucleus undergoes the fission reaction
²³⁵U + n $\rightarrow$ ¹⁴²Ba + ⁹²Kr + 2n
The masses needed are ²³⁵U,235.04 u; ¹⁴²Ba,141.92 u; ⁹²Kr,91.92 u; n,1.0087 u.

Question

Calculate the energy change when one ²³⁵U nucleus undergoes the fission reaction
²³⁵U + n

\rightarrow

¹⁴²Ba + ⁹²Kr + 2n
The masses needed are ²³⁵U,235.04 u; ¹⁴²Ba,141.92 u; ⁹²Kr,91.92 u; n,1.0087 u.

Quizplus · Accepted Answer

The energy change in a nuclear reaction can be calculated using the mass defect and converting it into energy using Einstein's equation $E = \Delta m c^2$, where $c$ is the speed of light. The mass defect, $\Delta m$, is the difference between the mass of the reactants and the products. In this case, the mass of the reactants is the mass of $^{235}U$ plus one neutron, and the mass of the products is the sum of the masses of $^{142}Ba$, $^{92}Kr$, and two neutrons. Calculating the mass of the reactants: $235.04 u + 1.0087 u = 236.0487 u$Calculating the mass of the products: $141.92 u + 91.92 u + 2(1.0087 u) = 234.8654 u$The mass defect, $\Delta m$, is the mass of the reactants minus the mass of the products: $236.0487 u - 234.8654 u = 1.1833 u$.To convert this mass defect into energy, we use the conversion factor $1 u = 931.5 MeV/c^2$: $1.1833 u \times 931.5 MeV/u = 1102.8 MeV$.Therefore, the energy released in this fission reaction is approximately $1102.8 MeV$, which corresponds to choice E.

Calculate the Energy Change When One 235U Nucleus Undergoes the Fission

Calculate the Energy Change When One ²³⁵U Nucleus Undergoes the Fission