When a neutron (n) collides with a uranium-235 nucleus it can induce a variety of fission reactions. One such reaction is U + n → Xe + Sr + 2n. How much energy is released in this reaction, given the following mass values: Xe: 139.921620 u Sr : 93.915367 u U: 235.043924 u n: 1.008665 u (1 u = 931.494 MeV/c2)

Respuesta :

Explanation:

Since, the given reaction is [tex]U + n \rightarrow Xe + Sr + 2n[/tex]

Sum of masses on both reactant and product side is as follows.

           235.043924 + 1.008665 = 139.921620 + 93.915367 + (2 × 1.008665)

                            = 0.198272 u

As it is known that relation between energy and mass is as follows.

                   Energy produced = [tex]\Delta m c^{2}[/tex]

Since, 1 u = 931.494 MeV/[tex]c^{2}[/tex]. Putting this value into the above formula as follows.

                   Energy produced = [tex]\Delta m c^{2}[/tex]

                                                  = [tex]0.198272 \times \frac{931.494}{c^{2}} \times c^{2}[/tex]

                                                   = 184.69 MeV

As 1 MeV equals [tex]1.602 \times 10^{-13}[/tex] joules.

Hence, 184.69 MeV will be converted into joules as follows.

            [tex]184.69 MeV \times \frac{1.602 \times 10^{-13}J}{1 MeV}[/tex]

                  = [tex]295.87 \times 10^{-13}[/tex] J

                  = [tex]2.95 \times 10^{-17}[/tex] J

Thus, we can conclude that energy released in this reaction is [tex]2.95 \times 10^{-15}[/tex] J.