A Uranium-235 atom undergoes fission in the following net reaction (induced fiss

Question

A Uranium-235 atom undergoes fission in the following net reaction (induced fission involves an intermediate step as U-236 which we will ignore):

U-235 --> X + Y + 2n

U-235 is the 'parent', X and Y are 'daughters' (= fission products), n = free neutron. 1 u = atomic mass unit = 1.66 x 10-27 kg mn = mass of a neutron = 1.008665 u mp = mass of a proton = 1.007825 u 1 eV = 1.602 x 10-19 J u = 931.494 MeV/c2

A. (3 pts) Give the values of Z, N and A for U-235.

B. (4 pts) The mass of a U-235 nucleus is 235.04394 u. What is the binding energy per nucleon in U-235? Express your answer in electron volts and in Joules (per nucleon).

C. (4 pts) Suppose X is Rb-90 and Y is Cs-143. The nuclear mass of Rb-90 is 89.9148 u and the nuclear mass of Cs-143 is 142.9273 u. What is the binding energy per nucleon in each of the two fission products?

D. (4 pts) Calculate the energy released in the fission of one U-235 nucleus (via the above reaction).

Explanation / Answer

A. Z=92 , N= 92 , A =238.04 u =3.95 *10 ^-25 kg

B.binding energy per nucleon in U-235

difference in the two energies by the number of nucleons and this will give you the average binding energy per nucleon.

=(atomic mass - mass of neutron + mass of electron + mass of proton)/number of nucleons

235 nucleons, so the binding energy per nucleon is 7.59 * 10 ^6 eV/nucleon

= 12.15 * 10 ^ -13 J/nucleon

c.) difference in the two energies by the number of nucleons and this will give you the average binding energy per nucleon.

=(atomic mass - mass of neutron + mass of electron + mass of proton)/number of nucleons

Cs has 143 nucleons and Rb has 90 nucleons

Cesium is 8.2MeV and of Rubidium is 8.6MeV

d.)balance the enrgy

rest mass energy of uranium = 218.89Gev

of Cs = 127.501 Gev

Rb = 88.3859 Gev

2n = 2 * 93956 =1.87912 Gev

so released energy = 1.13078Gev =1130.78 Mev

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