Question

Many transuranium elements, such as plutonium-232, have
very short half-lives. (For 232Pu, the half-life is 36 minutes.)
However, some, like protactinium-231 (half-life 5 3.34 3
104 years), have relatively long half-lives. calculate the change in energy when
1 mole of 232Pu nuclei and 1 mole of 231Pa nuclei are each
formed from their respective number of protons and neutrons.

PLEASE SHOW WORK, THANKS

Answer 1

Proton mass = 1.00728 amu

Neutron mass = 1.00867 amu

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For plutonium (Pu) Pu-232

Actual mass of Pu-232 = 232.041187 amu

proton = 94   neutron = 138    electron = 94

mass of proton + neutron = 94 x 1.00728 + 138 x 1.00867 g = 233.88078 amu

mass defect (dm) = 233.88078 - 232.041187 = 1.8396 amu

mass in kg = 1.8398/6.023 x 10^26 = 3.0543 x 10^-27 kg

change in energy = mc^2

                             = (3.0543 x 10^-27 kg)(3 x 10^8)^2/1 mole

                             = 2.75 x 10^-10 J/mole

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For protactinium (Pa) Pa-231

Actual mass of Pu-232 = 231.035884 amu

proton = 91   neutron = 140    electron = 91

mass of proton + neutron = 91 x 1.00728 + 140 x 1.00867 g = 232.87628 amu

mass defect (dm) = 232.87628 - 231.035884 = 1.8404 amu

mass in kg = 1.8404/6.023 x 10^26 = 3.05562 x 10^-27 kg

change in energy = mc^2

                             = (3.05562 x 10^-27 kg)(3 x 10^8)^2/1 mole

                             = 2.75 x 10^-10 J/mol