Question

# Proton mass mp = 1.00727647 u Neutron mass mn = 1.00866501 u 231Th mass = 231.036299...

Proton mass mp = 1.00727647 u
Neutron mass mn = 1.00866501 u
231Th mass = 231.036299 u

Question 1. 1. Alpha decay of uranium-235 to thorium

23592U 23190Th + 42He

2. Q = (Mp -Md-M?)amu.   Mp = mass of parent nuclei, Md = mass of daugther nuclei, M? = mass of alpha particle

Q = M23592U - (M23190Th - M 42He)

= M23592U - M23190Th + M 42He

= M 42He + M 42He

= 4.002603 u + 4.002603 u

Q = 8.005206 u

3. mass of uranium-235

Q = M23592U - (M23190Th - M 42He)

substitute all the values to calculate mass of uranium

8.005206 u = M23592U - (  231.036299 u - 4.002603 u)

8.005206 u + ( 231.036299 u - 4.002603 u) = M23592U

235.038902 u = M23592U

4. binding energy of the nucleus.

235 - 92 = 143 neutrons

Total mass of baryons is (92 x 1.00727647) + (143 x 1.00866501) = 236.9085188 u

Mass defect = 236.9085188 - 235.038902 = 1.8645889 u = 3.096222181 x 10-27 kg

E=mc^2 = 3.096222181 x 10-27 kg x (3.00x10^8)^2 = 2.86351 x 10^-10 J = 1.74 GeV