Question

In: Chemistry

What is in the last effects, the nuclear binding energy per atom, and the binding energy...

What is in the last effects, the nuclear binding energy per atom, and the binding energy per nucleon for U-238? (Isotopic mass of U-238=238.05078 amu)

Expert Solution

number of proton = 92

mass of each proton = 1.00727647

so, total mass of proton,

mp = 92 * 1.00727647

mp = 92.669435 amu

number of neutron = 146

mass of each neutron = 1.00866492

so, total mass of neutron,

mn = 146 * 1.00866492

mn = 147.265078 amu

Expected mass of nucleus = mass of protons + mass of neutrons

= 92.669435 + 147.265078

= 239.934514 amu

Actual mass of nucleus = 238.05078 amu

So, mass defect,

Δm = total mass of proton and neutron - actual mass of nucleus

Δm = 239.934514 - 238.05078

Δm = 1.883734 amu

This difference in mass need to be converted to binding energy

dm = 1.883734 u

1 u = 1.6605387E-27 Kg

So,

dm = 1.883734*1.6605387E-27

= 3.128*10^-27 Kg

mass can be converted to energy as given by:

E = m*c^2

so,

E = 3.128*10^-27*(3*10^8)^2 J

E = 2.815*10^-10 J

= 2.815*10^-10/(1.602E-19) eV

= 1.757*10^9 eV

E = 1.757*10^9 eV

E 1.757*10^3 MeV

Total Binding energy per atom = 1757 MeV

Number of nucleon = 238

Binding energy per nucleon = 1757/238

= 7.38 MeV/nucleon

Answer:

1757 MeV/atom

7.38 MeV/nucleon

queen_honey_blossom answered 2 years ago

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