Calculate the nuclear binding energy in mega-electronvolts (MeV) per nucleon for 179Hf if its nuclear mass...

Calculate the nuclear binding energy in mega-electronvolts (MeV) per nucleon for 179Hf if its nuclear mass is 178.946 amu.

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Expert Solution

Calculate the nuclear binding energy in mega-electronvolts (MeV) per nucleon for 179Hf if its nuclear mass is 178.946 amu.

The atomic mass of 179/72 Hf is 178.946 amu. Calculate the nuclear binding energy of this

nucleus and the corresponding nuclear binding energy per nucleon

Mass number = 179

No. of protons = 72, then

Neutrons = Mass number – proton number = 72 protons and 179-72= 107 neutrons are present

Mass of proton = 1.007316

Mass of neutrón = 1.008701

Total mass = 72*1.007316+ 107*1.008665 = 180.453907 amu

The mass defect:

180.453907-178.946 = -1.507907 amu

Mass = 1.507907 /(6.022*10^23) = 2.503*10^-24 g or -2.503*10^-27 kg

Energy released (Einstein E = mC^2)

E = m*C^2 = -2.503*10^-27 * (3*10^8)^2 = -2.2527*10^-10 J

Nuclear binding energy = E = -2.2527*10^-10 J

Nuclear binding energy per nucleon

Nucleon = neutron + protons = 179

E per nucleon = E / nucleon =(2.2527*10^-10)/( 179) = 1.258*10^-12 J/nucleon

change to meV

1 J = 6.242*10^12 MeV

1.258*10^-12 J --> x

x = ( 6.242*10^12)(1.258*10^-12) = 7.852436 MeV / nucleon

queen_honey_blossom answered 1 year ago

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