Nuclear Binding Energy

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Nuclear Binding Energy

Nuclear Binding Energy

  • There exists a difference in the theoretically calculated mass of nuclei (i.e. sum of masses of protons and neutrons) and the actual mass of the atomic nucleus. This difference in mass is called the mass defect (△m).
  • This mass defect is found by adding up the masses of all the individual particles (protons, neutrons and electrons) and subtracting the actual mass (m) of an atom.
Thus,
△m
= np mp+nn mn+ne me-zmA
  • Where ‘n’ refers to the number of particles, m the mass of particles and suffix p, n and e refer to proton, neutron and electrons respectively.
  • The mass defect is converted into energy in a nuclear reaction as given by Einstein law,
△E
= △m .C2
Where E = Energy in Joules, C =
Velocity of light = 3 x 108 m/s
and Am = mass defect in kg.
  • The energy associated with mass defect is known as binding energy of the nucleus.

Energy
equivalent of 1 gm = (1 x 10-3 kg) mass defect is,

△E = 1 x 10-3 x (3 x 10-8)2
= 9 x 1013 J = 9 x 1010 KJ

       = 9 x 107 MJ

Similarly
energy equivalent to 1 amu (1.66 x 10-27 Kg)

△E =
(1.66 x 10-27) x (3 x 108)2 = 14.94 x 10-11
J

       = 9.31 x 108 eV = 931 MeV

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