In: Physics
Calculate the binding energy per nucleon for 55Mn, 9Be, 14N, and 7Li. (For the atomic masses, see this table. Enter your answers to at least two decimal places.) (a) 55Mn MeV/nucleon (b) 9Be MeV/nucleon (c) 14N MeV/nucleon (d) 7Li MeV/nucleon
wasnt provided a table
mass of proton, mp = 1.00727 u
mass of neutron, mn = 1.00866 u
mass of 55Mn = 54.938043 u
mass of 9Be = 9.01218 u
mass of 14 N = 14.0067 u
mass of 7Li = 7.0160 u
binding energy per nucleon = binding energy/ A
binding energy, BE = mass defect x 931.5 MeV
(a )
Mass defect, Δm = ( mass of 25 protons + mass of 30 neutrons ) - mass of 55Mn
Δm = ( 25 x 1.00727 + 30 x 1.00866) - 54.938043 = 0.496493 u
Binding energy, BE = Δm x 931.5 = 0.496493 x 931.5 = 462.48 MeV
binding energy per nucleon = BE/ A = 462.48/55 = 8.41 MeV
binding energy per nucleon of 55 Mn = 8.41 MeV
( b)
Mass defect, Δm = ( mass of 4 protons + mass of 5 neutrons ) - mass of 9Be
Δm = ( 4 x 1.00727 + 5 x 1.00866) - 9.01218 = 0.0602u
Binding energy, BE = Δm x 931.5 = 0.0602 x 931.5 = 56.07 MeV
binding energy per nucleon = BE/ A = 56.07/9 = 6.23 MeV
binding energy per nucleon of 9Be = 6.23 MeV
( c )
Mass defect, Δm = ( mass of 7 protons + mass of 7 neutrons )- mass of 14N
Δm = ( 7 x 1.00727 + 7 x 1.00866) - 14.0067 =0.10481 u
Binding energy, BE = Δm x 931.5 = 0.10481 x 931.5 = 97.63 MeV
binding energy per nucleon = BE/ A = 97.63/14 = 6.97 MeV
binding energy per nucleon of 14N = 6.97 MeV
( d )
Mass defect, Δm = ( mass of 3 protons + mass of 4 neutrons )- mass of 7Li
Δm = ( 3 x 1.00727 + 4 x 1.00866) - 7.0160 =0.04135 u
Binding energy, BE = Δm x 931.5 = 0.04134 x 931.5 = 38.52 MeV
binding energy per nucleon = BE/ A = 38.52/7 = 5.50 MeV
binding energy per nucleon of 7Li = 5.50 MeV