Question

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

Answer 1

mass of proton, m_p = 1.00727 u

mass of neutron, m_n = 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