Question

Calculate the nuclear binding energy per nucleon for 176Hf if its nuclear mass is 175.941 amu.

Answer 1

Hf-176 has atomic number Z = 72

Hence Proton number P = electron number E = 72,

Neutron number N = Mass number – proton number = 176-72 = 104.

Let find Expected mass of Hf.

Mass of Proton = 1.00728 amu

Mass of neutron = 1.00867 amu

Expected mass of Hf = (Mass of proton x P) + (Mass of neutron x n)

                          = (1.00728x72) + (1.00867 x104)                                 

                              = 72.52416 + 104.90168

= 177.42584 amu

Or177.426 amu

Expected mass of Hf = 177.426 amu

Observed mass of Hf = 175.941amu

ii) Let us find out mass defect (Δm) = ?

Δm = Expected mass – Observed mass

Δm = 177.426 – 175.941

Δm = 1.485 amu.

iii) Calculation of binding energy B.E.

B.E = Mass defect x 931.5 MeV ……………. (since, 1amu = 931.5 MeV)

B.E. = 1.485 x 931.5

B.E. = 1383.2775 MeV

iv) B.E per nucleon = B.E. / Mass number

For Hf- 176 B.E. per nucleon = 1383.3 / 176

For Hf- 176 B.E. per nucleon 7.86 MeV.

B.E. per nucleon = 7.86 x (1.602x10^-13) J ............ (Since, 1MeV = 1.602 x 10^-13 J)

= 1.259 x 10^-12 J

Hence B.E. for Hf-176 is 1.259 x 10^-12 J/nucleon.