Question

Calculate the binding energies (E_b), in MeV, for ¹⁸⁴Os isotope given that c = 2.99792x10⁸ m/s. Helpful conversions: 1 u = 1.6605x10^-27 kg; 1 J = 6.2415x10¹² MeV.

a.) δ (kg) =

b.) δ/A (kg) =

c.) E_b (J) =

d.) E_b MeV =

Answer 1

¹⁸⁴Os₇₆ has 76 protons and 184-76 = 108 neutrons

We have,

Mass defect = m = [Mass of protons + Mass of neutrons] - Actual mass

       = (76 x 1.00728 + 108 x1.00867) -183.952491 = 1.5371 amu

1 amu = 1.6605 x 10^-27 kg

Therefore, m = 1.5371 x 1.6605x10^-27 = 2.55 x 10^-27 Kg

According to Einstein’s mass energy relationship,

E = mc² = 1.5371 x 1.6605x10^-27 x (2.99792x10⁸)² = 2.2939 x 10^-10J

1 J = 6.2415 x10¹² MeV

Therefore, E = 2.2939 x 10^-10 x 6.2415 x10¹² = 1431.759 MeV

Nuclear binding energy per nucleon (MeV/nucleon) = 1431.759 /184 = 7.781 MeV/nucleon