Question

The fact that BE/A is greatest for A near 60 implies that the range of the nuclear force is about the diameter of such nuclides.

(a) Calculate the diameter (in fm) of an A = 60 nucleus. ____ fm

(b) Calculate BE/A (in MeV) for 56Fe and 102Ru. The first is one of the most tightly bound nuclides, while the second is larger and less tightly bound. (Assume 1 u = 931.5 MeV/c2.)

56Fe ______MeV

102Ru _____ MeV

Answer 1

Part1. For Fe (Iron)

R = R0A1/3 = (1.2*10-15 m)*(56)1/3 = 4.6*10-15 m.
diameter = 2R = 9.2*10-15 m.

Part 2. BE/A

For 2656​Fe : mass defect ,Δm=[26mp​+(56−26)mn​]+MFe​

Δm=[26×1.007825+30×1.008665]−55.93492=0.5285amu

Binding energy per nucleon BE=AΔmc2​=560.5285c2​=0.0086c2amu=0.0094×931.5=8.76MeV  as (1amu=931.5MeV/c2