1000 Solved Problems in Modern Physics

428 8 Nuclear Physics – II

The shell model energy levels are:

[

1 s^12

][

1 p 32 , 1 p (^12)

][

1 d 52 , 2 s 12 , 1 d (^32)

][

1 f (^72)

][

2 p 32 , 1 f 52 , 2 p 12 , 1 g (^92)

]

[

1 g 72 , 2 d 52 , 2 d 32 , 3 s 12 , 1 h (^112)

]

... (8.4)

Liquid drop model (8.5)

M(atom)=ZMH+(A−Z)Mn−Δ (8.6)

Δ=mass defect

P=

M−A

A

=packing fraction. (8.7)

1amu=

1

12

of atomic mass of^12 C atom (8.8)

f=

B.E

A

(8.9)

1amu= 931 .5 Mev (8.10)

1amu= 1. 66 × 10 −^27 kg (8.11)

The f-A curve is shown in Fig. 8.1. A more detailed diagram is shown in
Problem 8.40

Fig. 8.1BE/A Versus A

Stability against decay

β−−decay :M(Z,A)≤M(Z+ 1 ,A) (8.12)

β+−decay :M(Z+ 1 ,A)≤M(Z,A)+ 2 Me (8.13)

e−capture :M(Z+ 1 ,A)≤M(Z,A) (8.14)

α−decay :M(Z,A)≤M(Z− 2 , A−4)+MHe 4 (8.15)

Assuming thatγ-ray precedes the decay, the energy released

Qβ−=[M(Z,A)−M(Z+ 1 ,A)]c^2 =Tmax+Tγ (8.16)

Qβ+=[M(Z+ 1 ,A)−M(Z,A)]c^2 = 2 Mec^2 +Tmax+Tγ (8.17)

QEC=[M(Z+ 1 ,A)−M(Z,A)]c^2 =Tv+Tγ (8.18)