22.02
INT R ODUCTION T O
APPLIED NUCLEAR PHY SICS
Lecture 2
1
SEMI-EMPIRIC AL MASS FORMULA
M ( Z, A ) = Z m ( 1 H ) + N m n − B ( Z, A ) /c 2
With binding energy given by:
B ( A, Z ) = a v A − a s A 2 / 3 − a c Z ( Z − 1) A − 1 / 3
( A − 2 Z ) 2
− 3 / 4
− a sy m + δ a p A A
Photo courtesy of cdw9 on Flickr. License CC BY-NC.
2
SEMI-EMPIRIC AL MASS FORMULA
M ( Z, A ) = Z m ( 1 H ) + N m n − B ( Z, A ) /c 2
With binding energy given by: Surface Coulomb
B ( A, Z ) = a v A − a s A 2 / 3 − a c Z ( Z − 1) A − 1 / 3
Volume
− a sy m
( A − 2 Z ) 2
A
+ δ a p A
− 3 / 4
{
symmetry pairing
Photo courtesy of cdw9 on Flickr. License CC BY-NC. 3
CHA R T of NUCLIDES (Z vs. A)
120 Z
100
Z=A/2
80
60
40
A
20
50 100 150 200 250
4
CHA R T of NUCLIDES (Z/A vs. A)
Z/A
0.55
0.50
0.45
0.40
0.35
A
50 100 150 200 250
5
B/A: MAXIMUM
B/A [MeV]
(binding energy per nucleon)
9
8
7
6 Fusion Fission
5
α-decay
4
3
A
0 50 100 150 200
(Mass number)
250
Maximum B/A for 50 < A < 100
6
RADI O A CTIVE DEC A Y CHAIN
N 1 ( t ) = N 0 e
− λ 1 t
N 2 ( t ) = N 0
λ 1 ( e − λ 1 t − e − λ 2 t ) λ 2 − λ 1
λ 1 ( 1 − e − λ 2 t ) − λ 2 ( 1 − e − λ 1 t )
λ
N 3 ( t ) = N 0
1
— λ 2 7
MASS P ARABOLA
M(Z,A=cst): Mass of nuclides at constant mass # A
49 In
n
50 S
A=125
b - b +
56 Ba
5
5 5 Cs
51 Sb
52 Te
8
53 I
54 Xe
MASS P ARABOLA
A=128
49 In
b - b +
57 La
50 Sn 51 Sb
52 Te
55 Cs
53 I 56 Ba
54 Xe
9
MASS P ARABOLA
M(Z,A=cst): Mass of nuclides at constant mass # A
A b
Odd A A = 135
? Even A
A = 102
?
-
-
Atomic Mass (M)
- EC
Od d Z , od d N
Atomic Mass (M)
Eve n Z , eve n N ?
+
- +
- -
+
La
Cs
Xe
T e I Ba
Nb Mo T c
Ru Rh Pd Ag Cd
Ce
52 53 54 55 56 57 58
41 42 43 44
45 46 47 48
Z Z A = 55.7 Z Z A = 44.7
Figure by MIT OpenCourseWare. After Meyerhof.
10
MIT OpenCourseWare http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
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