NE 301 - Introduction to Nuclear Science
Spring 2012
Classroom Session 3:
•Radioactive
Decay Types
•Radioactive Decay and Growth
•Isotopes and Decay Diagrams
•Nuclear Reactions
•
•
•
Energy of nuclear reactions
Neutron Cross Sections
Activation Calculations
Reminder
Load TurningPoint


Reset slides
Load List
2
Let’s do some accounting…
Mass of Oxygen Atom:
Mp=1.007276 amu
Mn=1.008665 amu
Me=5.48e-4 amu
16
8
O
1 amu = 931.49 MeV
Zm p  8 1.007276 amu
( A  Z )mn  8 1.008665 amu
Zme  8  5.48e  4 amu
16.131912 amu
M 16O  15.994915 amu
8
Mass Defect = Binding
Energy (BE)
3
931.49 MeV
BE 16 O = (16.131912-15.994915 amu) 
 127.61 MeV
1 amu
Chart of the Nuclides
Isobars
Isotopes
Z
Isotones
N
4
Notice radioactive decay stabilizes atoms:
Question:
Do fission products
normally have - or
+ decay?
5
Reaction Energetics
Reaction reactants and products
A + B  C + D + E
If E is positive: reaction exothermic
releases energy
If E is negative, reaction endothermic
requires energy
Endoergic and exoergic is sometimes used
The Energy Released (or consumed),
Q
A + B  C + D + E
Change in BE:
Q  BE  BEC  BED  ( BEA  BEB )
Or since BE is related to mass defect
Change in M:
Preferred!
because we have table B.1.
Q  M  M A  M B  (M C  M D )
Remember:
The Equation Has to Be
BALANCED!
Please remember…
BALANCE!
Before starting to work
Balancing Reactions
1
16
16
1
n
O
N
0
8
7
1p
nucleons  1 +16 = 16+1
Charges
(+) 

0+8= 7+1
(-) 
-0 -8 = -7 -0  e- missing
0
1
So in reality the reaction is:
1
0
n O  N  e p
1
0
n O  N  H
16
8
16
8
16
7
16
7
0
1
1
1
1
1
or
Calculating Q…
Q-value for the reaction is:
1
0
n O  N  H
16
8
16
7
1
1
Using atomic mass tables:
M  M A  M B  ( M C  M D )
M  1.008665  15.994915  16.006101  1.007825  0.010346 amu
931.494 MeV
 0.010346 amu 
 9.637 MeV
1 amu
Endothermic reaction. Only a
few fission neutrons can do it
A beryllium target is irradiated in a
proton accelerator to produce 10B.
What is Q of the reaction?
M
eV
85
M
6.
5
3M
eV
0%
eV
0%
eV
5.
7%
M
4.
14%
4.
5
3.
eV
2.
5.5 MeV
4.5 MeV
3 MeV
6.5 MeV
85 MeV
10
5
M
1.
p  Be  B  
9
4
5.
5
1
1
79%
11
For clicker
1
1
H  49 Be  105 B  
Q  (1.007825  9.012182  10.012937)  931.494  6.586 MeV
Excited Nuclei
Many reactions involve excited nuclei
Sometimes long lived states (isomers)
Excitation energy has to be added to the
mass of the excited nuclei when calculating Q
M  X  M  X  E
A
Z
e.g. The mass of
*
22Ne*
A
Z
10
c
2
at 1274 MeV is:
M 22 Ne*
 M 22 Ne   *  21.991386  1274 MeV 
10
*
1amu
 23.3591 amu
931.494MeV
13
Decay Series
The radioactive minerals contain many nuclides
All of them decay by either  or  decay
  A changes by 4, Z by 2
  A does not change, A by 1
Th has one long lived isotope 232Th
There are 3
U has two long lived 235U, 238U
natural series
Series identified by relation Parent to Dauthers mass:

A in multiples of 4
14
15
Notice
Branching
16
17
Series are:
A = 4n --- Thorium Series
A = 4n+2 -- Uranium Series
A = 4n+3 – Actinium Series
Which one is missing?
A = 4n+1 – Neptunium Series (Artificial)
18
It was there from the beginning… but
notice: half life of 237Np is relatively low.
19
Main Radioactive Decay Modes
Decay Type
Gamma ()
(Table 5.1 -page 89-Shultis)
Description
Emission
P*  ZA P  
Gamma photon
A
Z
Decay of excited nucleus
alpha ()
P  ZA24 D  
Alpha particle is emitted
Alpha particle
negatron (-)
np++e-+
A
A

Z P  Z 1 D   
Electron and antineutrino
positron (β+)
p+n+e++
A
A

P

D



Z
Z 1
Positron and neutrino
Electron Capture
(EC)
Orbital e- absorbed: p++e-n +
Neutrino
proton (p)
Proton ejected
Proton
neutron (n)
Neutron ejected
Neutron
Internal Conversion
(IC)
Electron (K-Shell)
ejected*

A *
A

 
Z P   Z P  e
Electron
Spontaneous Fission
(sf)
A
Z
A
Z

Pe 
A
Z
A
Z 1
D 
*
P  D1  D2  x n
Fission fragments
20
Comments:
, +, - are common modes of decay
Long T1/2 usually are -emitters
n, p emission are rare (excess p+ atoms)
 is predominant for Z>83 (above Bismuth) and
atoms away from the line of -stability.
Some high Z atoms (Z>96) have
dominant spontaneous fission
 mostly dominates again at Z>105
Modes of Decay
, +, - are common
modes of decay
Long T1/2 usually are emitters
n, p emission are rare
(excess p+ atoms)
 is predominant for Z>83
(above Bismuth) and atoms away
from the line of -stability.
Some high Z atoms (Z>96)
have dominant spontaneous
fission
 mostly dominates again at
Z>105
22
Solving momentum and KE equations
Remember the conditions:
1.
2.
3.
4.
Parent nucleus at rest (usually the case)
Binary products only (not -decay, but OK to Emax)
Calculate the correct Q (excited states are
prevalent, and balance)
Finally, there usually reaction paths with many
outcomes, therefore multiple Q-values
 m2 
KE1  Q 

 m1  m2 
 m1 
KE2  Q 

 m1  m2 
Kinetic Energy of Radioactive Decay Products
Parent nucleus is at rest (Eth~ 0.025 eV~17 oC)
Conservation of Linear Momentum and Kinetic
Energy requires products to travel in opposite
directions (2 product).
v2
m2
m2
m1
Original atom that will
split in 2 pieces
m1
v1
m1v1=m2v2
Q=½ m1v12+ ½ m2v22
What is the energy of emitted particle?
(it is what we measure)
24
Kinematics of radioactive decay…
1
1
2
Q= m1v1  m 2 v 2 2
2
2
m1v1 =m 2 v 2
v1 =
m2 v2
m1
replacing...
m2 v2 2 1
1
Q  m1 (
)  m2 v22
2
m1
2
1 m22 v22 1
Q
 m2 v22
2 m1
2
Q
m2
KE2  KE2
m1
 m1 
KE2  Q 

m

m
 1
2 
1
2
and replacing  m 2 v 2  by KE 2
2

solving for KE 2
similarly:
Notice 2:1
 m2 
KE1  Q 

m

m
 1
2 
25
Warm up:
What % of the energy should go to the -particle?
20%
5.
20%


m1
KE2  Q 

m

m
 1
2 


m2
KE1  Q 

m

m
 1
2 
1%
4.
10
%
3.
50
%
2.
98%
2%
50%
10%
1%
20%
4
2
2%
1.
20%
Th He
234
90
98
%
U
238
92
20%
26
Example of -spectroscopy?
241
Am  ? 
100%
1. 237Pa
2. 237U
3. 237Np
4. 237Pu
0%
23
7C
m
0%
23
7A
m
0%
23
7P
u
0%
23
7U
23
7P
a
6. 237Cm
0%
23
7N
p
5. 237Am
27
Find Q for:
241
95
Am 
237
93
Np  He
4
2
20%
20%
20%
M
eV
7.
63
8
M
eV
6.
63
8
M
eV
5.
63
8
5.
M
eV
4.
4.
63
8
3.
20%
MeV
MeV
MeV
MeV
MeV
M
eV
2.
3.638
4.638
5.638
6.638
7.638
3.
63
8
1.
20%
28
For Clicker slide:
Q=(241.056823-237.048167-4.002603)*931.494=5.638MeV
What is the KE of the  particle in
the radioactive decay of 241Am? (3 min)
25%
25%
eV
M
5.
64
eV
M
5.
54
eV
M
0.
98
4.
eV
3.
25%
MeV
MeV
MeV
MeV
M
2.
0.09
0.98
5.54
5.64
0.
09
1.
25%
30
For Clicker slide:
KE=5.638*237/(237+4)=5.545 MeV
Notice:
If alpha particle ALWAYS leaves with exactly
the same energy.
We would expect to detect a monoenergetic
beam of ’s.
In reality…
The real alpha
spectrum of 241Am is:
At least 5 different 
energies…
Why?
Excited Nuclei!
The real decay path of
241Am
There are actually
6 alpha peaks
Last two peaks are
too close to be
resolved
Notice frequencies
(%’s)
Every decay path
happens all the
time but not with
equal probability
Look in your book:
Page 578.
Taken from J. K. Beling, et al. Phys. Rev. 87 (1952) 670-671
241Am
Diagram means:
241
95
Am  237 Np*  4 He
93
2
*170 KeV
241
95
Am  237 Np*  4 He
93
2
*114 KeV
241
95
Am  237 Np*  4 He
93
2
*71 KeV
241
95
Am  237 Np*  4 He
93
2
Energy of the -particle?
Same old same old
Am  237 Np*  4 He
93
2
 m 
KE  Q 

m

m
2 
 
*43 KeV
241
95
*11 KeV
241
95
Am  237 Np  4 He
93
2
But Q is different each
time
35
3.6
36
37
4.0
By the way
Notice also
38
4.0
There are a lot more hard to see peaks
39
So how is the “real” diagram?
For that we need the
TABLE OF ISOTOPES
40
Diagram
241Am
- 1 of 2
41
Diagram
241Am
- 2 of 2
42
The Table also includes a more complete list of
particles emitted during decay
43
44
’s
’s
45
Main Radioactive Decay Modes
Decay Type
Gamma ()
(Table 5.1 -page 89-Shultis)
Description
Emission
P*  ZA P  
Gamma photon
A
Z
Decay of excited nucleus
alpha ()
P  ZA24 D  
Alpha particle is emitted
Alpha particle
negatron (-)
np++e-+
A
A

Z P  Z 1 D   
Electron and antineutrino
positron (β+)
p+n+e++
A
A

P

D



Z
Z 1
Positron and neutrino
Electron Capture
(EC)
Orbital e- absorbed: p++e-n +
Neutrino
proton (p)
Proton ejected
Proton
neutron (n)
Neutron ejected
Neutron
Internal Conversion
(IC)
Electron (K-Shell)
ejected*

A *
A

 
Z P   Z P  e
Electron
Spontaneous Fission
(sf)
A
Z
A
Z

Pe 
A
Z
A
Z 1
D 
*
P  D1  D2  x n
Fission fragments
46