NE 301 - Introduction to Nuclear ScienceSpring 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
2
ReminderLoad TurningPoint Reset slides Load List
Let’s do some accounting…Mass of Oxygen Atom:
Mp=1.007276 amuMn=1.008665 amuMe=5.48e-4 amu
3
168
16.131912 amu
8 1.007276 amu
( ) 8 1.008665 amu 15.994915 amu8 5.48 4 amu
p
n O
e
Zm
A Z m MZm e
Mass Defect = Binding
Energy (BE)
1 amu = 931.49 MeV
168O
16 O
931.49 MeVBE = (16.131912-15.994915 amu) 127.61 MeV1 amu
4
Chart of the Nuclides
Z
N
IsobarsIsotopes
Isotones
5
Notice radioactive decay stabilizes atoms:
Question:
Do fission products normally have - or + decay?
Reaction EnergeticsReaction reactants and products
If E is positive: reaction exothermic
releases energyIf E is negative, reaction endothermic
requires energyEndoergic and exoergic is sometimes used
A + B C + D + E
The Energy Released (or consumed), Q
Change in BE:
Or since BE is related to mass defect
Change in M:
A + B C + D + E
( )C D A BQ BE BE BE BE BE
( )A B C DQ M M M M M
Preferred!because we have table B.1.
Remember: The Equation Has to Be BALANCED!
Please remember…
BALANCE!
Before starting to work
Balancing Reactions
nucleons 1 +16 = 16+1Charges
01n 8
16O 716N1
1p
1 16 16 0 10 8 7 1 1
1 16 16 10 8 7 1
n O N e p or
n O N H
(+) 0 + 8 = 7 + 1(-) -0 -8 = -7 -0 e- missing
0 1So in reality the reaction is:
Calculating Q…
Q-value for the reaction is:
Using atomic mass tables:
1 16 16 10 8 7 1n O N H
( )1.008665 15.994915 16.006101 1.007825 0.010346 amu
931.494 MeV 0.010346 amu 9.637 MeV1 amu
A B C DM M M M MM
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?
11 5.5 M
eV
4.5 MeV
3 MeV
6.5 MeV
85 MeV
14%
0%7%
79%
0%
1 9 101 4 5p Be B
1. 5.5 MeV2. 4.5 MeV3. 3 MeV4. 6.5 MeV5. 85 MeV
For clicker
1 9 101 4 5
(1.007825 9.012182 10.012937) 931.494 6.586H Be BQ MeV
13
Excited NucleiMany reactions involve excited nucleiSometimes long lived states (isomers)Excitation energy has to be added to the mass of the excited nuclei when calculating Q
e.g. The mass of 22Ne* at 1274 MeV is:
M ZAX * M Z
AX E *
c 2
22 2210 10*
1amu* 21.991386 1274 MeV 23.3591 amu931.494MeVNe Ne
M M
14
Decay SeriesThe radioactive minerals contain many nuclidesAll 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 232ThU has two long lived 235U, 238U
Series identified by relation Parent to Dauthers mass:
A in multiples of 4
There are 3 natural series
15
16
NoticeBranching
17
18
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)
19
It was there from the beginning… but notice: half life of 237Np is relatively low.
20
Main Radioactive Decay Modes (Table 5.1 -page 89-Shultis)
Decay Type Description EmissionGamma ()
Decay of excited nucleusGamma photon
alpha ()Alpha particle is emitted
Alpha particle
negatron (-) np++e-+ Electron and anti-neutrino
positron (β+) p+n+e++ Positron and neutrino
Electron Capture (EC)
Orbital e- absorbed: p++e-n +
Neutrino
proton (p) Proton ejected Protonneutron (n) Neutron ejected Neutron
Internal Conversion (IC)
Electron (K-Shell) ejected*
Electron
Spontaneous Fission
(sf)
Fission fragments
*A AZ ZP P
1A AZ ZP D
42
A AZ ZP D
1A AZ ZP D
*1
A AZ ZP e D
*A AZ ZP P e
1 2 nAZ P D D x
Comments:, +, - are common modes of decayLong T1/2 usually are -emittersn, 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
Modes of Decay, +, - are common modes of decayLong T1/2 usually are -emittersn, 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
Solving momentum and KE equations
2 11 2
1 2 1 2
m mKE Q KE Qm m m m
Remember the conditions:1. Parent nucleus at rest (usually the case)2. Binary products only (not -decay, but OK to
Emax)3. Calculate the correct Q (excited states are
prevalent, and balance)4. Finally, there usually reaction paths with
many outcomes, therefore multiple Q-values
24
Kinetic Energy of Radioactive Decay ProductsParent 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).
m1v1=m2v2
Q=½ m1v12
+ ½ m2v22
What is the energy of emitted particle? (it is what we measure)
v1
m2
v2
m1m1
m2
Original atom that will split in 2 pieces
25
Kinematics of radioactive decay…2 2
1 1 2 2 1 1 2 2
2 21
1
2 22 21 2 2
1
2 22 22 2
2 2 2 2 21
22 2 2
1
2
1 1m v =m v Q= m v m v2 2
m vv = replacing...m
m v1 1m ( ) m v2 m 2
m v1 1 1m v and replacing m v by KE2 m 2 2m solving for KEm
Q
Q
Q KE KE
KE Q
1 21
1 2 1 2
similarly: m mKE Qm m m m
Notice 2:1
Warm up:What % of the energy should go to the -particle?
26
98% 2%50%
10% 1%
20% 20% 20%20%20%
HeThU 42
23490
23892
1 22 1
1 2 1 2
m mKE Q KE Qm m m m
1. 98%2. 2%3. 50%4. 10%5. 1%
Example of -spectroscopy?
27
237Pa 237U
237Np 237Pu
237Am 237Cm
0% 0% 0%0%0%
100%241 ?Am
1. 237Pa2. 237U3. 237Np4. 237Pu5. 237Am6. 237Cm
Find Q for:
28 3.638 M
eV
4.638 MeV
5.638 MeV
6.638 MeV
7.638 MeV
20% 20% 20%20%20%
241 237 495 93 2Am Np He
1. 3.638 MeV2. 4.638 MeV3. 5.638 MeV4. 6.638 MeV5. 7.638 MeV
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)
30 0.09 M
eV
0.98 MeV
5.54 MeV
5.64 MeV
25% 25%25%25%
1. 0.09 MeV2. 0.98 MeV3. 5.54 MeV4. 5.64 MeV
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 241AmThere are actually 6 alpha peaksLast two peaks are too close to be resolvedNotice frequencies (%’s)Every decay path happens all the time but not with equal probabilityLook in your book:
Page 578. 241AmTaken from J. K. Beling, et al. Phys. Rev. 87 (1952) 670-671
35
Diagram means:
Energy of the -particle?
Same old same old
But Q is different each time
24195
*170 KeV
24195
*114 KeV
24195
*71 KeV
24195
*43 KeV
24195
*11 KeV
24195
237 * 493 2
237 * 493 2
237 * 493 2
237 * 493 2
237 * 493 2
237 493 2
Am
Am
Am
Am
Am
Am
Np He
Np He
Np He
Np He
Np He
Np He
2
mKE Qm m
36
3.6
37
38
4.0
By the wayNotice also
39
4.0
There are a lot more hard to see peaks
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
45
’s
’s
46
Main Radioactive Decay Modes (Table 5.1 -page 89-Shultis)
Decay Type Description EmissionGamma ()
Decay of excited nucleusGamma photon
alpha ()Alpha particle is emitted
Alpha particle
negatron (-) np++e-+ Electron and anti-neutrino
positron (β+) p+n+e++ Positron and neutrino
Electron Capture (EC)
Orbital e- absorbed: p++e-n +
Neutrino
proton (p) Proton ejected Protonneutron (n) Neutron ejected Neutron
Internal Conversion (IC)
Electron (K-Shell) ejected*
Electron
Spontaneous Fission
(sf)
Fission fragments
*A AZ ZP P
1A AZ ZP D
42
A AZ ZP D
1A AZ ZP D
*1
A AZ ZP e D
*A AZ ZP P e
1 2 nAZ P D D x
Top Related