Nuclear notation and Binding energy
Contents:
•Atomic notation
•Isotopes
•Whiteboard
•Binding Energy
•AMU
•Making an atom
•Calculating binding energy
•Whiteboards
•The curve of binding energy and the strong nuclear force
(or why there is a limit to the periodic table)
Atomic notation
A
Z
12
6
X
C
X = Symbol (C, Au)
A = Atomic Mass Number = #nucleons
(Protons + Neutrons)
Z = Atomic Number = #protons
Carbon A = 12, Z = 6. #neutrons?
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Isotopes
12
6
14
6
C
C
Carbon 12 has 6 Neutrons
Carbon 14 has 8 Neutrons
Carbon 14 is an isotope of Carbon
Chemically the same
Nuclear-lly different (it’s unstable)
TOC
Whiteboards:
Atomic Notation
1|2|3|4|5
TOC
What is the Atomic notation for
tritium? (tritium is an isotope of
Hydrogen with 2 neutrons)
Hydrogen has a Z = 1, A = 1 p + 2 n = 3
3/1 H
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10 protons, 12 neutrons. What is its
atomic notation?
Z = 10, A = 10 + 12 = 22, element 10 is Ne
22/10 Ne
W
How many neutrons in U 235? (235 = A) (1)
U is element 92
235 - 92 = 143 neutrons
143
W
How many neutrons in Pb 208? (208 = A) (1)
Pb is element 82
208 - 82 = 126 neutrons
126
W
How many neutrons in Kr 78? (1)
Kr is element 36
78 - 36 = 42 neutrons
42
W
Binding energy - the energy to take an atom apart
Unified Mass Units: (u)
C 12 (neutral atom) = 12.0000000 u (defined)
1 u = 1.6605 x 10-27 kg = 931.5 MeV
Electron = .00054858 u (not useful)
Proton = 1.007276 u (not useful)
H (neutral atom) = 1.007825 u (very useful)
Neutron = 1.008665 u (very useful)
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Binding energy - the energy to take an atom apart
H (neutral atom) = 1.007825 u (very useful)
Neutron = 1.008665 u (very useful)
1 u = 931.5 MeV
To take an atom apart:
C 12 can be taken apart into:
6 H atoms:
6(1.007825 u) (i.e. 6 p + 6 e)
6 Neutrons:
6(1.008665 u)
Total “taken apart” mass = 6(1.007825 u) + 6(1.008665 u)
Total “taken apart” mass = 12.09894 u
Mass “defect” = 12.09894 u - 12.000000 u = .09894 u
.09894 u - Represents energy needed to take atom apart
Binding energy = (.09894 u)(931.5 MeV/u) = 92.16 MeV
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Binding energy - the energy to take an atom apart
H (neutral atom) = 1.007825 u (very useful)
Neutron = 1.008665 u (very useful)
1 u = 931.5 MeV
Binding energy in general
1. Look neutral atom mass in Appendix F (p 1064)
2. Break atom into H and n
3. Subtract neutral atom mass from taken apart mass
4. Multiply mass defect by 931.5 Mev/u
TOC
Whiteboards:
Binding Energy
1|2|3
TOC
What is the binding energy for
Nitrogen 13? (Z = 7)
N 13 mass = 13.005738 u
H = 1.007825 u
Neutron = 1.008665 u
1 u = 931.5 MeV
Atom mass = 13.005738
7H + 6n = 7(1.007825 u) +6(1.008665 u) = 13.106765 u
Binding energy = (13.106765 - 13.005738)931.5 MeV/u
= 94.11 MeV
94.11 MeV
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What is the binding energy for Carbon
14? (Z = 6)
C 14 mass = 14.003242 u
H = 1.007825 u
Neutron = 1.008665 u
1 u = 931.5 MeV
Atom mass = 14.003242
6H + 8n = 6(1.007825 u) +8(1.008665 u) = 14.11627 u
Binding energy = (14.11627 - 14.003242)931.5 MeV/u
= 105.3 MeV
Binding energy per nucleon:
C 12: 92.16/12 = 7.68 MeV/nucleon
C 14: 105.3/14 = 7.52 MeV/nucleon (less)
105.3 MeV
W
What is the binding energy for
Carbon 10? (Z = 6)
C 10 mass = 10.231610 u
H = 1.007825 u
Neutron = 1.008665 u
1 u = 931.5 MeV
Atom mass = 10.231610
6H + 4n = 6(1.007825 u) +4(1.008665 u) = 10.08161 u
Binding energy = (10.08161 - 10.23161)931.5 MeV/u
= -139.7 MeV (Carbon 10 does not exist)
-139.7
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The curve of binding energy
Binding energy per nucleon
Going to more tightly bound releases energy
Fission - splitting nuclei
Fusion - joining nuclei
Most tightly bound
Fission releases
energy
Fusion releases
energy
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Nuclear Stability
Coulombic force tries to tear apart nucleus
Strong Nuclear force holds it together (force between nucleons)
n p
p p
n p n
Strong Nuclear is very short range
As nucleus gets bigger
•Strong nuclear gets weaker
•Coulombic gets stronger
Neutrons add strong force, don’t repel
Trend with heavier elements
At some point neutrons don’t cut it
The crazy man at UMn
TOC