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?
TOC
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)
C-14, C-12
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
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How many neutrons in U 235? (235 = A) (1)
U is element 92
235 - 92 = 143 neutrons
143
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How many neutrons in Pb 208? (208 = A) (1)
Pb is element 82
208 - 82 = 126 neutrons
126
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How many neutrons in Kr 78? (1)
Kr is element 36
78 - 36 = 42 neutrons
42
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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 (show c = 2.998x108 m/s)
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)
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 14 has a mass of 14.003242 u (p. 1064 in text)
C 14 can be taken apart into:
6 H atoms:
6(1.007825 u) (i.e. 6 p + 6 e)
8 Neutrons:
8(1.008665 u)
Total “taken apart” mass = 6(1.007825 u) + 8(1.008665 u)
Total “taken apart” mass = 14.116270 u
Mass “defect” = 14.11627 u - 14.003242 u = 0.113028 u
0.113028 u - Represents energy needed to take atom apart
Binding energy = (0.113028 u)(931.5 MeV/u) = 105.3 MeV
TOC
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
12? (Z = 6)
C 12 mass = 12.000000 u (duh?)
H = 1.007825 u
Neutron = 1.008665 u
1 u = 931.5 MeV
Atom mass = 12.000000
6H + 6n = 6(1.007825 u) +6(1.008665 u) = 12.09894 u
Binding energy = (12.098940 – 12.000000)931.5 MeV/u
= 92.16 MeV
Binding energy per nucleon:
C 12: 92.16/12 = 7.68 MeV/nucleon
C 14: 105.3/14 = 7.52 MeV/nucleon (less)
92.16 MeV
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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
W