SME
General Chemistry II · Problem type
Nuclear binding energy per nucleon
Use this for “An O-16 atom has a mass of 15.994915 u. Find its binding energy per nucleon.”
Diagram
Oxygen-16: 8 protons, so atomic number Z = 8.
Mass number A = 8 + 8 = 16.
8 electrons: charge 8 − 8 = 0, a neutral atom.
Shells: 2, 6.
This is an example. Type your own values to start a new problem.
Z
Protons
example
N
Neutrons
example
m
Mass of the atom
example · u
Δm
Mass defect
calculated · u
Eb
Binding energy
calculated · MeV
Eb/A
Binding energy per nucleon
calculated · MeV
Formulas
Δm
=
Z
×
1.007825
+
N
×
1.008665
−
m
0.137005 = 8 × 1.007825 + 8 × 1.008665 − 15.994915
Eb = 931.494 × Δm
127.6 = 931.494 × 0.137005
Eb/A
=
Eb
Z
+
N
7.976
=
127.6
8 + 8
Assumptions
•
The mass defect is what the separate protons and neutrons weigh beyond the nucleus they make: that mass became the binding energy.
•
Each proton is counted as an H-1 atom (1.007825 u) so its electron comes along, and the atom’s mass with its electrons can be used.
•
A neutron is 1.008665 u, and 1 u of mass is 931.494 MeV of energy.
•
The picture draws nuclei up to xenon: 54 protons and 90 neutrons.
Step-by-step
WE KNOW
Z = 8, N = 8, m = 15.9949 u
FIND
mass defect (Δm), binding energy (Eb), binding energy per nucleon (Eb/A)
Step 1 · Find mass defect (Δm)
Use Δm = Z × 1.007825 + N × 1.008665 − m
Add up the H-1 atoms and the neutrons apart, then take away what the atom weighs.
Δm = 8 × 1.007825 + 8 × 1.008665 − 15.994915
Δm = 8.0626 + 8.06932 − 15.994915
Δm = 0.137005 u
Step 2 · Find binding energy (Eb)
Use Eb = 931.494 × Δm
Each unit of mass lost is 931.494 MeV of energy.
Eb = 931.494 × 0.137005
Eb = 127.62 MeV
Step 3 · Find binding energy per nucleon (Eb/A)
Use Eb/A = Eb ÷ (Z + N)
Share
the
binding
energy
among
the
A
=
Z
+
N
nucleons.
Eb/A
=
127.62
8 + 8
Eb/A
=
127.62
16
Eb/A = 7.976 MeV
Check
Put the numbers back in. Both sides should match.
0.137005 = 8 × 1.007825 + 8 × 1.008665 − 15.994915 ✓
127.62 = 931.494 × 0.137005 ✓
7.976
=
127.62
8 + 8
✓
Topic check
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