4.6 binding energy
TRANSCRIPT
Syllabus points Einstein’s mass/energy relationship relates the binding energy of a
nucleus to its mass defect
This includes the applying the relationship:∆𝐸 = ∆𝑚𝑐2
Einstein’s mass/energy relationship also applies to all energy changes and enables the energy released in nuclear reactions to be determined from the mass change in the reaction
Learning goals Define:
Mass-energy equivalence Mass defect Binding energy
Identify that stability is measured by the amount of binding energy emitted per nucleon
Use and rearrange ∆𝐸 = ∆𝑚𝑐2 to solve problems Identify that daughter products of decay have less mass because energy
has been emitted Analyse a nuclear equation to determine the mass defect and the binding
energy emission (or absorption) Calculate the amount of energy liberated by different nuclear processes Give the SI units for: energy, mass
Mass defect – Getting Started
What is the atomic weight of a Helium-4 Atom? (Google it)
What is the sum of all the parts of the Helium-4 atom? (ignore those pesky electrons)
Mass defect The total mass of a stable nucleus is always less than the sum of the
masses of its separate protons and neutrons
Mass defect = the difference between the mass of the nucleus and the sum of the masses of its parts
Example 1Calculate the mass defect of the Carbon-12 atom
Particle Mass (u)
Carbon-12 12
Proton/Neutron 1.006024
Example 1
Calculate the mass defect of the Carbon-12 atom
Particle Mass (u)
Carbon-12 12
Proton/Neutron 1.006024
Mass Defect
Mass defect is the difference between the mass of the atom and the sum of the masses of its constituent parts
This “missing” mass represents the binding energy of an atom
This principle is known as the mass-energy equivalence
Binding energy is the energy equivalent of the mass defect. Which can be calculated by Einstein's formula…
E = m c 2
Energy ( J )
Mass ( Kg )
Speed of Light( m/s )
Some Equation You’ve Probably never heard of…
Calculating Binding energy After finding the mass defect there are two ways to
calculate the binding energy, it depends on what units your are using (but both methods will give you the same answer)
If your mass defect is in atomic mass units (u) then:
1𝑢 = 931 𝑀𝑒𝑉
If your mass defect is in kilograms (kg) then:
∆𝐸 = ∆𝑚𝑐2
Example 2
Calculate the binding energy of the Carbon-12 atom in MeV.
(Remember from Example 1: ∆𝑚 = 0.072288 u)
Example 2
Calculate the binding energy of the Carbon-12 atom in MeV.
(Remember from Example 1: ∆𝑚 = 0.072288 u)
Example 3
Calculate the binding energy of the Carbon-12 atom (this time using the kilogram approach).
(Remember from Example 1: ∆𝑚 = 0.072288 u)
Example 3Calculate the binding energy of the Carbon-12 atom (this time using the kilogram approach).(Remember from Example 1: ∆𝑚 = 0.072288 u)
Bonus: Calculate the Binding Energy Per Nucleon
Binding Energy Per Nucleon
Fission
Fusion
ResourcesFurther Reading Nuclear Energy -
http://www.mpoweruk.com/nuclear_theory.htm Mass-energy equivalence -
http://www.aplusphysics.com/courses/honors/modern/mass-energy.html
Mass-energy equivalence -http://plato.stanford.edu/entries/equivME/
Nuclear Mass and Energy -http://www.launc.tased.edu.au/online/sciences/physics/massener.html
AV Khan Academy – Mass defect and binding energy (11:27)
How did you go? Define:
Mass-energy equivalence
Mass defect
Binding energy
Identify that stability is measured by the amount of binding energy emitted per nucleon
Use and rearrange ∆𝐸 = ∆𝑚𝑐2 to solve problems
Identify that daughter products of decay have less mass because energy has been emitted
Analyse a nuclear equation to determine the mass defect and the binding energy emission (or absorption)
Calculate the amount of energy liberated by different nuclear processes
Give the SI units for: energy, mass