3. Nuclear Masses Flashcards
(32 cards)
Z
- proton number / atomic number
- determines the place of an element in the periodic table
N
-neutron number
A
-mass number or nucleon number
A = Z + N
Nuclide
Definition
-a specific set of numbers Z, N, A determines a nuclide
Isobar
Definition
-nuclides with the same mass number, A, are isobars
Isotope
Definition
-nuclides with the same proton/atomic number, Z, are isotopes
Isotone
Definition
-nuclides with the same neutron number, N, are isotones
Why is this formula for nuclear mass incorrect?
M = Zmp + Nmn
-due to the strong force, we cannot simply calculate the nuclear mass in this way as the binding energy makes a large contribution
Nuclide Map
- a plot of neutron number N on the x axis and proton number Z on the y axis
- there is a line that is most stable and a region of lower stability but where nuclides can still exist, this is known as the valley of stability
- outside of this nuclides are so unstable that they cannot exist
- to decay a nuclide needs to transition to one of slightly lower mass close to it on the nuclide map
- i.e. if a nuclide is surrounded by higher mass nuclides on the map then it won’t decay
Binding Energy
Definition
-the energy required to release a nucleon from the nucleus
Eb = ∫ F ds
-where the integral is taken from the nuclear radius r to infinity
Nuclear Mass
Equation
M = Zmp + Nmn - Eb/c²
Binding Energy vs Ionisation Energy
- Eb accounts for around 1% of the nuclear mass
- comparing with the analogous electron ionisation energy:
- electron ionisation energy accounts for only ~10^(-9)% of the atomic mass
- it is clear that binding energy contributes a much more significant percentage and whilst we may be able to omit ionisation energy from atomic mass calculations, we must account for binding energy in nuclear mass calculations
Mass Defect
m = Eb / c²
Finding Binding Energy Experimentally
- found by measuring nuclear mass
- atomic masses may be measured by deflecting ions in electric and magnetic fields
- an ion in such a field follows a curved path with a particular radius of curvature
- |E gives re which is related to kinetic energy and |V give rmag which is related to momentum, from these we can determine mass
Mass Spectrometry
- particles pass through electric and magnetic fields on a curved path
- the radius of curvature is determined by energy for the electric field and momentum for the magnetic field
- the fields are tuned so that only particles of a particular mass will reach the detector
Atomic Mass Unit
-we measure atomic masses relative to the reference mass (12,6)C, carbon 12
-we define the atomic mass unit, where M is the mass of carbon 12, as:
1u = 1/12 M
1u = 1.66 x 10^(-27) kg
1u = 931.5 Me²/c²
When can’t mass spectrometry be used?
- for mass spectrometry to be useful, the nuclide must survive the journey through the instrument
- this method is unsuitable for very unstable short-lived nuclides
Q Value
Definition
-the change in binding energy before and after a collision event
-e.g. A + B -> C + D
Q = (mA+mB)c² - (mC+mD)c²
-this turns out to also be equivalent to the change in kinetic energy of the nuclides:
Q = EkC + EkD - EkA EkB
Q Values and Types of Reaction
-Q is defined such that:
Q>0 => exothermic reation
Q<0 => endothermic reaction
Q=0 => elastic collision
Nuclear Reactions and Calculating Mass
- if we know all the quantities in a reaction apart from one mass i.e. kinetic energies of all particles and mass of all except one, then we can calculate the unknown mass
- this is an alternative method to mass spectrometry
Q Value and Photon Energy
-as well as kinetic energy of the nuclides, the energy released can also be in the form of a photon
-Q is then a combination of photon energy and kinetic energy or recoil
-e.g. A -> B + γ
A + B -> C +γ
-in the centre of mass frame we have ptotal=0 so by conservation of momentum;
|mv| = |Eγ/c|
m²v² = Eγ²/c²
1/2mv² = Eγ²/2mc²
-where Eγ is the photon energy and m is the nuclide mass
-often Eγ<
Features of the Nuclear Binding Energy Graph
- plot nucleon number, A on the x axis and binding energy per nucleon Eb/A on the y axis
- gradual decrease in binding energy for large A
- peaks at regular intervals corresponding to sets of 4 nucleons (2xP & 2xN)
- low binding energy for small A
Liquid Drop Model
Description
- it is known from experiment that charge density of the nucleus is very uniform, adding more nucleons results in increased volume not density
- the forces inside the nucleus are very short range, SNF only effects closest neighbouring nucleons
- thus we can model the nucleus as a drop of liquid being pulled by its surface tension into a spherical shape
List the 5 contributions to binding energy in the liquid drop model
1) the volume term
2) the surface term
3) the coulomb term
4) the asymmetry term
5) the pairing term
