3.8.1.4-5 Nuclear instability and Nuclear radius Flashcards
When can a nucleus be unstable?
If it has;
- too many neutrons
- too many protons
- too many nucleons
- too much energy
Describe the NZ graph
Neutron number against proton number.
Line of stability
Beta - emitters above the line
Beta + emitters under the line
Alpha emitters towards the top of the line
For light isotopes Z<20
All nuclei tend to be stable
Follow a straight line, N=Z
For heavy isotopes Z>20
Neutron to proton ratio decreases
Stable nuclei have more neutrons than protons
Why is the imbalance in the neutron to proton ratio significant to the stability of nuclei?
Nucleons are bound by the strong nuclear force.
At longer ranges, the em force acts between protons, so more protons cause more instability.
Therefore, as mot protons are added to the nucleus, more neutrons are needed to add distance between protons to reduce electrostatic repulsion.
The extra neutrons increase the amount of binding force, which helps bind the nucleons together
Where are alpha emitters found on the NZ graph?
Beneath the line of stability when z>60 where there are too many nucleons in the nucleus. They have more protons than neutrons, but are too large to be stable,
because the strong nuclear force between nucleons is unable to overcome the electrostatic force of repulsion between protons
Where does electron capture occur on the NZ graph?
A proton in the nucleus is converted into a neutron, releasing a gamma ray and electron neutrino.
Occurs to the right of the stability line where nuclei are proton rich.
What is a nuclear excited state?
The emission of remaining energy after an alpha or beta decay in the form of a gamma photon happens when a daughter nucleus is in an excited state after a decay.
The state is usually short lived and the nucleus quickly moves to its ground state.
What is an application of excited nuclear states?
Tc99m is a gamma source in medical diagnosis.
m stands for metastable - meaning the nucleus exists in a particularly excited state.
Mo-99 -> Tc-99m + β- + ve(anti)
Tc-99m -> Tc-99 + γ
The half-life of molybdenum is 66 hours, which is long enough to be transported to hospitals.
Tc-99 has a short half life of 6 hours, which is an adequate time frame for examining a patient, and short enough to minimise damage to patient.
What are the methods used to calculate nuclear radius?
Closest approach method
Electron diffraction
Describe the closest approach method
At the point of closest approach, the repulsive force reduces the speed of alpha particles to zero momentarily, where Ek = Ep. The radius of closest approach can be found by equating the initial kinetic energy to the electric potential energy.
What are the advantages of the closest approach method?
Good estimate of the upper limit for a nuclear radius.
Maths is simple
Alpha particles are scattered by protons and not all the nucleons that make up the nucleus.
What are the disadvantages of the closest approach method?
Method does not give an accurate value as it will always be an overestimate.
Alpha particles are hadrons, so when they get close to the nucleus they are affected by the strong nuclear force so the mathematics does not account for this.
Gold nucleus will recoil as the alpha particle approaches.
Difficult to obtain alpha particles with a rebound of exactly 180 degrees.
Alpha particles in the beam must all have the exact same kinetic energy
Sample must be thin to prevent multiple scattering.
Describe the electron diffraction method
Electron accelerated to the speed of light have wave-like properties such as the ability to diffract and have a de Broglie wavelength;
λ=h/mv
The diffraction pattern forms a central bright spot with dimmer concentric circles around it. The graph of intensity against diffraction angle can be used to find the diffraction angle of the first minimum.
Nuclear radius is determined by;
Sin theta = 1.22λ/2R
What are the advantages of the electron diffraction method?
Much more accurate than closest approach
Direct measurement of nuclear radius
Electrons are leptons, so do not interact with the nucleons in the nucleus through the strong nuclear force
What are the disadvantages of electron diffraction?
Electrons must be accelerated to very high speeds to minimise de Broglie wavelength and increase resolution (significant diffraction takes place when the electron wavelength is similar to nuclear diameter)
Electrons can be scattered by both neutrons and protons (excessive amount of scattering means the first minimum of the diffraction pattern is difficult to determine)
What does the nuclear radius against nucleon number graph look like?
Graph starts steep at the origin
Gradient gradually decreases to almost horizontal
Hence;
As more nucleons are added to a nucleus, the nucleus gets bigger. However, the number of nucleons A is not proportional to size r
What is the relationship between nuclear radius and nucleon number?
R=R_0A^1/3
R = nuclear radius
A = nucleon/mass number
R_0 = constant of proportionality = 1.05 fm
- can be plotted as a y=mx+c graph
What is the derivation of the density of a nucleus equation?
V = 4/3πR^3
R = R_0A^1/3
Hence volume = 4/3π(R_0A^1/3)^3
m=Au (mass number*atomic mass unit)
density = Au/(4/3π(R_0A^1/3)^3)
- A cancels
Hence ρ = 3u/4πR_0^3
What are the properties of the density of the nucleus?
Constant - shows that nucleons are evenly separated throughout the nucleus regardless of their size
Independent of the radius
What does the accuracy of nuclear density depend on?
The accuracy of the constant R_0
What does the nuclear density being significantly larger than atomic density suggest?
Majority of the atom’s mass is contained in the nucleus.
Nucleus is very small compared to the atom.
Atoms are predominantly empty space.
