8.3 - Nuclear Instability & Radius Flashcards
What are more stable, lighter or heavier elements?
Lighter.
Z < 20
What are 4 things that will make a nucleus unstable?
- too many neutrons
- too many protons
- too many nucleons
- too much energy
On an N against Z graph, what proves the sample is an alpha emitter?
- Occur beneath the line of stability when Z > 60 (too many nucleons)
- Number of protons > number of neutrons
- strong force between nucleons is unable to overcome the electrostatic force of repulsion between the protons
On an N against Z graph, what proves the sample is a beta-minus emitter?
- Occur to the left of the stability line where isotopes are neutron-rich
- Neutron is converted to a proton
On an N against Z graph, what proves the sample is a beta-plus emitter?
- Occur to the right of the stability line where the isotopes are proton-rich
- Proton is converted to a neutron
On an N against Z graph, what proves the sample undergoes electron capture?
- When a nucleus captures one pf its own orbiting electrons
- occurs to the right of the stability line - proton-rich
What is a nuclear excited state?
When an unstable nucleus decays, it may emit remaining energy in the form of a gamma photon. (does not change number of nucleons, just a release of energy)
What is technetium-99m used for? (and what does the m stand for)
- Used as a gamma source in medical diagnoses
- The m stands for metastable - nucleus exists in a particularly stable excited state
What are nuclear energy levels?
The nucleus, like the atom, has discrete energy levels whose location and properties are governed by the rules of quantum mechanics.
When does alpha emission occur?
When there are TOO MANY NUCLEONS in a nucleus.
- too large to be stable as the strong nuclear force between the nucleons is unable to overcome the electrostatic force of repulsion between the protons.
When does Beta-minus emission occur?
- When an atom is neutron rich.
- neutron decays into a proton (+ anti-electron neutrino)
When does Beta-plus emission occur?
- When an atom is proton rich.
- proton decays into neutron (+ electron neutrino)
When does electron capture occur?
- When a nucleus captures one of its own orbiting electrons
- a proton in the nucleus is converted into a neutrino, releasing a gamma-ray (+ electron neutrino)
If a nucleus has too much energy, what does it emit?
Gamma rays.
(often happens after alpha/beta decay as the nucleus often has excess energy)
What does Beta minus emission look like on an N/Z graph?
N - 1
Z + 1
So graphically it will go down to the right diagonally.
What does Beta plus emission look like on an N/Z graph?
N +1
Z - 1
So graphically it will go up and to the left diagonally.
What does alpha emission look like on an N/Z graph?
N - 2
Z - 2
So graphically it goes down and to the left by 2 squares
What does gamma emission look like on an N/Z graph?
There is no change to the nuclear constituents in gamma emission as its just letting out energy.
How does a nucleus exist in an excited state?
It’s the same as electrons. A system is given additional energy and this causes it to move to an excited state for a short amount of time.
What does the energy level diagram for nuclear reactions look like for alpha decay of uranium?
(Search it up). It moves diagonally to the bottom right.
What are the 2 methods to measure the nuclear radius?
- rutherford scattering (the closest approach method)
- electron scattering
How is Rutherford scattering used to measure the nuclear radius?
- initial kinetic energy of alpha particle = max electric potential energy (closest approach)
- initial Ek = Qq/4πε0r
q = 2e (ALPHA PARTICLE)
Q = 79e (GOLD)
This can then be rearranged for the radius
What does the Rutherford scattering experiment show us about the atom’s structure?
- There must be a positive nucleus as there electrostatic repulsion between the nucleus and alpha particle - (some alpha particles are deflected at great angles)
- atom must be mostly empty space as lots of alpha particles move straight through the gold foil
What is the typical value for a nuclear radius?
1fm (1 x 10^-15)
What are 3 advantages of the closest approach method?
- good estimate of the upper limit for a nuclear radius
- maths simple
- alpha particles only scatter by protons (not nucleons).
What are 4 disadvantages to the closest approach method?
Always an overestimate of radius (as it measures the smallest separation not the radius):
- does not account for strong nuclear force effects
- gold nucleus recoils as alpha particle approaches
- very few alpha particles rebound at exactly 180 degrees.
How does electron diffraction estimate the nuclear radius?
- A beam of electrons are directs at a nucleus (thin foil) and they diffract around it
- the pattern formed by this diffraction has a predictable minimum which forms at an angle X to the original direction according to the equation
sinX = λ /d
sinX = angle of the first minimum
λ = de broglie wavelength (h/mv)
d = size of the nucleus
Where is the first minimum of electron diffraction pattern? (after beam of electrons if fired at thin foil)
sinX = 1.22λ /2R
What are is the advantage of electron scattering?
- electron scattering is much more accurate than closest approach (as strong nuclear force is not in play)
What are 2 disadvantages of electron scattering?
- electrons must be accelerated to very high speeds to maximise the resolution
(this is because significant diffraction takes place when the electron wavelength is similar to size of nucleus (λ ∝ 1/v) ) - electrons can be scattered by both protons and neutrons - excessive scattering, difficult to determine first minima
How does intensity vary with angle in electron scattering?
intensity of the maxima decreases as the angle of diffraction increases.
What is the nuclear radius proportional to?
The cube root of the nucleon number
What is the equation to show the relationship between the nuclear radius and the nucleon number?
R = R₀A¹/³
R = nuclear radius
A = nucleon/mass number
R₀ = constant of proportionality = 1.05fm
Make the equation for the relationship between nuclear radius and nucleon number into a straight line graph?
lnR = ln(R₀A¹/³)
lnR = lnR₀ + lnA¹/³
lnR = lnR₀ + 1/3lnA
y = c + mx
m = 1/3
y = lnR
x = lnA
c = lnR₀
what is the mass of the nucleus equal to?
m = Au
A = mass number
u = atomic mass unit - 1u = 1.661x10^-27
How can you prove that all nuclei have a similar density?
p = m/v = A x m(of nucleon) / 4/3πR³ = A x m(of nucleon / 4/3π(R₀A¹/³)³ = 3m(of nucleon)/ 4πR₀³ = constant
What is the density of a nucleus?
p = 3u/4πR₀³
