8.3 - Nuclear Instability & Radius

Question 1

What are more stable, lighter or heavier elements?

Answer 1

Lighter.
Z < 20

Question 2

What are 4 things that will make a nucleus unstable?

Answer 2

• too many neutrons
• too many protons
• too many nucleons
• too much energy

Question 3

On an N against Z graph, what proves the sample is an alpha emitter?

Answer 3

• 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

Question 4

On an N against Z graph, what proves the sample is a beta-minus emitter?

Answer 4

• Occur to the left of the stability line where isotopes are neutron-rich
• Neutron is converted to a proton

Question 5

On an N against Z graph, what proves the sample is a beta-plus emitter?

Answer 5

• Occur to the right of the stability line where the isotopes are proton-rich
• Proton is converted to a neutron

Question 6

On an N against Z graph, what proves the sample undergoes electron capture?

Answer 6

• When a nucleus captures one pf its own orbiting electrons
• occurs to the right of the stability line - proton-rich

Question 7

What is a nuclear excited state?

Answer 7

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)

Question 8

What is technetium-99m used for? (and what does the m stand for)

Answer 8

• Used as a gamma source in medical diagnoses
• The m stands for metastable - nucleus exists in a particularly stable excited state

Question 9

What are nuclear energy levels?

Answer 9

The nucleus, like the atom, has discrete energy levels whose location and properties are governed by the rules of quantum mechanics.

Question 10

When does alpha emission occur?

Answer 10

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.

Question 11

When does Beta-minus emission occur?

Answer 11

• When an atom is neutron rich.
• neutron decays into a proton (+ anti-electron neutrino)

Question 12

When does Beta-plus emission occur?

Answer 12

• When an atom is proton rich.
• proton decays into neutron (+ electron neutrino)

Question 13

When does electron capture occur?

Answer 13

• 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)

Question 14

If a nucleus has too much energy, what does it emit?

Answer 14

Gamma rays.
(often happens after alpha/beta decay as the nucleus often has excess energy)

Question 15

What does Beta minus emission look like on an N/Z graph?

Answer 15

N - 1
Z + 1
So graphically it will go down to the right diagonally.

Question 16

What does Beta plus emission look like on an N/Z graph?

Answer 16

N +1
Z - 1
So graphically it will go up and to the left diagonally.

Question 17

What does alpha emission look like on an N/Z graph?

Answer 17

N - 2
Z - 2
So graphically it goes down and to the left by 2 squares

Question 18

What does gamma emission look like on an N/Z graph?

Answer 18

There is no change to the nuclear constituents in gamma emission as its just letting out energy.

Question 19

How does a nucleus exist in an excited state?

Answer 19

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.

Question 20

What does the energy level diagram for nuclear reactions look like for alpha decay of uranium?

Answer 20

(Search it up). It moves diagonally to the bottom right.

Question 21

What are the 2 methods to measure the nuclear radius?

Answer 21

• rutherford scattering (the closest approach method)
• electron scattering

Question 22

How is Rutherford scattering used to measure the nuclear radius?

Answer 22

• 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

Question 23

What does the Rutherford scattering experiment show us about the atom’s structure?

Answer 23

• 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

Question 24

What is the typical value for a nuclear radius?

Answer 24

1fm (1 x 10^-15)

Question 25

What are 3 advantages of the closest approach method?

Answer 25

• good estimate of the upper limit for a nuclear radius
• maths simple
• alpha particles only scatter by protons (not nucleons).

Question 26

What are 4 disadvantages to the closest approach method?

Answer 26

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.

Question 27

How does electron diffraction estimate the nuclear radius?

Answer 27

• 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

Question 28

Where is the first minimum of electron diffraction pattern? (after beam of electrons if fired at thin foil)

Answer 28

sinX = 1.22λ /2R

Question 29

What are is the advantage of electron scattering?

Answer 29

• electron scattering is much more accurate than closest approach (as strong nuclear force is not in play)

Question 30

What are 2 disadvantages of electron scattering?

Answer 30

• 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

Question 31

How does intensity vary with angle in electron scattering?

Answer 31

intensity of the maxima decreases as the angle of diffraction increases.

Question 32

What is the nuclear radius proportional to?

Answer 32

The cube root of the nucleon number

Question 33

What is the equation to show the relationship between the nuclear radius and the nucleon number?

Answer 33

R = R₀A¹/³
R = nuclear radius
A = nucleon/mass number
R₀ = constant of proportionality = 1.05fm

Question 34

Make the equation for the relationship between nuclear radius and nucleon number into a straight line graph?

Answer 34

lnR = ln(R₀A¹/³)
lnR = lnR₀ + lnA¹/³
lnR = lnR₀ + 1/3lnA
y = c + mx
m = 1/3
y = lnR
x = lnA
c = lnR₀

Question 35

what is the mass of the nucleus equal to?

Answer 35

m = Au
A = mass number
u = atomic mass unit - 1u = 1.661x10^-27

Question 36

How can you prove that all nuclei have a similar density?

Answer 36

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

Question 37

What is the density of a nucleus?

Answer 37

p = 3u/4πR₀³