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PHYS3001: Atoms, Photons and Fundamental Particles > 2. Nuclear Stability and the Liquid Drop Model > Flashcards

2. Nuclear Stability and the Liquid Drop Model Flashcards

1
Q

Why does the nucleus have less mass than the sum of individual nucleons?

A

The attractive strong nuclear force

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2
Q

The binding energy is the energy _______ when constituent protons and neutrons are brought together. It can also be thought of as the _______ __________ to separate a nucleus into constituent protons and neutrons.

A

Released
Energy released

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3
Q

What is the mass defect?

A

The mass difference between the mass of individual nucleons and their mass within a nucleus.

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4
Q

The _______ the mass defect, the greater the energy release when constituent nucleons are brought together to form a nucleus.

A

Higher

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5
Q

Give the equation for the nuclear binding energy

A

B = nuclear binding energy
Z = atomic number
m_p = proton mass
N = number of neutrons
m_n = neutron mass
M_N = M_A - Zm_e = nuclear mass of the nucleus ᴬX
c =speed of light

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6
Q

What is the difference between the mass of an atom and the mass of the constituent nucleus and electrons?

A

The sum of the electronic binding energies

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7
Q

Give the equation for the relation between the nuclear mass energy and the atomic mass energy

A

c = speed of light
M_N = nuclear mass
M_A = atomic mass
Z = atomic number
m_e = electron mass
B_i = electronic binding energy of the i-th electron

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8
Q

What is the usual value of electronic binding energies?

A

~ 10-100 keV

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9
Q

What is the usual value of atomic mass energies?

A

~ 1000’s of MeV

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10
Q

Why are electronic binding energies usually ignored?

A

Because they are much smaller than atomic mass energies.

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11
Q

Write the nuclear binding energy equation in terms of the atomic mass

A

B = nuclear binding energy
Z = atomic number
m_p = proton mass
N = number of neutrons
m_n = neutron mass
M_A = atomic mass of the nucleus ᴬX
m_e = electron mass
c =speed of light

[term] = M_N of the nucleus ᴬX

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12
Q

The most stable elements have the _______ binding energy per nucleon.

A

Highest

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13
Q

Describe the shape of the binding energy v. mass number curve

A

Iron is at the peak of the curve so is the most stable.

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14
Q

Give the equation for the volume of a nucleon

A

v = nucleon volume
r0 = radius of nucleon

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15
Q

Give the equation for the volume of a nucleus with A nucleons

A

V = nucleus volume
A = number of nucleons
v = nucleon volume

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16
Q

State the equation that relates the volume of a nucleus to its radius

A

V = nucleus volume
r = nucleus radius

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17
Q

Give the equation that relates the radius of a nucleus to the radius of its constituent nucleons

A

r = nucleus radius
r0 = nucleon radius
A = number of nucleons

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18
Q

What is the experimental value of the radius of a nucleon?

A
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19
Q

What is the Semi-Empirical Binding Energy model?

A

The simplest binding energy model that combines theory and experimental data to fit the binding energy curve. It treats the nucleus as a drop of incompressible fluid.

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20
Q

What are the 5 terms that contribute to the energy of the droplet in the Semi-Empirical Binding Energy model?

A
  • Volume: from short-range (nearest neighbour) interactions
  • Surface: from some nuclei being on the surface
  • Coulomb: from repulsion between charged protons
  • Asymmetry: due to energy levels of nucleus
  • Pairing: from preference of nucleus to have even N and even Z
21
Q

What is the Semi-Empirical Binding Energy volume term?

A

An observation that for all but the lightest nuclei, the binding energy per nucleon (B/A) is approximately constant because the binding energy is proportional to the number of interactions between nuclei (mediated by the strong nuclear force). This means that B is proportional to A.

22
Q

Give the equation for the volume contribution to the Semi-Empirical Binding Energy

A

B_v = volume contribution to binding energy
a1 = constant
A = mass number

23
Q

The volume term causes an ________ in binding energy.

A

Increase

24
Q

The strong nuclear force is a _____ _____ force so it only interacts with its _______ _________. It is also charge ___________.

A

Short-range
Nearest neighbours
Charge independent

25
Q

Describe the B/A against A plot containing only the volume contribution

A
26
Q

What is the Semi-Empirical Binding Energy surface term?

A

Some nuclei are on the surface of the droplet, resulting in a lower binding energy as there are fewer nearest neighbour interactions.

27
Q

Give the equation for the surface contribution to the Semi-Empirical Binding Energy

A

B_s = surface contribution to binding energy
a2 = constant
A = mass number

28
Q

The surface term causes a ________ in binding energy.

A

Decrease

29
Q

Describe the B/A against A plot containing only the volume and surface contributions

A
30
Q

What is the Semi-Empirical Binding Energy coulomb term?

A

Some nuclei are protons with repulsive Coulomb interaction (i.e. they repulse each other). There are Z(Z-1)/2 pairs of protons in a nucleus with an atomic number, Z. Each pair give a negative contribution to the binding energy.

31
Q

Give the equation for the coulomb contribution to the Semi-Empirical Binding Energy

A

B_c = coulomb contribution to binding energy
a3 = constant
Z = atomic number
A = mass number

32
Q

The coulomb term causes a ________ in binding energy.

A

Decrease

33
Q

Describe the B/A against A plot containing only the volume, surface, and coulomb contributions

A
34
Q

What is the Semi-Empirical Binding Energy asymmetry term?

A

The shell model tells us the spacing between energy levels scales as 1/A, meaning that states with N ~ Z are now favoured.

35
Q

What spin do protons and neutrons have?

A

1/2

36
Q

What spin states can protons and neutrons have?

A

Spin up and spin down

37
Q

What are half-integer spin particles known as?

A

Fermions

38
Q

State the Pauli exclusion principle

A

No two IDENTICAL fermions can be in the same quantum state.

39
Q

The state with the _______ energy has an equal number of protons and neutrons.

A

Minimum

40
Q

Give the equation for the energy excess due to a difference between the number of neutrons and the atomic number

A

∆E = energy excess
N = number of neutrons
Z = atomic number
ε = spacing between energy levels

41
Q

Give the equation for the asymmetry contribution to the Semi-Empirical Binding Energy

A

B_a = asymmetric contribution to binding energy
a4 = constant
A = mass number
Z = atomic number

42
Q

The asymmetry term causes a ________ in binding energy.

A

Decrease

43
Q

Describe the B/A against A plot containing only the volume, surface, coulomb, and asymmetry contributions

A
44
Q

What is the Semi-Empirical Binding Energy pairing term?

A

In nature, we observe that nuclei with pairs of protons and pairs of neutrons are the most stable. This ‘pairing effect’ is more important for lighter nuclei.

45
Q

Give the equation for the pairing contribution to the Semi-Empirical Binding Energy

A

B_p = pairing contribution to binding energy
a5 = constant
A = mass number

+ for even Z, even N
0 for even Z, odd N (or vice versa)
- for odd Z, odd N

46
Q

What does the contribution of the pairing term depend on in the Semi-Empirical Binding Energy?

A

The atomic number and the neutron number within the nucleus.

Increase in energy:
+ for even Z, even N

Same energy:
0 for even Z, odd N (or vice versa)

Decrease in energy:
- for odd Z, odd N

47
Q

Describe the B/A against A plot containing the volume, surface, coulomb, asymmetry, and pairing contributions

A
48
Q

What is SEMF?

A

The semi-empirical binding mass formula for nuclear mass. It is the mass-equivalent to the semi-empirical binding energy formula.

49
Q

State the semi-empirical binding mass formula for nuclear mass

A

M_N = nuclear mass
Z = atomic number
m_p = proton mass
A = mass number
a-terms = -B = - binding mass

PHYS3001: Atoms, Photons and Fundamental Particles (11 decks)

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