Nuclear stability and liquid drop model Flashcards
What is binding energy?
The energy is required to separate the nucleus into its constituent protons and neutrons.
What is mass defect
Mass difference between nucleus and constituent protons and neutrons
Binding energy equation
B = [Z(mass of protons) + N(mass of neutrons) − M(nuclear)]c^2
Nucleus radius equation
R = R(radius of individual nucleons) *(A= number of nucleons)^(1/3)
The binding energy for heavier nuclei?
constant for atoms of Z> 60
B ∝ A - indicating nucleons only interact with nearest neighbours
Why is the description of nuclear stability incomplete with the current model?
The model doesn’t account for the fact that isotopes of hydrogen (Z = 1) do not have arbitrarily large numbers of neutrons.
What term is introduced to encourage nuclei to have approximately equal numbers of protons and neutrons?
The asymmetry energy term
Ba = −a[(A-2Z)^2 /a]
is introduced.
What is the physical origin of the asymmetry term in nuclear stability?
The asymmetry term arises from considering nucleons as occupying energy levels in a potential well, where protons and neutrons obey the Pauli exclusion principle.
How does the asymmetry term contribute to the binding energy?
The asymmetry term contributes to the binding energy by favoring nuclei with approximately equal numbers of protons and neutrons, with the term proportional to
(N−Z) ^2
.
How does the energy level spacing relate to the asymmetry term?
The energy level spacing varies as
A ^(−1), resulting in the asymmetry term being proportional to
[(N−Z) ^2]/2
What is the energy difference between isobars due to asymmetry?
The energy difference between isobars due to asymmetry is given by
ΔE= [ϵ (N−Z)^2]/8
ϵ is the energy level spacing.
What term is introduced to account for the stability of nuclei with pairs of protons and neutrons?
The pairing energy term
Bp = (±,0)a(A^3/4) is introduced, where Bp
is positive for even-even nuclei, 0 for even-odd and odd-even nuclei, and negative for odd-odd nuclei.
How does the pairing term affect the stability of nuclei?
Nuclei with pairs of protons and neutrons (even-even) are the most stable, and the pairing of nuclei becomes less important for heavier nuclei.
What does the (±, 0) notation for the pairing term signify?
It denotes: + for even Z, even N; 0 for even Z, odd N or odd Z, even N; and - for odd Z, odd N.
What is a common misunderstanding regarding the pairing term?
A common misunderstanding is misinterpreting the notation; it’s crucial to understand that the pairing term can be positive, zero, or negative depending on the combination of even and odd protons and neutrons.
