9:22 Messages Х NPA Main Exam-2023-24 v2 PDF - 146 KB Page 4 Turn over SPA5302 (2024) SECTION B Answer ONLY TWO questions in Section B Question B1 a) Describe 5 key components of the nuclear force, including a statement of the Pauli Exclu- sion Principle. b) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A) ay A-aɛA²/³ – ac² Z(Z-1) A1/3 A (A-2Z)² A +8(Z, A). [5 marks] Name and state the origin of the first three terms. Name and give a formula for the last term. Give a discussion of the origin of the fourth term in the SEMF. Use a sketch to illustrate the contribution of each of the first 4 terms. [10 marks] c) Using the SEMF show that the neutron separation energy S₁ = B(Z, A) B(Z, A-1) is given approximately by Sav 2as ac 22 + 3A1/3 A² - 4Z² 3 A4/3 - ал A² You may use the approximations Z(Z-1) Z2, A(A-1) A² and (A-1)"A" – nA"-¹, and ignore the pairing term. [5 marks] d) Consider an isobar with A20. Use the formula in part (c) to find the nucleus on this isobar which is only just stable against neutron emission. Open Microsoft 365 (Office) SPA5302 (2024) [5 marks] Page 5
9:22 Messages Х NPA Main Exam-2023-24 v2 PDF - 146 KB Page 4 Turn over SPA5302 (2024) SECTION B Answer ONLY TWO questions in Section B Question B1 a) Describe 5 key components of the nuclear force, including a statement of the Pauli Exclu- sion Principle. b) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is B(Z, A) ay A-aɛA²/³ – ac² Z(Z-1) A1/3 A (A-2Z)² A +8(Z, A). [5 marks] Name and state the origin of the first three terms. Name and give a formula for the last term. Give a discussion of the origin of the fourth term in the SEMF. Use a sketch to illustrate the contribution of each of the first 4 terms. [10 marks] c) Using the SEMF show that the neutron separation energy S₁ = B(Z, A) B(Z, A-1) is given approximately by Sav 2as ac 22 + 3A1/3 A² - 4Z² 3 A4/3 - ал A² You may use the approximations Z(Z-1) Z2, A(A-1) A² and (A-1)"A" – nA"-¹, and ignore the pairing term. [5 marks] d) Consider an isobar with A20. Use the formula in part (c) to find the nucleus on this isobar which is only just stable against neutron emission. Open Microsoft 365 (Office) SPA5302 (2024) [5 marks] Page 5
College Physics
11th Edition
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Х
NPA Main Exam-2023-24 v2
PDF - 146 KB
Page 4
Turn over
SPA5302 (2024)
SECTION B
Answer ONLY TWO questions in Section B
Question B1
a) Describe 5 key components of the nuclear force, including a statement of the Pauli Exclu-
sion Principle.
b) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is
B(Z, A) ay A-aɛA²/³ – ac²
Z(Z-1)
A1/3
A
(A-2Z)²
A
+8(Z, A).
[5 marks]
Name and state the origin of the first three terms. Name and give a formula for the last
term.
Give a discussion of the origin of the fourth term in the SEMF.
Use a sketch to illustrate the contribution of each of the first 4 terms.
[10 marks]
c) Using the SEMF show that the neutron separation energy S₁ = B(Z, A) B(Z, A-1) is
given approximately by
Sav
2as
ac 22
+
3A1/3
A² - 4Z²
3 A4/3
- ал
A²
You may use the approximations Z(Z-1) Z2, A(A-1) A² and (A-1)"A" – nA"-¹,
and ignore the pairing term.
[5 marks]
d) Consider an isobar with A20. Use the formula in part (c) to find the nucleus on this
isobar which is only just stable against neutron emission.
Open Microsoft 365 (Office)
SPA5302 (2024)
[5 marks]
Page 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c0d52ac-ebeb-4643-8051-a3a6486fdce4%2Facb6c3ce-377e-4d14-86f5-e3a8a8f15d55%2Fzoazh8n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9:22
Messages
Х
NPA Main Exam-2023-24 v2
PDF - 146 KB
Page 4
Turn over
SPA5302 (2024)
SECTION B
Answer ONLY TWO questions in Section B
Question B1
a) Describe 5 key components of the nuclear force, including a statement of the Pauli Exclu-
sion Principle.
b) The semi-empirical mass formula (SEMF) for the binding energy of a nucleon is
B(Z, A) ay A-aɛA²/³ – ac²
Z(Z-1)
A1/3
A
(A-2Z)²
A
+8(Z, A).
[5 marks]
Name and state the origin of the first three terms. Name and give a formula for the last
term.
Give a discussion of the origin of the fourth term in the SEMF.
Use a sketch to illustrate the contribution of each of the first 4 terms.
[10 marks]
c) Using the SEMF show that the neutron separation energy S₁ = B(Z, A) B(Z, A-1) is
given approximately by
Sav
2as
ac 22
+
3A1/3
A² - 4Z²
3 A4/3
- ал
A²
You may use the approximations Z(Z-1) Z2, A(A-1) A² and (A-1)"A" – nA"-¹,
and ignore the pairing term.
[5 marks]
d) Consider an isobar with A20. Use the formula in part (c) to find the nucleus on this
isobar which is only just stable against neutron emission.
Open Microsoft 365 (Office)
SPA5302 (2024)
[5 marks]
Page 5
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