Nuclear Forces - UNSOLVED PRACTICE SET

Q7. What are nuclear forces? Name two properties that distinguish them from electrostatic forces.

Q8. Why do protons in the nucleus not repel each other and fly apart despite having the same charge?

Q9. Explain the short-range nature of nuclear forces. What happens when nucleons are separated by more than a few femtometres?

Q10. What is meant by the saturation property of nuclear forces? How does this explain the constancy of nuclear density?

Q11. Compare the relative strengths of gravitational force, electrostatic force, and nuclear force between two protons separated by 1 fm.

Q12. Why is the neutron-proton ratio higher in heavy stable nuclei than in light stable nuclei?

Q13. Describe the properties of nuclear forces. Discuss their strength, range, charge independence, spin dependence, and saturation property.

Q14. Explain why nuclear forces must be much stronger than electrostatic repulsion to hold the nucleus together. Calculate the approximate ratio of nuclear force to electrostatic force between two protons at a distance of 1 fm.

Q15. Discuss the role of neutrons in stabilizing the nucleus. Why do light nuclei have approximately equal numbers of protons and neutrons, while heavy nuclei have more neutrons than protons?

Q16. Two protons in a nucleus are separated by a distance of 2 fm.

(a) Calculate the electrostatic repulsive force between them.

(b) Estimate the nuclear attractive force between them if the binding energy per nucleon is about 8 MeV and the range is about 2 fm.

(c) Compare these two forces and explain how the nucleus remains stable.

Q17. In a nucleus of lead-208, there are 82 protons and 126 neutrons.

(a) Calculate the total electrostatic repulsive energy using the formula E = (3/5) × (Ze)²/(4πε₀R).

(b) Given that the total binding energy is about 1636 MeV, estimate the contribution of nuclear forces to the binding energy.

(c) Explain why the presence of 126 neutrons is necessary for the stability of this nucleus.

Q18. In your school's physics exhibition, a student creates a model to explain nuclear forces.

(a) She uses two magnets to represent the attractive nuclear force between nucleons. Explain why this is only a rough analogy and what important properties of nuclear forces it fails to capture.

(b) The student calculates that the gravitational force between two protons at 1 fm is about 10⁻³⁴ N, while the electrostatic force is about 230 N. Calculate the ratio of electrostatic force to gravitational force and explain why gravity is negligible in nuclear physics.

(c) She explains that nuclear forces have a 'hard core' — they become strongly repulsive at distances less than about 0.5 fm. Explain why this hard core is necessary to prevent the nucleus from collapsing to a point.

(d) A classmate asks why we need the concept of exchange particles (like pions) to understand nuclear forces, when we don't need them for gravity or electromagnetism. Explain the significance of Yukawa's meson exchange theory in understanding the short range of nuclear forces.

(e) In particle physics research at institutions like SINP Kolkata and TIFR Mumbai, scientists study quarks and gluons — the constituents of protons and neutrons. Explain how our understanding of nuclear forces has evolved from the simple nucleon-nucleon interaction to the more fundamental strong interaction between quarks.