Nuclear Density - UNSOLVED PRACTICE SET
Chapter: Nuclei | Topic: Nuclear Density
NUCLEAR DENSITY - UNSOLVED PRACTICE SET
Topic: Nuclear Density
Multiple Choice Questions
Q1. The density of nuclear matter is approximately:
- 10³ kg/m³
- 10⁶ kg/m³
- 10¹⁷ kg/m³
- 10²⁰ kg/m³
Q2. Nuclear density is:
- Different for different nuclei
- Approximately the same for all nuclei
- Zero for light nuclei
- Infinite for heavy nuclei
Q3. The nuclear density being constant implies that:
- Nucleons are tightly packed like marbles in a bag
- Nucleons are far apart from each other
- The nucleus is mostly empty space
- The nucleus behaves like a gas
Q4. The mass of a nucleon is approximately:
- 1.6 × 10⁻²⁷ kg
- 9.1 × 10⁻³¹ kg
- 1.6 × 10⁻¹⁹ kg
- 1.6 × 10⁻²⁰ kg
Q5. The volume of a nucleus is proportional to:
- The square of the mass number
- The mass number
- The cube root of the mass number
- The inverse of the mass number
Q6. If the mass number of a nucleus is doubled, its density:
- Doubles
- Becomes half
- Remains approximately constant
- Becomes four times
Short Answer Questions
Q7. Show that nuclear density is independent of the mass number A.
Q8. Calculate the approximate density of nuclear matter given that the mass of a nucleon is 1.67 × 10⁻²⁷ kg and the nuclear radius constant R₀ = 1.2 fm.
Q9. Why is nuclear density so much greater than the density of ordinary matter?
Q10. Compare the density of a nucleus with the density of water. By what factor is nuclear density greater?
Q11. What does the constancy of nuclear density tell us about the nature of nuclear forces?
Q12. If the Earth were compressed to nuclear density, what would be its approximate radius? (Mass of Earth = 6 × 10²⁴ kg)
Long Answer Questions
Q13. Derive the expression for nuclear density. Show mathematically that it is approximately constant for all nuclei and calculate its value.
Q14. Explain why nuclear density is approximately the same for all nuclei, from the lightest hydrogen to the heaviest uranium. What does this imply about the structure of the nucleus and the nature of nuclear forces?
Q15. Compare nuclear density with the density of ordinary matter. Discuss the implications of this enormous difference for our understanding of atomic structure and the forces that hold matter together.
Numerical & Application-based Problems
Q16. Calculate the nuclear density for an iron-56 nucleus.
(a) Calculate the radius of the iron-56 nucleus.
(b) Calculate the volume of the nucleus.
(c) Calculate the mass of the nucleus (assume mass = 56 u).
(d) Calculate the density and express it in kg/m³.
Q17. A neutron star has a mass of 2 × 10³⁰ kg and a radius of 10 km.
(a) Calculate the average density of the neutron star.
(b) Compare this with typical nuclear density.
(c) If this neutron star were composed entirely of nuclear matter, what would be its radius?
(d) Explain why neutron stars are sometimes called 'giant nuclei.'
Q18. In your school's science fair, a student creates a demonstration about nuclear density.
(a) She calculates that a teaspoon (5 mL) of nuclear matter would have a mass of about 5 × 10¹² kg. Verify this calculation using the typical nuclear density of 2.3 × 10¹⁷ kg/m³.
(b) She then compares this to real objects: calculate how many Eiffel Towers (mass ≈ 10,000 tonnes each) would be equivalent to the mass of one teaspoon of nuclear matter.
(c) The student explains that if a cricket ball (radius 3.5 cm) were made of nuclear matter, it would be incredibly heavy. Calculate its mass and compare it with the mass of a typical cricket ball (about 160 g).
(d) A classmate asks why nuclear density is so much higher than the density of atoms. Explain using the concept of atomic structure and the relative sizes of nucleus and atom.
(e) In India, research at BARC (Bhabha Atomic Research Centre) involves studying nuclear matter under extreme conditions. Explain why understanding nuclear density is crucial for designing nuclear reactors and predicting the behavior of neutron stars.