Atomic Mass and Nuclear Size - UNSOLVED PRACTICE SET
Chapter: Nuclei | Topic: Atomic Mass and Nuclear Size
ATOMIC MASS AND NUCLEAR SIZE - UNSOLVED PRACTICE SET
Topic: Atomic Mass and Nuclear Size
Multiple Choice Questions
Q1. The atomic mass unit (u) is defined as:
- The mass of one proton
- 1/12th the mass of a carbon-12 atom
- The mass of one neutron
- The mass of one hydrogen atom
Q2. The empirical relation for the radius of a nucleus is:
- R = R₀A
- R = R₀A^(1/3)
- R = R₀A²
- R = R₀/A^(1/3)
Q3. The value of R₀ in the nuclear radius formula is approximately:
- 1.2 × 10⁻¹⁵ m
- 1.2 × 10⁻¹⁰ m
- 1.2 × 10⁻⁸ m
- 1.2 × 10⁻² m
Q4. The volume of a nucleus is proportional to:
- A
- A²
- A³
- A^(1/3)
Q5. Isotopes of an element have:
- Same number of protons but different number of neutrons
- Same number of neutrons but different number of protons
- Same number of both protons and neutrons
- Different number of both protons and neutrons
Q6. The mass number A of a nucleus is equal to:
- The number of protons only
- The number of neutrons only
- The total number of protons and neutrons
- The number of electrons
Short Answer Questions
Q7. Define atomic mass unit (u). Express it in kilograms and in MeV/c².
Q8. Write the empirical formula for nuclear radius and explain the meaning of each term.
Q9. The radius of a nucleus of mass number 27 is 3.6 fm. Calculate the radius of a nucleus of mass number 125.
Q10. Why is the electron not considered when calculating the mass of a nucleus?
Q11. What are isotopes, isobars, and isotones? Give one example of each.
Q12. How does Rutherford's alpha scattering experiment provide an estimate of nuclear size?
Long Answer Questions
Q13. Explain how the size of the nucleus is determined experimentally. Discuss the empirical relation for nuclear radius and show that nuclear volume is proportional to the mass number.
Q14. Describe the composition of the nucleus in terms of protons and neutrons. Explain the terms mass number, atomic number, and how they relate to the notation ᴬZX.
Q15. Discuss the methods used to measure nuclear size. How does electron scattering differ from alpha particle scattering in providing information about nuclear structure?
Numerical & Application-based Problems
Q16. The radius of a gold nucleus (¹⁹⁷Au) is approximately 7.0 fm.
(a) Calculate the value of R₀ using the empirical formula.
(b) Calculate the radius of an oxygen nucleus (¹⁶O).
(c) Calculate the ratio of the nuclear volume of gold to that of oxygen.
(d) Compare the nuclear radius of gold with the radius of a gold atom (approximately 1.35 Å).
Q17. A nucleus has a mass number of 64.
(a) Calculate its radius.
(b) Calculate its volume.
(c) If the mass of this nucleus is 63.5 u, calculate the nuclear density.
(d) Compare this density with the density of ordinary matter.
Q18. In your school's physics lab, a student is studying nuclear sizes using models and calculations.
(a) She makes a scale model where the nucleus of a hydrogen atom is represented by a ball of diameter 2 cm. If the actual diameter of a hydrogen atom is about 10⁻¹⁰ m and the nuclear diameter is about 2 × 10⁻¹⁵ m, calculate the diameter of the ball representing the atom in her model.
(b) The student then calculates the radius of a uranium-238 nucleus. Given R₀ = 1.2 fm, calculate this radius and express it in metres.
(c) She learns that protons and neutrons have approximately the same mass (about 1.67 × 10⁻²⁷ kg). Calculate the approximate mass of the uranium-238 nucleus and express it in atomic mass units.
(d) A classmate argues that since the nucleus is so small, it contributes very little to the atom's mass. Explain why this is incorrect and calculate what fraction of the hydrogen atom's mass is in its nucleus.
(e) In medical applications like PET scans, doctors need to know the precise mass of radioactive isotopes. Explain why knowing the exact nuclear mass (not just the mass number) is important for calculating energy released in nuclear reactions.