Rutherfords Model and Alpha Scattering Experiment - UNSOLVED PRACTICE SET
Chapter: Atoms | Topic: Rutherfords Model and Alpha Scattering Experiment
RUTHERFORDS MODEL AND ALPHA SCATTERING EXPERIMENT - UNSOLVED PRACTICE SET
Topic: Rutherfords Model and Alpha Scattering Experiment
Multiple Choice Questions
Q1. In Rutherford's alpha scattering experiment, the source of alpha particles was:
- A radioactive uranium sample
- A radioactive polonium or radium sample
- An X-ray tube
- A cathode ray tube
Q2. The thickness of the gold foil used in Rutherford's experiment was approximately:
- 1 cm
- 1 mm
- 100 nm
- 1 m
Q3. Most alpha particles passed straight through the gold foil, indicating that:
- The atom is a solid sphere
- Most of the atom is empty space
- Alpha particles are not charged
- Gold atoms are very small
Q4. The fact that some alpha particles were scattered at angles greater than 90ยฐ led Rutherford to conclude that:
- The positive charge is spread uniformly
- The positive charge is concentrated in a very small volume (the nucleus)
- Electrons are heavy particles
- Alpha particles are neutral
Q5. According to Rutherford's model, the size of the nucleus is about:
- 10โปยนโฐ m
- 10โปยนโด m to 10โปยนโต m
- 10โปโธ m
- 10โปยฒ m
Q6. The distance of closest approach of an alpha particle to the nucleus is the distance where:
- The alpha particle stops momentarily
- The kinetic energy of the alpha particle is completely converted into electrostatic potential energy
- Both (a) and (b)
- The alpha particle enters the nucleus
Short Answer Questions
Q7. Describe Rutherford's alpha scattering experiment with a labelled diagram.
Q8. What were the three main observations of Rutherford's alpha scattering experiment?
Q9. How did Rutherford's model differ from Thomson's model in terms of the distribution of positive charge?
Q10. Why did Rutherford choose gold foil for his experiment? Why was it made very thin?
Q11. What is the distance of closest approach? Write the expression for it.
Q12. Why did Rutherford's model predict that atoms should emit continuous spectra, contrary to observation?
Long Answer Questions
Q13. Describe Rutherford's alpha scattering experiment in detail. Explain the observations and how they led to the nuclear model of the atom.
Q14. Derive the expression for the distance of closest approach of an alpha particle to a nucleus. Explain the assumptions made and the significance of this distance.
Q15. Discuss the limitations of Rutherford's model. Why could it not explain the stability of the atom and the line spectrum of hydrogen?
Numerical & Application-based Problems
Q16. In Rutherford's experiment, alpha particles of kinetic energy 5 MeV are directed at a gold foil (Z = 79).
(a) Calculate the distance of closest approach for a head-on collision.
(b) Calculate the velocity of the alpha particles.
(c) Estimate the upper limit of the nuclear radius of gold based on this distance of closest approach.
Q17. An alpha particle with kinetic energy 8 MeV is scattered by a silver nucleus (Z = 47).
(a) Calculate the distance of closest approach for a head-on collision.
(b) If the impact parameter is 10โปยนโด m, calculate the scattering angle using the formula cot(ฮธ/2) = 2b/d, where d is the distance of closest approach for head-on collision.
(c) Explain why the actual scattering angle would be different from this calculated value.
Q18. In your school's science fair, a student creates a simulation of Rutherford's alpha scattering experiment.
(a) She uses a steel ball of mass 10 g fired at a speed of 2 m/s towards a heavy magnet representing the nucleus. Explain how this demonstrates the principle of alpha particle scattering, and calculate the kinetic energy of the steel ball.
(b) The student calculates that if the alpha particle has a charge of +2e and the gold nucleus has a charge of +79e, the electrostatic repulsive force at a distance of 10โปยนโด m is enormous. Calculate this force and compare it with the gravitational force between the alpha particle and the gold nucleus at the same distance.
(c) A classmate asks why Rutherford didn't use electrons instead of alpha particles for the scattering experiment. Explain the practical reasons and what would have happened if electrons were used.
(d) The student learns that the Geiger-Marsden experiment (Rutherford's experiment) was conducted in Manchester, England. Explain why this experiment was considered a 'black swan' event in physics โ an unexpected result that overturned established theory.
(e) In modern India, particle accelerators at institutions like BARC and SINP use similar scattering principles to study nuclear structure. Explain how high-energy scattering experiments today build upon Rutherford's original idea but use much higher energies.