Wave Nature of Matter de Broglie Hypothesis - UNSOLVED PRACTICE SET
Chapter: Dual Nature of Radiation and Matter | Topic: Wave Nature of Matter de Broglie Hypothesis
WAVE NATURE OF MATTER DE BROGLIE HYPOTHESIS - UNSOLVED PRACTICE SET
Topic: Wave Nature of Matter de Broglie Hypothesis
Multiple Choice Questions
Q1. According to de Broglie's hypothesis, matter exhibits:
- Only particle nature
- Only wave nature
- Both particle and wave nature
- Neither particle nor wave nature
Q2. The de Broglie wavelength associated with a particle of momentum p is:
- ฮป = h/p
- ฮป = p/h
- ฮป = hp
- ฮป = h/pยฒ
Q3. The de Broglie wavelength of an electron accelerated through a potential difference V is proportional to:
- V
- โV
- 1/โV
- 1/V
Q4. For a particle of mass m and kinetic energy K, the de Broglie wavelength is:
- ฮป = h/โ(2mK)
- ฮป = hโ(2mK)
- ฮป = h/(2mK)
- ฮป = hK/โ(2m)
Q5. The de Broglie wavelength of a particle is independent of:
- Its mass
- Its velocity
- Its charge
- The medium through which it moves
Q6. An electron and a proton have the same de Broglie wavelength. Then:
- They have the same momentum
- They have the same kinetic energy
- They have the same velocity
- The proton has greater momentum
Short Answer Questions
Q7. State de Broglie's hypothesis. What is a matter wave?
Q8. Calculate the de Broglie wavelength of an electron moving with a velocity of 10โถ m/s.
Q9. Why is the wave nature of matter not observable in everyday objects like cricket balls
Q10. An electron and a proton are accelerated through the same potential difference. Which one will have a smaller de Broglie wavelength? Give reason.
Q11. What is the significance of de Broglie wavelength in the Bohr model of the atom?
Q12. How does the de Broglie wavelength of a particle change when its kinetic energy is doubled?
Long Answer Questions
Q13. State de Broglie's hypothesis and derive the expression for the de Broglie wavelength of a particle. Show that for an electron accelerated through a potential difference V, ฮป = h/โ(2meV).
Q14. Explain why the wave nature of matter is significant for microscopic particles like electrons but negligible for macroscopic objects. Use numerical examples to support your answer.
Q15. Discuss the dual nature of matter. How does de Broglie's hypothesis provide a physical interpretation for Bohr's quantization condition of angular momentum?
Numerical & Application-based Problems
Q16. An electron is accelerated through a potential difference of 100 V.
(a) Calculate the kinetic energy gained by the electron in eV and in joules.
(b) Calculate the velocity of the electron.
(c) Calculate the de Broglie wavelength of the electron.
(d) Compare this wavelength with the wavelength of visible light (ฮป โ 500 nm).
Q17. A proton and an alpha particle are accelerated through the same potential difference of 1000 V.
(a) Calculate the de Broglie wavelength of the proton.
(b) Calculate the de Broglie wavelength of the alpha particle.
(c) Compare the two wavelengths and explain the result.
(d) Calculate the kinetic energy of each particle in MeV.
Q18. In your school's physics lab, a student is studying the wave nature of matter using an electron beam.
(a) She accelerates electrons through a potential difference of 50 V. Calculate their de Broglie wavelength.
(b) She then wants to produce electrons with a de Broglie wavelength of 0.1 nm (comparable to atomic spacing in crystals). Calculate the accelerating potential required.
(c) The student compares the de Broglie wavelength of a 1 kg cricket ball moving at 10 m/s with that of the electron in part (a). Calculate both wavelengths and explain why we don't observe wave properties of the cricket ball.
(d) A classmate argues that since electrons have wave nature, they should show interference and diffraction like light. Design an experiment (based on real physics) that could demonstrate this, and explain what spacing or dimensions would be needed.
(e) In India, electron microscopes are used in research institutions like IISc Bangalore to image structures at the nanoscale. Explain why electrons with de Broglie wavelength of about 0.01 nm can resolve details much smaller than visible light microscopes.