Quantum Mechanical Model de Broglie Heisenberg - UNSOLVED PRACTICE SET

Q7. State de Broglie's hypothesis. What is the significance of the de Broglie equation? 

Q8. State Heisenberg's uncertainty principle. Why is this principle significant only for microscopic particles and not for macroscopic objects?

Q9. Why does the wave nature of matter become significant only for subatomic particles and not for everyday objects? 

Q10. What is the physical significance of the de Broglie wavelength? How does it differ for an electron and a proton moving with the same velocity? 

Q11. Your cricket coach throws a ball at you. You can clearly see where the ball is and how fast it's coming. But your chemistry teacher says that if the ball were an electron, you could never know both its exact position and exact speed at the same time. Why does this uncertainty principle not affect your ability to catch the cricket ball? 

Q12. How did the Davisson-Germer experiment confirm the wave nature of electrons?

Q13. Explain de Broglie's hypothesis of matter waves. Derive the de Broglie equation and discuss its physical significance. Why is the wave nature of matter not observable in daily life? How was de Broglie's hypothesis experimentally verified?

Q14. State and explain Heisenberg's uncertainty principle. Derive the mathematical expression. Discuss its implications for:

(a) The concept of definite paths or trajectories of electrons

(b) The Bohr model of the atom

(c) The development of the quantum mechanical model

Why does this principle not affect the motion of planets or cricket balls? 

Q15. A debate arises in your class about whether electrons are particles or waves.

(a) Student A says: "Electrons are particles because they have mass and charge." Student B says: "Electrons are waves because they show diffraction." Who is correct? Explain.

(b) How does the de Broglie wavelength of an electron compare to that of a proton if both are accelerated through the same potential difference?

(c) Heisenberg's principle forced scientists to abandon the idea of well-defined electron orbits. What replaced orbits in the quantum mechanical model?

(d) If an electron were confined to a nucleus of radius 10⁻¹⁵ m, use Heisenberg's principle to show why electrons cannot exist inside the nucleus.

Q16. Calculate the de Broglie wavelength of:

(a) An electron moving with a velocity of 2 × 10⁶ m/s

(b) A cricket ball of mass 150 g moving at 30 m/s

(c) Compare the two wavelengths and explain why the wave nature is significant for the electron but not for the cricket ball.

(Planck's constant h = 6.626 × 10⁻³⁴ J·s, mass of electron = 9.1 × 10⁻³¹ kg)

Q17. An electron is accelerated through a potential difference of 100 V.

(a) Calculate the kinetic energy gained by the electron 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 X-rays (approximately 0.1 nm). What does this comparison suggest?

(Charge on electron = 1.6 × 10⁻¹⁹ C, mass of electron = 9.1 × 10⁻³¹ kg, h = 6.626 × 10⁻³⁴ J·s)

Q18. According to Heisenberg's uncertainty principle, if the uncertainty in the position of an electron is 1 Å (10⁻¹⁰ m):

(a) Calculate the minimum uncertainty in its momentum.

(b) Calculate the minimum uncertainty in its velocity.

(c) If the electron is in the first Bohr orbit (radius = 0.529 Å), is the uncertainty in position smaller or larger than the orbit itself? What does this imply about the concept of a definite orbit?

(d) Repeat the calculation for a dust particle of mass 10⁻⁶ kg with position uncertainty of 10⁻⁶ m. Compare with the electron case.

(h = 6.626 × 10⁻³⁴ J·s, mass of electron = 9.1 × 10⁻³¹ kg)