Quantum mechanics

1. What is the importance of a wave function? How do you represent it? [2]2. Explain blackbody radiation. [2]3. Explain how Quantum mechanics is different from Classical Mechanics. [2]4. Defiine probability density? How can it be calculated? [2]5. Explain Photo electric effect? Arrive at an equation for the same. [2]6. Arrive equations for wavelength of matter waves. [5]7. Explain the Schrödinger’s wave equation for a free particle. [5]8. Derive equation for time dependent Schrödinger equation. [5]9. Derive equation for time independent Schrödinger equation. [5]10. What are the properties of wave function? [2]11. Derive time independent wave equation. [5]12. What are matter waves? How can you prove the existence of them? [2]13. Write any four properties of matter waves? [2]14. State and explain Heisenberg’s uncertainty principle? [2]15. Explain two forms of uncertainty principle? [2]16. What do you mean by eigen value and eigen function? [2]17. Derive an equation for energy of a particle in a box. [5]18. What are expectation values? Write equations for the same. [5]19. Find the de broglie wavelength of an electron travelling at a velocity of 600km/s. [5]20. Find the de broglie wavelength of an electron moving through a potential of 300V. [5]21. If the kinetic energy of the neutron is 0.5eV, calculate its de Broglie wavelength. [5]22. The uncertainity in position of electron inside the nucleus is 10-15 m. Calculate the

uncertainity in momentum of the same. [5]23. The uncertainity in frequency of electron in the excited orbit is of the order of 10-8 s.

Calculate the uncertainity in Energy of the same. [5]24. Calculate the energy of hydrogen atom if the uncertainity in radius of electron orbit of

hydrogen atom is 5.3 x 10-11m.[5]