State de Broglie's duality principle. Describe the experiment which led to its direct experimental verification.

Write down Schrodinger's time independent wave equation for matter wave. Calculate energy levels of a particle confined in an infinite potential well. Discuss how these results differ from classical results.

Using Schrodinger's time dependent equation, obtain Schrodinger's time independent equation. Hence obtain eigen values of a particle in an infinite potential well.

State Planck's quantum hypothesis. Why is it considered as a radical departure from classical theory?

Cite an example from daily experience where energy changes in steps.

Show that the orbit nearest to the nucleus in a hydrogen atom accommodates one electron wave. Given that the energy of the electron in the orbit is 13.6 eV.

An X-ray photon of wavelength 0.3 AU is scattered through an angle of 45 degrees by a loosely bound electron. Find the wavelength of the scattered photon.

Draw a sketch showing the variation of kinetic energy of electrons with frequency of the incident radiation in a photoelectric effect experiment. Where does the plot intersect the frequency axis? Explain how quantum theory provided satisfactory explanation of the features shown on the plot drawn by you.

What is the potential difference that must be applied to stop the fastest photoelectron emitted by a nickel surface when UV light of 2000 AU wavelength is incident on it? The work function of nickel is 5 eV.

State the expression for Compton shift. Why it is not observable in the visible region of electromagnetic spectrum?

Photoelectric effect is a frequency dependent phenomenon and not an intensity dependent one. Explain.

X-rays of wavelength 1 AU are scattered from a carbon block. The scattered radiation is viewed at right angles to incident direction. Calculate the observed Compton shift. What kinetic energy is imparted to the recoil electron?

Explain deBroglie's concept of matter waves. Give an account of Davission and Germer experiment to show the wavelike character of a beam of electrons.

An electron and a bullet (mass = 50 grams) are travelling with the same velocity of 300 m/sec. Assuming an accuracy of 0.01 percent in velocity measurement, calculate the accuracy in location of their positions. What inference can be drawn from this result?

Photons collide elastically with loosely bound electrons of a Graphite sample. Show that the wavelength shift of the scattered photons depends only on the scattering angle and not on the incident wavelength.

You wish to pick a substance for a potocell operable with visible light. Which of the following substances will you choose? (work function in parenthesis) :
Tantalum (4.2 eV), Barium (2.5 eV), Lithium (2.3 eV).

Why it is impossible for a free electron to completely absorb a photon?

Describe an experiment to show that electrons in motion exhibit wave-like properties.

Discuss the similarities and dis-similarities of matter-waves with electromagnetic waves.

The speed of an electron is measured to be 5000 m/s to an accuracy of 0.003 percent. Find the uncertainty in the determination of the position of this electron.

Does Einstein's theory of photoelectricity, in which light is postulated to be a photon, invalidates Young's interference experiment?

Show how the quantization of angular momentum follows from the concept of matter waves.

The energy required to remove an electron from Sodium is 2.3 eV. Does Sodium show a photoelectric effect for orange light having wavelength 6800 AU.

Why is the wave nature of matter not apparent to our daily observation? Give a suitable example to illustrate the point.

Using uncertainty relation Delta L x Delta (theta) is greater than or equal to h, or otherwise show why the concept of Bohr orbit violet the uncertainty principle? Here symbols have their usual meaning.

Show that the solution of Schrodinger's equation for a particle in an infinite potential well leads to the concept of quantization of energy.

Assume that a fine dust particle having mass of 1 micro gram is confined to move between two rigid walls seperated by 0.1 mm. The speed of the particle is 0.000001 m/s. Use the result of question above to comment on the quantum number associated with this motion. Does this result support the quantization of the energy?