• Understand the dual nature of radiation and matter.
• Explain the photoelectric effect and its significance in physics.
• Calculate the work function and threshold frequency for various materials.
• Analyze the relationship between stopping potential and maximum kinetic energy of emitted electrons.
• Apply the concepts of Planck's constant and de Broglie wavelength in problem-solving.

Chapter 11: Dual Nature of Radiation and Matter

11.1 Introduction

• The wave nature of light was established through Maxwell's equations and Hertz's experiments.
• Key discoveries include X-rays by Roentgen (1895) and the electron by J.J. Thomson (1897).
• Discharge tubes showed that electric discharge through gases at low pressure could produce cathode rays.

11.2 Key Concepts

Physical Quantities

11.3 Points to Ponder

1. Free electrons in metals move in a constant potential but require additional energy to escape.
2. Electrons have a distribution of energies at a given temperature, differing from Maxwell's distribution due to Pauli's exclusion principle.
3. The work function is the minimum energy required for an electron to escape the metal.
4. Energy absorption during light-matter interaction occurs in discrete units of hv.
5. The stopping potential's independence of intensity is crucial for distinguishing between wave and photon models of the photoelectric effect.
6. The de Broglie wavelength has physical significance, while phase velocity does not; group velocity equals the particle's velocity.

11.4 Experimental Study of Photoelectric Effect

• Setup: An evacuated glass tube with a photosensitive plate and an anode.
• Process: Monochromatic light strikes the photosensitive plate, emitting electrons collected by the anode.
• Measurements: Current (μA) and potential difference (V) are monitored.

11.5 Observations on Photoelectric Effect

• Maximum kinetic energy of photoelectrons varies linearly with frequency, independent of intensity.
• No emission occurs below the threshold frequency, regardless of intensity.
• Emission starts instantaneously (~10⁻⁹ s) when frequency exceeds the threshold.

11.6 Examples

• Example 11.1: Photon energy and number of photons emitted by a laser.
• Example 11.2: Calculating threshold frequency and wavelength based on work function and stopping potential.

11.7 Exercises

1. Calculate maximum kinetic energy and stopping potential for caesium with given frequency.
2. Determine the threshold frequency and wavelength for various metals and light conditions.