Comprehensive NEET Physics Notes for Dual Nature of Radiation and Matter

Dual Nature of Radiation and Matter

1. Introduction

Maxwell’s equations and Hertz’s experiments in the late 19th century established the wave nature of light. Significant discoveries, such as Roentgen’s X-rays (1895) and J.J. Thomson’s electron (1897), advanced the understanding of atomic structure. Experiments with low-pressure gases in discharge tubes revealed that cathode rays consist of fast-moving negatively charged particles.

Did You Know?

J.J. Thomson won the Nobel Prize in Physics in 1906 for his discovery of the electron.

2. Electron Emission

Metals have free electrons responsible for conductivity, but these electrons cannot escape the metal surface due to the positive pull from the metal ions. The energy required for an electron to escape is called the work function, denoted by $ϕ_{0}$ and measured in electron volts (eV).

Types of Electron Emission:

Thermionic Emission: Electrons gain energy from heat.
Field Emission: Strong electric fields pull electrons out.
Photoelectric Emission: Light of suitable frequency causes electron emission.

Example:

The work function for sodium is 2.75 eV.

3. Photoelectric Effect

3.1 Hertz’s Observations

Heinrich Hertz discovered the photoelectric effect in 1887, observing that ultraviolet light enhanced spark discharge.

3.2 Hallwachs’ and Lenard’s Observations

Wilhelm Hallwachs and Philipp Lenard observed that ultraviolet light causes metals to emit electrons. They discovered the threshold frequency below which no electrons are emitted, regardless of light intensity.

Common Misconception:

Higher intensity light always increases electron energy. In reality, electron energy depends on light frequency, not intensity.

4. Experimental Study of Photoelectric Effect

The experimental setup consists of a photosensitive plate (emitter) and a collector plate in a vacuum tube. Light of varying intensity and frequency is used to study the effect on photoelectric current.

Key Observations:

Effect of Light Intensity: Photoelectric current increases linearly with light intensity.
Effect of Potential: The photocurrent increases with collector potential until it reaches saturation.
Effect of Frequency: The stopping potential depends on light frequency and is independent of intensity.

NEET Tip:

Understand the relationship between stopping potential and light frequency to solve related problems.

5. Einstein’s Photoelectric Equation

Einstein proposed that light consists of quanta (photons) with energy $E = h ν$ . An electron absorbs a photon’s energy, and if this exceeds the work function, it is emitted with kinetic energy:

$K_{max} = h ν - ϕ_{0}$

Implications:

The kinetic energy of photoelectrons is independent of light intensity.
A minimum frequency (threshold frequency) is required for electron emission.

Mnemonic:

"Higher frequency, higher energy" - Photon energy increases with frequency.

6. Wave Nature of Matter

Louis de Broglie proposed that particles have wave-like properties, with wavelength given by:

$λ = \frac{h}{p}$

where $p = m v$ is the momentum of the particle.

Example:

The de Broglie wavelength of an electron moving at $5.4 \times 1 0^{6} m / s$ is approximately $0.135 nm$ .

Concept Connection:

The dual nature of light and matter links to quantum mechanics, explaining phenomena like interference and diffraction for particles.

Practice Questions

Explain the difference between Thomson’s and Rutherford’s atomic models.
Derive the expression for the radius of an electron’s orbit in Bohr’s model.
Calculate the energy of an electron in the n=3 orbit of a hydrogen atom.
Define half-life and calculate the half-life of a substance with a decay constant of $0.693, d a y^{- 1}$ .
Describe the process of nuclear fusion and provide an example.

Answers to Practice Questions

Thomson’s model describes the atom as a positively charged sphere with embedded electrons, whereas Rutherford’s model has a dense nucleus with electrons orbiting around it.
Using Bohr’s quantization condition and Coulomb’s law, the radius of the nth orbit is given by: $r_{n} = \frac{n ^{2} h ^{2}}{4 π ^{2} m e ^{2} ϵ _{0}}$
The energy of an electron in the n=3 orbit is: $E_{3} = - \frac{13.6}{3 ^{2}}, e V = - 1.51, e V$
The half-life is: $T_{1/2} = \frac{0.693}{0.693 , d a y ^{- 1}} = 1, d a y$
Nuclear fusion involves combining light nuclei to form a heavier nucleus. Example: Two hydrogen nuclei fuse to form helium in the sun.

Glossary

Photon: A quantum of light with energy $E = h ν$ .
Work Function: The minimum energy required for electron emission from a metal surface.
Photoelectric Effect: Emission of electrons from a metal when illuminated by light.
Threshold Frequency: The minimum frequency of light required to emit electrons from a metal.
de Broglie Wavelength: The wavelength associated with a moving particle, given by $λ = \frac{h}{p}$ .

Concept Connection

Link to NEET Physics: Quantum Mechanics Understanding the dual nature of radiation and matter is crucial for NEET Physics, as it forms the basis for numerous applications in modern physics and technology.