Generic Elective Physics - II Notes

 Notes on Generic Elective Physics - II

Atomic and Nuclear Physics

Inadequacy of classical physics:

Classical physics, also called Newtonian physics, is a scientific framework that was developed to describe the motion of objects on macroscopic scales. It is highly successful in explaining and predicting the behavior of everyday objects, such as the motion of planets, the behavior of fluids, and the mechanics of solid objects. However, classical physics has certain limitations and fails to adequately describe certain phenomena observed in the natural world. Here are a few areas where classical physics is inadequate:

1.Quantum Mechanics: Classical physics cannot explain the behavior of particles on the atomic and subatomic scale. Quantum mechanics, a branch of physics developed in the early 20th century, provides a more accurate description of the behavior of particles at these scales. Quantum mechanics introduces concepts such as wave-particle duality, superposition, and uncertainty, which are not accounted for in classical physics.

2.Relativity: Classical physics does not incorporate Einstein's theory of relativity, which describes the behavior of objects moving at speeds close to the speed of light or in the presence of strong gravitational fields. Special relativity, developed in 1905, showed that the laws of physics are the same for all observers in uniform motion relative to each other. General relativity, developed in 1915, provided a new understanding of gravity as the curvature of space-time. Classical physics fails to accurately describe phenomena such as time dilation, length contraction, and gravitational lensing, which are central to the theory of relativity.

3.Wave-particle duality: Classical physics treats particles and waves as separate entities. However, experiments such as the double-slit experiment demonstrate that particles like electrons and photons can exhibit both wave-like and particle-like properties. This wave-particle duality is a fundamental aspect of quantum mechanics and is not accounted for in classical physics.

4.Black body radiation and the ultraviolet catastrophe: Classical physics predicts that the intensity of electromagnetic radiation emitted by a black body should increase indefinitely as the frequency increases. This prediction, known as the ultraviolet catastrophe, contradicted experimental observations. It was later resolved by Max Planck's introduction of the quantum concept, which led to the development of quantum mechanics.

5.Anomalous precession of Mercury: Classical physics fails to explain the anomalous precession of the orbit of Mercury. The observed precession did not match the predictions based on classical gravitational theory. It was later explained by Einstein's general theory of relativity, which accounts for the curvature of space-time around massive objects

Black body radiation:

It refers to the electromagnetic radiation emitted by an idealized object called a black body. A black body is an object that absorbs all incident radiation and, in thermal equilibrium, emits radiation at all wavelengths and intensities.

Definition: Black body radiation is the thermal radiation emitted by a black body due to its temperature alone, without any external excitation.


Characteristics: Black body radiation exhibits several important characteristics.

Firstly, it is continuous, meaning it covers a broad range of wavelengths. It is isotropic, meaning the radiation is emitted uniformly in all directions.

Secondly, for a given temperature when λ increases, Eλ also increases, then it attains a maximum for a particular wavelength (λmax) and then decreases.

Thirdly, when temperature increases the maximum (λmax) wavelength decreases.

Next, the intensity of the emitted radiation at different wavelengths follows a specific distribution, known as the Planck's law.

Planck's Law: Max Planck formulated a mathematical expression, known as Planck's law, to describe the spectral distribution of black body radiation. Planck's law states that the intensity of radiation emitted by a black body at a given wavelength is proportional to the wavelength's power and inversely proportional to the temperature of the black body.

Wien's Displacement Law: Wien's displacement law, derived from Planck's law, establishes a relationship between the peak wavelength of the emitted radiation and the temperature of the black body. It states that the peak wavelength is inversely proportional to the temperature.

Mathematically, λmax  α   1/T

Stefan-Boltzmann Law: The Stefan-Boltzmann law, derived from Planck's law, states that the total power radiated by a black body is proportional to the fourth power of its absolute temperature. This law quantifies the total energy emitted by a black body at all wavelengths.

α  T^4                =>  E  =  σ T^4

Applications: Black body radiation has significant implications in various fields. It is a fundamental concept in thermodynamics and quantum physics. It helps explain the temperature dependence of the color of objects and is used in the study of stars, as they closely approximate black bodies.

Rayleigh-Jeans' law:

It was formulated by Lord Rayleigh and Sir James Jeans, is a classical approximation that describes the spectral distribution of the intensity (energy emitted per unit area per unit time) of black body radiation with respect to frequencies or wavelengths.

According to Rayleigh-Jeans' law, the spectral intensity (I) of black body radiation is directly proportional to the square of the frequency (ν) and the temperature (T) of the body. Mathematically, it can be expressed as:

I (ν, T) = (8πν^2kT) / c^3,

where k is the Boltzmann constant and c is the speed of light.

This law suggests that the intensity of black body radiation increases with both frequency and temperature. As the frequency increases, more energy is associated with each oscillating charge within the black body, resulting in a higher intensity. Similarly, as the temperature increases, the average energy of the oscillating charges also increases, leading to an increase in the intensity of radiation.


However, one of the significant implications of Rayleigh-Jeans' law is the prediction of an infinite amount of energy being emitted at high frequencies. This divergence in the prediction is known as the "ultraviolet catastrophe" and is in contrast to the observed experimental results. This discrepancy arises because Rayleigh-Jeans' law fails to account for the quantization of energy and the discrete nature of electromagnetic radiation.

Despite its limitations, Rayleigh-Jeans' law can be useful in certain practical applications. It provides an approximation for the behavior of thermal radiation at low frequencies or long wavelengths, which is relevant in areas such as radio and microwave technology.

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