Notes On Gaseous State This page provides you all details about the gaseous state of BSc standard. Concerned problems will be solved at the end of each concept. Continue till the end to find the easiest explanation of every concept you need in this regard . Postulates of Kinetic Theory of Gases: 1. All gas consist of a very large number of minute particles, called molecules. 2. The gas molecules are extremely small in size and are separated by large distance. The actual volume of the gas molecules is thus negligible as compared to the total volume occupied by the gas. 3. The pressure exerted by the gas is due to the bombardment of the molecules on the walls of the vessel. 4. The gas molecules collide with one another and also with the walls of the vessels. These collisions are perfectly elastic and there is no loss of energy during these collisions. 5. The distance between the gas molecules are very large. Thus, there is no effective force of attraction or r
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.
E 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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